Fast Ion Distribution Research Articles

Synergy of coupled kink and tearing modes in fast ion transport

One aspect of the interaction between fast ions and magnetohydrodynamic (MHD) instabilities is the fast ion transport. Coupled kink and tearing MHD instabilities have also been reported to cause fast ion transport. Recently, the ‘kick’ model has been developed to compute the evolution of the fast ion distribution from neutral beam injection using instabilities as phase-space resonance sources. The goal of this paper is to utilize the kick model to understand the physics of fast ion transport caused by the coupled kink and tearing modes. Soft x-ray diagnostics are used to identify the mode parameters in the National Spherical Torus Experiment. The comparison of neutron rates measured and computed from time-dependent TRANSP simulation with the kick model shows that the coupling of kink and tearing mode is important in determination of the fast ion transport. The numerical scan of the mode parameters shows that the relative phase of the kink and tearing modes and the overlapping of kink and tearing mode resonances in the phase space can affect the fast ion transport, suggesting that the synergy of the coupled modes may be causing the fast ion transport.

Explanation of core ion cyclotron emission from beam-ion heated plasmas in ASDEX Upgrade by the magnetoacoustic cyclotron instability

Bursts of ion cyclotron emission (ICE), with spectral peaks corresponding to the hydrogen cyclotron harmonic frequencies in the plasma core are detected from helium plasmas heated by sub-Alfvénic beam-injected hydrogen ions in the ASDEX Upgrade tokamak. Based on the fast ion distribution function obtained from TRANSP/NUBEAM code, together with a linear analytical theory of the magnetoacoustic cyclotron instability (MCI), the growth rates of MCI could be calculated. In our theoretical and experimental studies, we found that the excitation mechanism of core ICE driven by sub-Alfvénic beam ions in ASDEX Upgrade is MCI as the time evolution of MCI growth rates is broadly consistent with measured ICE amplitudes. The MCI growth rate is very sensitive to the energy and velocity distribution of beam-injected ions and is suppressed by the slowing down of the dominant beam-injected ion velocity and the spreading of the fast ion distribution profile. This may help to account for the experimental observation that ICE signals disappear within ∼3 ms after the NBI turn-off time, much faster than the slowing down times of the beam ions.

Neutron rate estimates in MAST based on gyro-orbit modelling of fast ions

A discrepancy between predicted and measured neutron rates on MAST using TRANSP/NUBEAM has previously been observed and a correction factor of about 0.6 was needed to match the two: this correction factor could not be accounted for by the experimental uncertainties in the plasma kinetic profiles nor in the NBI energy and power (Cecconello et al 2019 Nucl. Fusion 59 016006). Further causes of this discrepancy are here studied by means of TRANSP/NUBEAM and ASCOT/BBNBI simulations. Different equilibria, toroidal field ripples, uncertainties on the NBI divergence value and gyro-orbit effects were studied and simulations were performed with both transport codes. It was found that the first three effects accounted for only a 5% variation in the fast ion density. On the other hand, full gyro-orbit simulations of the fast ions dynamics carried out in ASCOT/BBNBI resulted in an approximately 20% reduction of the fast ion population compared to TRANSP/NUBEAM. A detailed analysis of the fast ion distributions showed how the drop occurred regardless of the energy at pitch values ⩽−0.4. The DRESS code was then used to calculate the neutron rate at the neutron camera detector’s location showing that the discrepancy is considerably reduced when the full gyro-orbit fast ion distribution is used, with now the correction factor, used to match experimental and predicted neutron rates, being around 0.9.

