Fast Ion Distribution Research Articles

Resonance broadened quasi-linear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes

The burning plasma performance is limited by the confinement of the super-alfvénic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfvénic eigenmodes (AEs) (Gorelenkov et al 2014 Nucl. Fusion 54 125001). In this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently (Duarte 2017 PhD Thesis University of São Paulo, Brazil). The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. In RBQ1D applications we reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then solved simultaneously for all particles along the angular momentum direction.We make initial applications of the RBQ1D to a DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties (Collins et al (The DIII-D Team) 2016 Phys. Rev. Lett. 116 095001). AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.

Global Alfvén eigenmode scaling and suppression: experiment and theory

The spherical tokamak NSTX has been upgraded to include a second neutral beam line, with three independent beam sources, and to be capable of higher toroidal fields and longer duration plasmas (Ono et al 2015 Nucl. Fusion 55 073007). In this paper we describe some of the initial observations of the affect that the higher field and the modified fast-ion distributions have had on the nature of the global Alfvén eigenmodes (GAE). We also report that the GAE excited through a Doppler-shifted ion cyclotron resonance (DCR) were suppressed in a large number of shots with the injection of a small amount of high pitch (V||/V) fast ions, consistent with the predictions of an analytic theory (Gorelenkov et al 2003 Nucl. Fusion 43 228). We show that the experimental scaling of the GAE frequency and toroidal mode numbers with toroidal field is qualitatively consistent with the predictions of the analytic theory, providing validation for the DCR model. The observed suppression of GAE has also been reproduced in simulations with the hybrid ideal stability code HYM (Belova et al 2017 Phys. Plasmas 24 042505).

Energetic-particle-modified global Alfvén eigenmodes

Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function—the normalized injection velocity v0/vA and central pitch—are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v0/vA. This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE. Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.

Analysis of resonant fast ion distributions during combined ICRF and NBI heating with transients using neutron emission spectroscopy

ICRF heating at the fundamental cyclotron frequency of a hydrogen minority ion species also gives rise to a partial power absorption by deuterium ions at their second harmonic resonance. This paper studies the deuterium distributions resulting from such 2nd harmonic heating at JET using neutron emission spectroscopy data from the time of flight spectrometer TOFOR. The fast deuterium distributions are obtained over the energy range 100 keV to 2 MeV. Specifically, we study how the fast deuterium distributions vary as ICRF heating is used alone as well as in combination with NBI heating.When comparing the different heating scenarios, we observed both a difference in the shapes of the distributions as well as in their absolute level. The differences are most pronounced below 0.5 MeV. Comparisons are made with corresponding distributions calculated with the code PION. We find a good agreement between the measured distributions and those calculated with PION, both in terms of their shapes as well as their amplitudes.However, we also identified a period with signs of an inverted fast ion distribution, which showed large disagreements between the modeled and measured results. Resonant interactions with tornado modes, i.e. core localized toroidal alfven eigenmodes (TAEs), are put forward as a possible explanation for the inverted distribution.

Bayesian Integrated Data Analysis of Fast-Ion Measurements by Velocity-Space Tomography

Bayesian integrated data analysis combines measurements from different diagnostics to jointly measure plasma parameters of interest such as temperatures, densities, and drift velocities. Integrated data analysis of fast-ion measurements has long been hampered by the complexity of the strongly non-Maxwellian fast-ion distribution functions. This has recently been overcome by velocity-space tomography. In this method two-dimensional images of the velocity distribution functions consisting of a few hundreds or thousands of pixels are reconstructed using the available fast-ion measurements. Here we present an overview and current status of this emerging technique at the ASDEX Upgrade tokamak and the JET toamak based on fast-ion D-alpha spectroscopy, collective Thomson scattering, gamma-ray and neutron emission spectrometry, and neutral particle analyzers. We discuss Tikhonov regularization within the Bayesian framework. The implementation for different types of diagnostics as well as the uncertainties are discussed, and we highlight the importance of integrated data analysis of all available detectors.

Electrostatic potential generated by perpendicular neutral-beam injection to a tokamak plasma

The electrostatic potential generated by neutral-beam-injection (NBI) heating in a tokamak plasma is investigated using numerical simulations. The density distribution of the NBI fast ions in an assumed tokamak is evaluated using the GNET drift-kinetic-equation solver which is based on the Monte Carlo method. The electrostatic potential is evaluated assuming an adiabatic response of the electrons to the fast-ion density distribution in the plasma. It is found that an electrostatic potential peak is generated near the beam-injection point owing to the trapped fast ions satisfying the zero-precession condition. An analytic model expressing the expected potential except for the peak is derived and shows a good agreement with the radial distribution and linear dependence on the electron temperature predicted by the simulation within a factor of 1–2. The existence of three-dimensional electrostatic trapping may break the poloidally-closed particle orbits, and may change the spatial distribution and transport of high-Z impurity ions.

