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We demonstrate the measurement of a 2D MeV-range ion velocity distribution function by velocity-space tomography at JET. Deuterium ions were accelerated into the MeV-range by third harmonic ion cyclotron resonance heating. We made measurements with three neutron emission spectrometers and a high-resolution γ-ray spectrometer detecting the γ-rays released in two reactions. The tomographic inversion based on these five spectra is in excellent agreement with numerical simulations with the ASCOT-RFOF and the SPOT-RFOF codes. The length of the measured fast-ion tail corroborates the prediction that very few particles are accelerated above 2 MeV due to the weak wave-particle interaction at higher energies.

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

We demonstrate the measurement of a 2D MeV-range ion velocity distribution function by velocity-space tomography at JET. Deuterium ions were accelerated into the MeV-range by third harmonic ion cyclotron resonance heating. We made measurements with three neutron emission spectrometers and a high-resolution γ-ray spectrometer detecting the γ-rays released in two reactions. The tomographic inversion based on these five spectra is in excellent agreement with numerical simulations with the ASCOT-RFOF and the SPOT-RFOF codes. The length of the measured fast-ion tail corroborates the prediction that very few particles are accelerated above 2 MeV due to the weak wave-particle interaction at higher energies.

Recent JET experiments have been dedicated to the studies of fusion reactions between deuterium (D) and Helium-3 (3He) ions using neutral beam injection (NBI) in synergy with third harmonic ion cyclotron radio-frequency heating (ICRH) of the beam. This scenario generates a fast ion deuterium tail enhancing DD and D3He fusion reactions. Modelling and measuring the fast deuterium tail accurately is essential for quantifying the fusion products. This paper presents the modelling of the D distribution function resulting from the NBI+ICRF heating scheme, reinforced by a comparison with dedicated JET fast ion diagnostics, showing an overall good agreement. Finally, a sawtooth activity for these experiments has been observed and interpreted using SPOT/RFOF simulations in the framework of Porcelli's theoretical model, where NBI+ICRH accelerated ions are found to have a strong stabilizing effect, leading to monster sawteeth.

Velocity-space tomography of the fast-ion distribution function in a fusion plasma is usually a photon-starved tomography method due to limited optical access and signal-to-noise ratio of fast-ion Dα (FIDA) spectroscopy as well as the strive for high-resolution images. In high-definition tomography, prior information makes up for this lack of data. We restrict the target velocity space through the measured absence of FIDA light, impose phase-space densities to be non-negative, and encode the known geometry of neutral beam injection (NBI) sources. We further use a numerical simulation as prior information to reconstruct where in velocity space the measurements and the simulation disagree. This alternative approach is demonstrated for four-view as well as for two-view FIDA measurements. The high-definition tomography tools allow us to study fast ions in sawtoothing plasmas and the formation of NBI peaks at full, half and one-third energy by time-resolved tomographic movies.

Recent JET experiments have been dedicated to the studies of fusion reactions between deuterium (D) and Helium-3 (3He) ions using neutral beam injection (NBI) in synergy with third harmonic ion cyclotron radio-frequency heating (ICRH) of the beam. This scenario generates a fast ion deuterium tail enhancing DD and D3He fusion reactions. Modelling and measuring the fast deuterium tail accurately is essential for quantifying the fusion products. This paper presents the modelling of the D distribution function resulting from the NBI+ICRF heating scheme, reinforced by a comparison with dedicated JET fast ion diagnostics, showing an overall good agreement. Finally, a sawtooth activity for these experiments has been observed and interpreted using SPOT/RFOF simulations in the framework of Porcelli's theoretical model, where NBI+ICRH accelerated ions are found to have a strong stabilizing effect, leading to monster sawteeth.

Velocity-space tomography of the fast-ion distribution function in a fusion plasma is usually a photon-starved tomography method due to limited optical access and signal-to-noise ratio of fast-ion Dα (FIDA) spectroscopy as well as the strive for high-resolution images. In high-definition tomography, prior information makes up for this lack of data. We restrict the target velocity space through the measured absence of FIDA light, impose phase-space densities to be non-negative, and encode the known geometry of neutral beam injection (NBI) sources. We further use a numerical simulation as prior information to reconstruct where in velocity space the measurements and the simulation disagree. This alternative approach is demonstrated for four-view as well as for two-view FIDA measurements. The high-definition tomography tools allow us to study fast ions in sawtoothing plasmas and the formation of NBI peaks at full, half and one-third energy by time-resolved tomographic movies.

Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zerothand first-order Tikhonov regularization. The inversion methods are applied to fast-ion Dα measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high confidence regions, all methods agree that ions with pitch values close to zero, as well as ions with large pitch values, are ejected from the plasma center by the sawtooth crash, and that this ejection depletes the ion population with large pitch values more strongly.

Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zerothand first-order Tikhonov regularization. The inversion methods are applied to fast-ion Dα measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high confidence regions, all methods agree that ions with pitch values close to zero, as well as ions with large pitch values, are ejected from the plasma center by the sawtooth crash, and that this ejection depletes the ion population with large pitch values more strongly.

Observations made in a JET experiment aimed at accelerating deuterons to the MeV range by third harmonic radio-frequency (RF) heating coupled into a deuterium beam are reported. Measurements are based on a set of advanced neutron and gamma-ray spectrometers that, for the first time, observe the plasma simultaneously along vertical and oblique lines of sight. Parameters of the fast ion energy distribution, such as the high energy cut-off of the deuteron distribution function and the RF coupling constant, are determined from data within a uniform analysis framework for neutron and gamma-ray spectroscopy based on a one-dimensional model and by a consistency check among the individual measurement techniques. A systematic difference is seen between the two lines of sight and is interpreted to originate from the sensitivity of the oblique detectors to the pitch-angle structure of the distribution around the resonance, which is not correctly portrayed within the adopted one dimensional model. A framework to calculate neutron and gamma-ray emission from a spatially resolved, two-dimensional deuteron distribution specified by energy/pitch is thus developed and used for a first comparison with predictions from ab initio models of RF heating at multiple harmonics. The results presented in this paper are of relevance for the development of advanced diagnostic techniques for MeV range ions in high performance fusion plasmas, with applications to the experimental validation of RF heating codes and, more generally, to studies of the energy distribution of ions in the MeV range in high performance deuterium and deuterium-tritium plasmas.

Observations made in a JET experiment aimed at accelerating deuterons to the MeV range by third harmonic radio-frequency (RF) heating coupled into a deuterium beam are reported. Measurements are based on a set of advanced neutron and gamma-ray spectrometers that, for the first time, observe the plasma simultaneously along vertical and oblique lines of sight. Parameters of the fast ion energy distribution, such as the high energy cut-off of the deuteron distribution function and the RF coupling constant, are determined from data within a uniform analysis framework for neutron and gamma-ray spectroscopy based on a one-dimensional model and by a consistency check among the individual measurement techniques. A systematic difference is seen between the two lines of sight and is interpreted to originate from the sensitivity of the oblique detectors to the pitch-angle structure of the distribution around the resonance, which is not correctly portrayed within the adopted one dimensional model. A framework to calculate neutron and gamma-ray emission from a spatially resolved, two-dimensional deuteron distribution specified by energy/pitch is thus developed and used for a first comparison with predictions from ab initio models of RF heating at multiple harmonics. The results presented in this paper are of relevance for the development of advanced diagnostic techniques for MeV range ions in high performance fusion plasmas, with applications to the experimental validation of RF heating codes and, more generally, to studies of the energy distribution of ions in the MeV range in high performance deuterium and deuterium-tritium plasmas.

Fast-ion transport caused by the combination of MHD and a mock-up test-blanket module (TBM) coil is measured in the DIII-D tokamak. The primary diagnostic is an infrared camera that measures the heat flux on the tiles surrounding the coil. The combined effects of the TBM and four other potential sources of transport are studied: neoclassical tearing modes, Alfn eigenmodes, sawteeth, and applied resonant magnetic perturbation fields for the control of edge localized modes. A definitive synergistic effect is observed at sawtooth crashes where, in the presence of the TBM, the localized heat flux at a burst increases from 0.36 ± 0.27 to 2.6 ±0.5 MW m-2.