Validation of neutron emission and neutron energy spectrum calculations on a Mega Ampere Spherical Tokamak with directional relativistic spectrum simulator

The recently developed directional relativistic spectrum simulator (DRESS) code has been validated for the first time against numerical calculations and experimental measurements performed on the Mega Ampere Spherical Tokamak. In this validation, the neutron emissivities and rates computed by DRESS are benchmarked against TRANSP/NUBEAM predictions while the neutron energy spectra provided by DRESS taking as input TRANSP/NUBEAM and ASCOT/BBNBI in Gyro-Orbit mode fast ion distributions are validated against proton pulse height spectra measured by the neutron flux monitor. Excellent agreement was found between DRESS and TRANSP/NUBEAM predictions of local and total neutron emission.

Generation and observation of fast deuterium ions and fusion-born alpha particles in JET plasmas with the 3-ion radio-frequency heating scenario

Dedicated experiments to generate energetic D ions and fusion-born alpha particles were performed at the Joint European Torus (JET) with the ITER-like wall (ILW). Using the 3-ion radio frequency (RF) heating scenario, deuterium ions from neutral beam injection (NBI) were accelerated in the core of mixed plasmas to higher energies with ion cyclotron resonance frequency (ICRF) waves, in turn leading to a core-localized source of alpha particles. The fast-ion distribution of RF-accelerated D-NBI ions was controlled by varying the ICRF and NBI power ( 4–6 MW, 3–20 MW), resulting in rather high D-D neutron (≈ 1 × 1016 s−1) and alpha rates (≈ 2 × 1016 s−1) at moderate input heating power. Theory and TRANSP analysis shows that large populations of co-passing MeV-range D ions were generated using the 3-ion ICRF scenario. This important result is corroborated by several experimental observations, in particular gamma-ray measurements. The developed experimental scenario at JET provides unique conditions for probing several aspects of future burning plasmas, such as the contribution from MeV range ions to global confinement, but without introducing tritium. Dominant fast-ion core electron heating with and a rich variety of fast-ion driven Alfvén eigenmodes (AEs) were observed in these plasmas. The observed AE activities do not have a detrimental effect on the thermal confinement and, in some cases, may be driven by the fusion born alpha particles. A strong continuous increase in neutron rate was observed during long-period sawteeth (1 s), accompanied by the observation of reversed shear AEs, which implies that a non monotonic q profile was systematically developed in these plasmas, sustained by the large fast-ion populations generated by the 3-ion ICRF scenario.

Fast-ion velocity-space tomography using slowing-down regularization in EAST plasmas with co- and counter-current neutral beam injection

We demonstrate 2D reconstructions of the fast-ion velocity distribution from two-view fast-ion D-alpha (FIDA) measurements at the EAST tokamak. By expressing the distribution in a basis relying on the fast-ion slowing-down process in fusion plasmas, the smoothness and velocity-space resolution of reconstructions are improved. We reconstruct distributions of fast ions born from simultaneous co- and counter-current neutral beam injection and detect the expected distinct change in fast-ion birth pitch when comparing discharges utilizing different neutral beam injectors. For purely co-current injection, we find a good agreement between TRANSP-predicted and reconstructed fast-ion densities, pressures and current densities for energies above 20 keV. We furthermore illustrate the improvement of the reconstructed high-energy range (> 40 keV) of the distribution by combining FIDA with neutron emission spectroscopy measurements with the compact single-plate EJ301 scintillator.

Fast-ion D alpha diagnostic with 3D-supporting FIDASIM in the Large Helical Device