The effects of electron cyclotron heating and current drive on toroidal Alfvén eigenmodes in tokamak plasmas

Dedicated studies performed for toroidal Alfvén eigenmodes (TAEs) in ASDEX-Upgrade (AUG) discharges with monotonic q-profiles have shown that electron cyclotron resonance heating (ECRH) can make TAEs more unstable. In these AUG discharges, energetic ions driving TAEs were obtained by ion cyclotron resonance heating (ICRH). It was found that off-axis ECRH facilitated TAE instability, with TAEs appearing and disappearing on timescales of a few milliseconds when the ECRH power was switched on and off. On-axis ECRH had a much weaker effect on TAEs, and in AUG discharges performed with co- and counter-current electron cyclotron current drive (ECCD), the effects of ECCD were found to be similar to those of ECRH. Fast ion distributions produced by ICRH were computed with the PION and SELFO codes. A significant increase in Te caused by ECRH applied off-axis is found to increase the fast ion slowing-down time and fast ion pressure causing a significant increase in the TAE drive by ICRH-accelerated ions. TAE stability calculations show that the rise in Te causes also an increase in TAE radiative damping and thermal ion Landau damping, but to a lesser extent than the fast ion drive. As a result of the competition between larger drive and damping effects caused by ECRH, TAEs become more unstable. It is concluded, that although ECRH effects on AE stability in present-day experiments may be quite significant, they are determined by the changes in the plasma profiles and are not particularly ECRH specific.

Synthetic NPA diagnostic for energetic particles in JET plasmas

Neutral particle analysis (NPA) is one of the few methods for diagnosing fast ions inside a plasma by measuring neutral atom fluxes emitted due to charge exchange reactions. The JET tokamak features an NPA diagnostic which measures neutral atom fluxes and energy spectra simultaneously for hydrogen, deuterium and tritium species. A synthetic NPA diagnostic has been developed and used to interpret these measurements to diagnose energetic particles in JET plasmas with neutral beam injection (NBI) heating. The synthetic NPA diagnostic performs a Monte Carlo calculation of the neutral atom fluxes in a realistic geometry. The 4D fast ion distributions, representing NBI ions, were simulated using the Monte Carlo orbit-following code ASCOT. Neutral atom density profiles were calculated using the FRANTIC neutral code in the JINTRAC modelling suite. Additionally, for rapid analysis, a scan of neutral profiles was precalculated with FRANTIC for a range of typical plasma parameters. These were taken from the JETPEAK database, which includes a comprehensive set of data from the flat-top phases of nearly all discharges in recent JET campaigns. The synthetic diagnostic was applied to various JET plasmas in the recent hydrogen campaign where different hydrogen/deuterium mixtures and NBI configurations were used. The simulated neutral fluxes from the fast ion distributions were found to agree with the measured fluxes, reproducing the slowing-down profiles for different beam isotopes and energies and quantitatively estimating the fraction of hydrogen and deuterium fast ions.

High-field neutral beam injection for improving the Q of a gas dynamic trap-based fusion neutron source

In order to improve the fusion energy gain (Q) of a gas dynamic trap (GDT)-based fusion neutron source, a method in which the neutral beam is obliquely injected at a higher magnetic field position rather than at the mid-plane of the GDT is proposed. This method is beneficial for confining a higher density of fast ions at the turning point in the zone with a higher magnetic field, as well as obtaining a higher mirror ratio by reducing the mid-plane field rather than increasing the mirror field. In this situation, collision scattering loss of fast ions with higher density will occur and change the confinement time, power balance and particle balance. Using an updated calculation model with high-field neutral beam injection for a GDT-based fusion neutron source conceptual design, we got four optimal design schemes for a GDT-based fusion neutron source in which Q was improved to two- to three-fold compared with a conventional design scheme and considering the limitation for avoiding plasma instabilities, especially the fire-hose instability. The distribution of fast ions could be optimized by building a proper magnetic field configuration with enough space for neutron shielding and by multi-beam neutral particle injection at different axial points.

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

Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Furthermore, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown.

