Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Todo, Y.

doi:10.1007/s41614-018-0022-9

Cited by 97 publications

(102 citation statements)

References 109 publications

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“…Higher AE drive means that more modes are likely to be destabilized. In addition, some models of AE saturation predict that the saturated mode amplitude increases with linear growth rate, such that modes with higher drive will also be larger and thus more likely to drive energetic particle transport (Briguglio et al 2017;Todo 2019). To assess the relevance of studies of AE amplitude and spectrum in SPARC to expected behaviour in ITER and ARC, we compare the predicted β α /β based on physics-based models for SPARC to published estimates for ITER and ARC.…”

Section: Expected Trends In Ae Behaviourmentioning

confidence: 99%

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Fast-ion physics in SPARC

et al. 2020

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Potential loss of energetic ions including alphas and radio-frequency tail ions due to classical orbit effects and magnetohydrodynamic instabilities (MHD) are central physics issues in the design and experimental physics programme of the SPARC tokamak. The expected loss of fusion alpha power due to ripple-induced transport is computed for the SPARC tokamak design by the ASCOT and SPIRAL orbit-simulation codes, to assess the expected surface heating of plasma-facing components. We find good agreement between the ASCOT and SPIRAL simulation results not only in integrated quantities (fraction of alpha power loss) but also in the spatial, temporal and pitch-angle dependence of the losses. If the toroidal field (TF) coils are well-aligned, the SPARC edge ripple is small (0.15–0.30 %), the computed ripple-induced alpha power loss is small ( ${\sim } 0.25\,\%$ ) and the corresponding peak surface power density is acceptable ( $244\ \textrm{kW}\ \textrm {m}^{-2}$ ). However, the ripple and ripple-induced losses increase strongly if the TF coils are assumed to suffer increasing magnitudes of misalignment. Surface heat loads may become problematic if the TF coil misalignment approaches the centimetre level. Ripple-induced losses of the energetic ion tail driven by ion cyclotron range of frequency (ICRF) heating are not expected to generate significant wall or limiter heating in the nominal SPARC plasma scenario. Because the expected classical fast-ion losses are small, SPARC will be able to observe and study fast-ion redistribution due to MHD including sawteeth and Alfvén eigenmodes (AEs). SPARC's parameter space for AE physics even at moderate $Q$ is shown to reasonably overlap that of the demonstration power plant ARC (Sorbom et al., Fusion Engng Des., vol. 100, 2015, p. 378), and thus measurements of AE mode amplitude, spectrum and associated fast-ion transport in SPARC would provide relevant guidance about AE behaviour expected in ARC.

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Section: Expected Trends In Ae Behaviourmentioning

confidence: 99%

“…In addition, some models of AE saturation predict that the saturated mode amplitude increases with linear growth rate, such that modes with higher drive will also be larger and thus more likely to drive energetic particle transport (Briguglio et al. 2017; Todo 2019).…”

Section: Expected Trends In Ae Behaviourmentioning

confidence: 99%

Fast-ion physics in SPARC

et al. 2020

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“…Toroidal Alfvén eigenmode saturation has been estimated using a variety of methods. Some works balance the linear growth rate of the instability with the rate at which particles get trapped by the wave and flatten the gradient driving the instability, sometimes including collisions that restore the original gradient (Wu & White 1994; Fu & Park 1995; Wang & Briguglio 2016; Zhou & White 2016; Todo 2019). Other works consider the effects of zonal flows and nonlinear mode couplings (Spong, Carreras & Hedrick 1994; Chen & Zonca 2012).…”

Section: Toroidal Alfvén Eigenmode Fluxmentioning

confidence: 99%

“…(2008). Todo (2019) discusses these results and the importance of developing energetic particle transport theories that self-consistently treat both of these components.…”

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confidence: 99%

Drift kinetic theory of alpha transport by tokamak perturbations

Tolman

Catto

2021

J. Plasma Phys.

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Upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

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“…Much work has been done on this subject during the last several decades, as can be appreciated from recent reviews and tutorials, such as Refs. [1][2][3]. However, there is more to be learned about these important and fascinating phenomena, and about the underlying nonlinear self-organization processes that occur when the plasma is driven away from equilibrium under the influence of strong sources, sinks and dissipation.…”

Section: Introductionmentioning

confidence: 99%

On the Effect of Beating during Nonlinear Frequency Chirping

Bierwage

Roscoe

Duarte

2021

Plasma and Fusion Research

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Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. A key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O-and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and, on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.

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Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Cited by 97 publications

References 109 publications

Fast-ion physics in SPARC

Fast-ion physics in SPARC

Drift kinetic theory of alpha transport by tokamak perturbations

On the Effect of Beating during Nonlinear Frequency Chirping

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