For understanding the physics of energetic particles, the deuterium experimental campaigns started in Large Helical Device (LHD) from March 2017. To investigate the behavior of energetic particles, a Fast-ion D Alpha (FIDA) diagnostic was installed on the LHD. In the FIDA diagnostic, the Doppler-shifted D alpha light from fast-neutrals are utilized as signals of energetic particles, where these fast-neutrals are produced by the charge exchange process between fast-ions in the plasma and actively injected neutrals by neutral beam (NB). The advantages of the FIDA diagnostic are the velocity and the spatially resolved measurement of fast-ions at the crossing point between its line of sight (LOS) and the incident line of NB. The most recent FIDASIM is enhanced to simulate signals produced in three-dimensional magnetic configurations. The new version of FIDASIM uses the fast-ion distribution function produced by GNET as input to simulate FIDA signals at LHD. In order to validate the new version of the code, measurements of radial profiles of fast-ions using the FIDA diagnostic are performed in magnetohydrodynamic (MHD)-quiescent plasmas. The measured spectra are in good agreement with the theoretical prediction by 3D-supporting FIDASIM at the center of the plasma (R= 3.5 m∼3.7 m, reff/a99= −0.28∼0.05) on the LHD when the line averaged electron density is ne_avg < 1.23 × 1019 m−3. On the other hand, the measured spectra are in disagreement with the theoretical prediction by 3D-supporting FIDASIM at even the center of the plasma when the line averaged electron density is ne_avg ≥ 1.23 × 1019 m−3.

Cause and impact of low-frequency chirping modes in DIII-D hybrid discharges

Significant variations in MHD activity and fast-ion transport are observed in the DIII-D high-beta, steady-state hybrid discharges with a mixture of electron cyclotron (EC) waves and neutral beam injection (NBI). When electron cyclotron heating (ECH) or current drive (ECCD) is applied, Alfvén eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor . The lower ratio of fast-ion injection speed vinj to Alfvén speed valfven and slight drop of during ECCD also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction is less than 0.53 and is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with is weaker, and is around unity in all the cases. The reason why the instability transition correlates with and is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes (referred to as chirping (N)TMs), i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and ‘Kick’ model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.

Resolving the fast ion distribution from imaging neutral particle analyzer measurements

A recently developed imaging neutral particle analyzer (INPA) on the DIII-D tokamak (Du 2018 Nucl. Fusion 58 082006) enables fast ion velocity-space tomography of high fidelity at the interrogated phase space. To accomplish this, the spatial and energy depending fast (E < 80 keV) neutral flux towards the INPA stripping foils is calculated with FIDASIM and a newly developed code INPASIM simulates the INPA instrumental response to this neutral flux. Included in INPASIM is the neutral-foil interaction, the Larmor orbit tracing between the foil and the phosphor, the phosphor response to the incident ion flux as well as camera focusing. Benefiting from heavy, localized velocity-space weights and excellent signal to noise, computed tomography using the Ridge regression method is able to successfully reconstruct fine-scale velocity-space structures produced by multiple neutral beams separated by as small as ∼3 keV in tests. Applying the inversion method to a sawtooth crash event reveals a significant profile flattening of confined passing particles across q = 1 flux surface, as well as a redistribution of fast ions into the trapped orbits at the plasma edge close to the last closed flux surface.

Progress in modelling fast-ion D-alpha spectra and neutral particle analyzer fluxes using FIDASIM

FIDASIM is a code that models signals produced by charge-exchange reactions between neutrals and ions (both fast and thermal) in magnetically confined plasmas. With the ion distribution function as input, the code predicts the efflux to a neutral particle analyzer diagnostic and the photon radiance of Balmer-alpha light to a fast-ion D diagnostic, in addition to many other related quantities. A new, parallelized version of the Monte Carlo code FIDASIM has been developed in Fortran90 that is substantially faster than the original interactive data language version. Modified algorithms include more accurate treatments of the time dependent collisional-radiative equations that describe neutral energy levels, of the cloud of ‘halo’ neutrals that surround the injected neutral beam, and of finite Larmor radius effects. Enhanced physics capabilities include modelling ‘passive’ signals from cold edge neutrals, the ability to treat general three-dimensional magnetic confinement configurations, and calculations of diagnostic-specific weight functions that enable tomographic reconstructions of the fast-ion distribution function. Neutral beam attenuation, beam emission, and fast-ion birth profiles are also modelled. The new algorithms have been successfully validated against experimental data and new features have been tested through benchmarks between two independently developed versions of the code.

