Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions

Stagner, L.; Heidbrink, W. W.

doi:10.1063/1.4990391

Cited by 40 publications

(51 citation statements)

References 24 publications

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“…Both studies thus demonstrate the inadequacy of the 0-D 2-V FP treatment at high energy and high pitch angle (where the synchrotron image originates), and opens the door to new physics being important to capture the f e in this region of phase space. Future work in this area will aim to extend model validation of synchrotron images to fully 3-D magnetic configurations (ie, tokamak discharges with magnetic islands) [50], and incorporate synchrotron image data in unified multi-diagnostic inversions to better infer f e [45].…”

Section: Re Distribution Validation Via Synchrotron Imagingmentioning

confidence: 99%

Recent DIII-D advances in runaway electron measurement and model validation

Paz-Soldan¹,

Eidietis²,

Hollmann³

et al. 2019

Nucl. Fusion

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Novel measurements and modeling of runaway electron (RE) dynamics in DIII-D have resolved experimental discrepancies and validated predictions for ITER, improving confidence that RE avoidance and mitigation can be predictably achieved. Considering RE formation, first experimental assessments of the RE seed current demonstrates that present hot-tail theories are not yet accurate and require improved treatment of the pellet dynamics. Novel measurements of kinetic instabilities in the MHz-range have been made in the RE formation phase, with the intensity of these modes correlated with previously unexplained empirical thresholds for RE generation. Controlled RE dissipation experiments in quiescent regimes have validated RE distribution function dependencies on collisional and synchrotron damping, both in terms of distribution function shape and dissipation rates. Measurements of RE bremsstrahlung and synchrotron emission are now used in tandem to resolve energy and pitch-angle effects. A resolution to long-standing dissipation anomalies in the quiescent regime is offered by taking into account kinetic instability effects on RE phase-space dynamics. Kinetic instabilities in the 100-200 MHz range are directly observed, though modeling finds the largest dissipation arises from GHz range instabilities that are beyond the reach of existing diagnostics. Kinetic instabilities are also observed in the mature post-disruption RE plateau phase, so long as the collisional damping rate is reduced with low-Z injection. Experiments with high-Z injection find that the dissipation rate saturates with injection quantity, likely due to neutral diffusion rates being slower than vertical instability rates in DIII-D. Considering the final loss, a 0D model for first-wall Joule heating is found to be in agreement with experiment, and controlled access to RE equilibria with edge safety factor of two identifies novel dynamics brought about by large-scale kink instabilities. These dynamics are typified by fast (tens of microseconds) RE loss rates without RE beam regeneration. The above measurements and comparison with theory represent significant advances in the understanding of RE dynamics and indicate possible new opportunities for RE avoidance or mitigation via kinetic instabilities.

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Section: Re Distribution Validation Via Synchrotron Imagingmentioning

confidence: 99%

Recent DIII-D advances in runaway electron measurement and model validation

Paz-Soldan¹,

Eidietis²,

Hollmann³

et al. 2019

Nucl. Fusion

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show abstract

“…III B further work should enable full 2-D inversions. Alternate inversion processes are also possible, either using weightfunction techniques [45,46] or tools such as DeGaSum [47,48].…”

Section: A Inversion Techniquementioning

confidence: 99%

Resolving runaway electron distributions in space, time, and energy

et al. 2018

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Areas of agreement and disagreement with present-day models of RE evolution are revealed by measuring MeV-level bremsstrahlung radiation from runaway electrons (REs) with a pinhole camera. Spatially-resolved measurements localize the RE beam, reveal energy-dependent RE transport, and can be used to perform full two-dimensional (energy and pitch-angle) inversions of the RE phasespace distribution. Energy-resolved measurements find qualitative agreement with modeling on the role of collisional and synchrotron damping in modifying the RE distribution shape. Measurements are consistent with predictions of phase-space attractors that accumulate REs, with non-monotonic features observed in the distribution. Temporally-resolved measurements find qualitative agreement with modeling on the impact of collisional and synchrotron damping in varying the RE growth and decay rate. Anomalous RE loss is observed and found to be largest at low energy. Possible roles for kinetic instability or spatial transport to resolve these anomalies are discussed.

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“…(132) The mixing of position space and velocity space makes it difficult to give analytic models for this distribution. Nevertheless, the phase-space distribution is highly important for stability calculations, and it could be possible to measure it in the future [44]. To have a simple analytic model, one can assume the distribution to be separable according to [45] f 6D…”

Section: Phase-space Distribution Functionsmentioning

confidence: 99%

Bi-Maxwellian, slowing-down, and ring velocity distributions of fast ions in magnetized plasmas

Moseev

Salewski

2019

Physics of Plasmas

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We discuss analytic fast-ion velocity distribution functions which are useful for basic plasma modelling as illustrated for typical parameters of the future fusion plasma in the tokamak ITER. The Maxwellian is by far the most widespread model for ions and electrons in tokamaks and stellarators. The bi-Maxwellian and the drifting (bi-)Maxwellian are extensions allowing for anisotropy and bulk plasma flow, respectively. For example, fast ions generated by wave heating in the ion cyclotron range of frequencies are often described by bi-Maxwellians or so-called tail temperatures. The ring distribution can serve as a basic building block for arbitrary distributions or as bump-on-tail in stability studies. The isotropic slowing-down distribution is a good model for fusion α-particles. The anisotropic slowing-down distribution occurs for anisotropic particle sources as is typical for neutral beam injection. We physically motivate these distribution functions and present analytic models in various coordinate systems commonly used by theorists and experimentalists. We further calculate 1D projections of the distribution functions onto a diagnostic line-of-sight to gain insight into measurements relying on the Doppler shift.

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Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions

Cited by 40 publications

References 24 publications

Recent DIII-D advances in runaway electron measurement and model validation

Recent DIII-D advances in runaway electron measurement and model validation

Resolving runaway electron distributions in space, time, and energy

Bi-Maxwellian, slowing-down, and ring velocity distributions of fast ions in magnetized plasmas

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