Fast-ion transport caused by the combination of MHD and a mock-up test-blanket module (TBM) coil is measured in the DIII-D tokamak. The primary diagnostic is an infrared camera that measures the heat flux on the tiles surrounding the coil. The combined effects of the TBM and four other potential sources of transport are studied: neoclassical tearing modes, Alfn eigenmodes, sawteeth, and applied resonant magnetic perturbation fields for the control of edge localized modes. A definitive synergistic effect is observed at sawtooth crashes where, in the presence of the TBM, the localized heat flux at a burst increases from 0.36 ± 0.27 to 2.6 ±0.5 MW m-2.

Doppler tomography is a well-known method in astrophysics to image the accretion flow, often in the shape of thin discs, in compact binary stars. As accretion discs rotate, all emitted line radiation is Doppler-shifted. In fast-ion Dα (FIDA) spectroscopy measurements in magnetically confined plasma, the Dα-photons are likewise Doppler-shifted ultimately due to gyration of the fast ions. In either case, spectra of Doppler-shifted line emission are sensitive to the velocity distribution of the emitters. Astrophysical Doppler tomography has lead to images of accretion discs of binaries revealing bright spots, spiral structures and flow patterns. Fusion plasma Doppler tomography has led to an image of the fast-ion velocity distribution function in the tokamak ASDEX Upgrade. This image matched numerical simulations very well. Here we discuss achievements of the Doppler tomography approach, its promise and limits, analogies and differences in astrophysical and fusion plasma Doppler tomography and what can be learned by comparison of these applications.

Doppler tomography is a well-known method in astrophysics to image the accretion flow, often in the shape of thin discs, in compact binary stars. As accretion discs rotate, all emitted line radiation is Doppler-shifted. In fast-ion Dα (FIDA) spectroscopy measurements in magnetically confined plasma, the Dα-photons are likewise Doppler-shifted ultimately due to gyration of the fast ions. In either case, spectra of Doppler-shifted line emission are sensitive to the velocity distribution of the emitters. Astrophysical Doppler tomography has lead to images of accretion discs of binaries revealing bright spots, spiral structures and flow patterns. Fusion plasma Doppler tomography has led to an image of the fast-ion velocity distribution function in the tokamak ASDEX Upgrade. This image matched numerical simulations very well. Here we discuss achievements of the Doppler tomography approach, its promise and limits, analogies and differences in astrophysical and fusion plasma Doppler tomography and what can be learned by comparison of these applications.

The velocity-space observation regions and sensitivities in fast-ion Dα(FIDA) spectroscopy measurements are often described by so-called weight functions. Here we derive expressions for FIDA weight functions accounting for the Doppler shift, Stark splitting, and the charge-exchange reaction and electron transition probabilities. Our approach yields an efficient way to calculate correctly scaled FIDA weight functions and implies simple analytic expressions for their boundaries that separate the triangular observable regions in (vv, vb)-space from the unobservable regions. These boundaries are determined by the Doppler shift and Stark splitting and could until now only be found by numeric simulation.

The velocity-space observation regions and sensitivities in fast-ion Dα(FIDA) spectroscopy measurements are often described by so-called weight functions. Here we derive expressions for FIDA weight functions accounting for the Doppler shift, Stark splitting, and the charge-exchange reaction and electron transition probabilities. Our approach yields an efficient way to calculate correctly scaled FIDA weight functions and implies simple analytic expressions for their boundaries that separate the triangular observable regions in (vv, vb)-space from the unobservable regions. These boundaries are determined by the Doppler shift and Stark splitting and could until now only be found by numeric simulation.

A comprehensive description of methods, suitable for solving the kinetic equation for fast ions and impurity species in tokamak plasmas using a Monte Carlo approach, is presented. The described methods include Hamiltonian orbit-following in particle and guiding center phase space, test particle or guiding center solution of the kinetic equation applying stochastic differential equations in the presence of Coulomb collisions, neoclassical tearing modes and Alfvén eigenmodes as electromagnetic perturbations relevant to fast ions, together with plasma flow and atomic reactions relevant to impurity studies. Applying the methods, a complete reimplementation of the well-established minority species code ASCOT is carried out as a response both to the increase in computing power during the last twenty years and to the weakly structured growth of the code, which has made implementation of additional models impractical. Also, a benchmark between the previous code and the reimplementation is accomplished, showing good agreement between the codes. © 2014 Elsevier B.V. All rights reserved.