Benchmark of multi-phase method for the computation of fast ion distributions in a tokamak plasma in the presence of low-amplitude resonant MHD activity

The transport of fast ions in a beam-driven JT-60U tokamak plasma subject to resonant magnetohydrodynamic (MHD) mode activity is simulated using the so-called multi-phase method, where 4 ms intervals of classical Monte-Carlo simulations (without MHD) are interlaced with 1 ms intervals of hybrid simulations (with MHD). The multi-phase simulation results are compared to results obtained with continuous hybrid simulations, which were recently validated against experimental data (Bierwage et al., 2017). It is shown that the multi-phase method, in spite of causing significant overshoots in the MHD fluctuation amplitudes, accurately reproduces the frequencies and positions of the dominant resonant modes, as well as the spatial profile and velocity distribution of the fast ions, while consuming only a fraction of the computation time required by the continuous hybrid simulation. The present paper is limited to low-amplitude fluctuations consisting of a few long-wavelength modes that interact only weakly with each other. The success of this benchmark study paves the way for applying the multi-phase method to the simulation of Abrupt Large-amplitude Events (ALE), which were seen in the same JT-60U experiments but at larger time intervals. Possible implications for the construction of reduced models for fast ion transport are discussed.

Comprehensive magnetohydrodynamic hybrid simulations of fast ion driven instabilities in a Large Helical Device experiment

Alfvén eigenmodes (AEs) destabilized by the neutral beam injection (NBI) in a Large Helical Device experiment are investigated using multi-phase magnetohydrodynamic (MHD) hybrid simulation, which is a combination of classical and MHD hybrid simulations for fast ions. The fast ion distribution is simulated with NBI, collisions, and losses in the equilibrium magnetic field in the classical simulation, while the MHD hybrid simulation takes account of the interaction between fast ions and an MHD fluid, in addition to the classical dynamics. It is found in the multi-phase hybrid simulation that the stored fast ion energy is saturated due to the interaction with AEs at a lower level than that of the classical simulation. Two groups of AEs with frequencies close to those observed in the experiment are destabilized alternately at each hybrid simulation. Firstly destabilized are two toroidal Alfvén eigenmodes whose frequency is close to the local minimum of the upper Alfvén continuous spectrum. Secondly destabilized is a global Alfvén eigenmode whose frequency is located well inside the Alfvén continuous spectrum gap. In addition, two AEs whose frequencies are close to that of the ellipticity-induced Alfvén eigenmode are observed with a lower amplitude. When the hybrid simulation is run continuously, the interchange mode grows more slowly than the AEs, but becomes dominant in the long time scale. The interchange mode oscillates with a constant amplitude and a frequency of ∼1 kHz. The interchange mode reduces the stored fast ion energy to a lower level than that of the AEs.

Energy distributions of superthermal ions in regime with sawtooth oscillations during neutral beam injection at the Globus-M tokamak

Specific features of the energy distributions of fast ions during neutral beam injection at the Globus-М tokamak are considered. Different loss mechanisms that can lead to the formation of a specific shape of the energy spectrum of superthermal ions are analyzed. The effect of sawtooth oscillations on the loss of fast ions is discussed.

Phase-space dependent critical gradient behavior of fast-ion transport due to Alfvén eigenmodes

Experiments in the DIII-D tokamak show that many overlapping small-amplitude Alfvén eigenmodes (AEs) cause fast-ion transport to sharply increase above a critical threshold in beam power, leading to fast-ion density profile resilience and reduced fusion performance. The threshold is above the AE linear stability limit and varies between diagnostics that are sensitive to different parts of fast-ion phase-space. Comparison with theoretical analysis using the nova and orbit codes shows that, for the neutral particle diagnostic, the threshold corresponds to the onset of stochastic particle orbits due to wave-particle resonances with AEs in the measured region of phase space. The bulk fast-ion distribution and instability behavior was manipulated through variations in beam deposition geometry, and no significant differences in the onset threshold outside of measurement uncertainties were found, in agreement with the theoretical stochastic threshold analysis. Simulations using the ‘kick model’ produce beam ion density gradients consistent with the empirically measured radial critical gradient and highlight the importance of including the energy and pitch dependence of the fast-ion distribution function in critical gradient models. The addition of electron cyclotron heating changes the types of AEs present in the experiment, comparatively increasing the measured fast-ion density and radial gradient. These studies provide the basis for understanding how to avoid AE transport that can undesirably redistribute current and cause fast-ion losses, and the measurements are being used to validate AE-induced transport models that use the critical gradient paradigm, giving greater confidence when applied to ITER.