A code thatmodels signals produced by charge-exchange reactions between fast ions and injected neutral beams in tokamak plasmas is described. With the fastion distribution function as input, the code predicts the efflux to a neutral particle analyzer (NPA) diagnostic and the photon radiance of Balmer-alpha light to a fastion Dá (FIDA) diagnostic. Reactions with both the primary injected neutrals and with the cloud of secondary "halo" neutrals that surround the beam are treated. Accurate calculation of the fraction of neutrals that occupy excited atomic states (the collisionalradiative transition equations) is an important element of the code. Comparison with TRANSP output and other tests verify the solutions. Judicious selection of grid size and other parameters facilitate efficient solutions. The output of the code has been validated by FIDA measurements on DIII-D but further tests are warranted. © 2011 Global-Science Press.

A code thatmodels signals produced by charge-exchange reactions between fast ions and injected neutral beams in tokamak plasmas is described. With the fastion distribution function as input, the code predicts the efflux to a neutral particle analyzer (NPA) diagnostic and the photon radiance of Balmer-alpha light to a fastion Dá (FIDA) diagnostic. Reactions with both the primary injected neutrals and with the cloud of secondary "halo" neutrals that surround the beam are treated. Accurate calculation of the fraction of neutrals that occupy excited atomic states (the collisionalradiative transition equations) is an important element of the code. Comparison with TRANSP output and other tests verify the solutions. Judicious selection of grid size and other parameters facilitate efficient solutions. The output of the code has been validated by FIDA measurements on DIII-D but further tests are warranted. © 2011 Global-Science Press.

A summary of fast ion experiments in the DIII-D lokamak is given. Most of the experiments involve ∼80-keV deuterium beam ions. Deceleration of dilute fast-ion populations is accurately described by coulomb scattering theory. Fast waves with frequencies several times the deuterium cyclotron frequency interact with beam ions when the product of wave number and gyroradius k ⊥ρi is ≳1.4. Global confinement of fast ions is often excellent although sawteeth, tearing modes, and beam-driven instabilities can cause additional transport. Intense beamion populations often drive instabilities. Toroidicity-induced Alfvén eigenmodes (TAE) and somewhat lower frequency modes (originally called beta-induced Alfvén eigenmodes) are often observed in a wide variety of plasma conditions. Over 50% of the beam power is lost during strong activity. Damping mechanisms such as mode coupling or radiative damping are needed to explain the observed TAE stability threshold. The most unstable toroidal mode number agrees well with theoretical expectations, but the radial and poloidal structure of the mode and the observed beam-ion transport have not been adequately explained. The modes with frequencies below the TAE are probably two types of energetic particle modes: the resonant TAE and the resonant kinetic ballooning mode.

A summary of fast ion experiments in the DIII-D lokamak is given. Most of the experiments involve ∼80-keV deuterium beam ions. Deceleration of dilute fast-ion populations is accurately described by coulomb scattering theory. Fast waves with frequencies several times the deuterium cyclotron frequency interact with beam ions when the product of wave number and gyroradius k ⊥ρi is ≳1.4. Global confinement of fast ions is often excellent although sawteeth, tearing modes, and beam-driven instabilities can cause additional transport. Intense beamion populations often drive instabilities. Toroidicity-induced Alfvén eigenmodes (TAE) and somewhat lower frequency modes (originally called beta-induced Alfvén eigenmodes) are often observed in a wide variety of plasma conditions. Over 50% of the beam power is lost during strong activity. Damping mechanisms such as mode coupling or radiative damping are needed to explain the observed TAE stability threshold. The most unstable toroidal mode number agrees well with theoretical expectations, but the radial and poloidal structure of the mode and the observed beam-ion transport have not been adequately explained. The modes with frequencies below the TAE are probably two types of energetic particle modes: the resonant TAE and the resonant kinetic ballooning mode.