The DTT device: System for heating

The proposed Divertor Test Tokamak, DTT, aims at studying power exhaust and divertor load in an integrated plasma scenario. Additional heating systems have the task to provide heating to reach a reactor relevant power flow in the SOL and guarantee the necessary PSEP/R together with adequate plasma performances. About 40MW of heating power are foreseen to have PSEP/R≥15MW/m. A mix of the three heating systems has been chosen, assuring the necessary flexibility in scenario development. An ECRH system at 170GHz will provide 10MW at plasma for several tasks, such as: bulk electron heating, localized CD, avoidance of impurity accumulation and MHD control. In addition 15MW of ICRH in the range 60–90MHz will provide the remaining bulk plasma heating power, on both electrons and ions. ICRH, in minority scheme, will produce fast ions, allowing the study of fast particle driven instabilities like alphas in D-T burning plasmas. The heating schemes foreseen in DTT are 3He and H minority as well as Deuterium 2nd harmonic. The addition of 15MW of NBI, later in the project, could provide a mainly parallel fast ion distribution to simulate the alpha heating scheme of a reactor. The NBI primary aim is to support plasma heating during the flat top phase when the need of central power deposition and the minimization of the shine-through risk suggests a beam energy around 300keV. In the first phase of the DTT project the available power will be at least 25MW, to be increased during the lifetime of the machine.

Formation of the charge distribution of fast multicharged ions passing through a carbon target

The equilibrium and nonequilibrium charge distributions of ions with nuclear charges from 10 to 18 are analyzed by evaluating ion charge-exchange cross sections with the density effect taken into account. It is shown that the increase in the cross section for electron loss and the decrease in the cross section for electron capture by ions in a solid target (carbon) compared with gases is maximum in the region of 0.1–0.2MeV/nucleon. It is also shown that, in the case of a solid target, the energy by ion cross section for electron loss by an ion becomes maximum decreases, which is explained by a decrease in the binding energy of the active electron in the ion because of the presence of excited states. This leads to an increase in the average equilibrium ion charge in solid targets compared with the value in gases. The results of calculations agree with the experimental data in the entire considered energy region. The proposed method for calculating the ion charge-exchange cross sections in solid targets also makes it possible to qualitatively describe the dependence of the average ion charge on the target thickness and calculate the thickness (required to determine the equilibrium charge distribution) for different energies and charges of the ion nucleus.

Full-wave simulations of ICRF heating regimes in toroidal plasma with non-Maxwellian distribution functions

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely (Stix 1975 Nucl. Fusion 15 737), with consequent changes in wave propagation and in the location and amount of absorption. In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC (Brambilla 1999 Plasma Phys. Control. Fusion 41 1 and Brambilla 2002 Plasma Phys. Control. Fusion 44 2423), have been extended to allow the prescription of arbitrary velocity distributions of the form . For hydrogen (H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional H absorption varies significantly with changes in parallel temperature but is essentially independent of perpendicular temperature. On the other hand, for HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies mainly with changes in the perpendicular temperature. The evaluation of the wave-field and power absorption, through the full wave solver, with the ion distribution function provided by either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with respect to the equivalent Maxwellian distribution.

Numerical and semi-analytical treatments of neutral beam current drive in DEMO-FNS

Neutral Beam Current Drive (NBCD) is considered as a highly attractive mechanism for a steady state regime in such contemporary projects as a tokamak based Fusion Neutron Source (FNS) or a DEMO type thermonuclear reactor. In this report numerical calculations of NBCD with a Monte Carlo code NUBEAM are complemented by a semi-analytical treatment of fast ion velocity distribution function. Spectral distributions of fast ions injected with neutral beams to FNS plasma are obtained for DEMO-FNS and a Spherical Tokamak Neutron Source FNS-ST. A detailed comparison of NUBEAM and semi-analytical approaches is presented on the basis of ASTRA transport code provided equilibrium data for different plasma regimes. The applicability of the semi-analytical approach is discussed.

Self-consistent calculation of the effects of RF injection in the HHFW heating regimes on the evolution of fast ions in toroidal plasmas

A critical question for the use of ion cyclotron range of frequency (ICRF) heating in the ITER device and beyond is interaction of fast waves with energetic ion populations from neutral beam injection (NBI), fusion reactions, and minority ions accelerated by the RF waves themselves. Several experiments have demonstrated that the interaction between fast waves and fast ions can indeed be strong enough to significantly modify the NB ion population. To model the RF/fast ion interaction and the resulting fast ion distribution, a recent extension of the full wave solver TORIC v.5 that includes non-Maxwellian effects has been combined with the Monte Carlo NUBEAM code through an RF “kick” operator. In this work, we present an initial verification of the NUBEAM RF “kick” operator for high harmonic fast wave (HHFW) heating regime in NSTX plasma.

High-definition velocity-space tomography of fast-ion dynamics

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.