Fishbone instability driven by trapped fast ions in a toroidal plasma with reversed magnetic shear

Based on the non-perturbative approach, the hybrid code MARS-K is applied to study fishbone (FB) instabilities driven by trapped fast ions in a toroidal plasma with q profile nearly being flat or non-monotonic. We explore the dependency of the FB with variation in the fast ion distribution, thermal particle kinetic effects, safety factor (q) profile and plasma resistivity. When the safety factor minimum value is larger than unity (i.e. ), the mode can be excited by isotropic or anisotropic fast ions, with the latter strongly enhancing the mode growth rate. The mode frequency increases with increasing , and is more easily triggered in a equilibrium with two q = 1 surfaces, compared with the case with one or no q = 1 surface. Kinetic contributions from transit resonance of passing fast ions and from bounce resonance of trapped fast ions strongly enhance mode instability. The passing thermal ions induced Landau damping has a strong stabilization effect. Furthermore, in such a weak, even reversed magnetic shear plasma, the radial mode structure of FB mode monotonically decreases to zero at q = 1 flux surface instead of a step-like function, and it depends on the kinetic contributions from particles. In addition, the plasma resistivity significantly stabilizes the mode near the marginally unstable point.

Observation of Alfvén Eigenmodes driven by off-axis neutral beam injection in the TCV tokamak

Fast-particle driven Alfvén Eigenmodes have been observed in low-collisionality discharges with off-axis neutral beam injection (NBI), electron cyclotron resonance heating (ECRH) and a reduced toroidal magnetic field. During NBI and ECRH, toroidicity induced Alfvén Eigenmodes (TAEs) appear in frequency bands close to 200 kHz and energetic-particle-induced geodesic acoustic modes (EGAMs) are observed at about 40 and 80 kHz. When turning off ECRH in the experiment, those beam-driven modes disappear which can be explained by a modification of the fast-ion slowing down distribution. In contrast, coherent fluctuations close to the frequency of the beam-driven TAEs are present throughout the experiment. The modes are even observed during ohmic plasma conditions, which clearly demonstrates that they are not caused by fast particles and suggests an alternative drive, such as turbulence. The mode-induced fast-ion transport has been found to be weak and marginal in terms of the fast-ion diagnostic sensitivities. Measurements of the plasma stored energy, neutron rates, neutral particle fluxes and fast-ion D-alpha spectroscopy show good agreement with neoclassical modelling results from TRANSP. This is further supported by a similarly good agreement between measurement and modelling in cases with and without ECRH and therefore with and without the modes. Instead, a significant level of charge exchange losses are predicted and observed which generate a bump-on-tail fast-ion distribution function that can provide the necessary free energy to EGAMs.

Numerical simulations of NBI fast ion loss with RMPs on the EAST tokamak

Fast ion losses in the presence of resonant magnetic perturbations (RMPs) on the EAST tokamak have been simulated by using the Monte Carlo orbit-following code GYCAVA (Xu et al 2019 Comput. Phys. Comm. 244 40). Fast ions produced by the co-current tangential neutral beam injection (NBI) were considered. The initial distribution of NBI fast ions was numerically computed by the TGCO code and the n = 1 vacuum and response RMP fields were numerically computed by the MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). It is found that fast ion losses increase almost linearly with the RMP coil current. Poincaré plots show that fast ion losses in the presence of RMPs on EAST are mainly due to the orbit stochasticity induced by RMPs. The collision effect, including the slowing down and the pitch angle scattering, on fast ion losses have also been numerically studied. The synergy effect of RMPs and collision-induced pitch angle scattering can enhance the particle loss of fast ions. The collision effect, including the effective ion charge number effect, on the power loss of fast ions is weak. Fast ion losses increase with the effective ion charge number increasing, which is related to the pitch angle scattering effect. The plasma response to RMPs can enhance or reduce fast ion losses. The plasma response effect on fast ion losses depends on the RMP coil phasing, that is, the phase difference between the upper and lower coils. The heat loads on the outer wall clearly follow the n = 1 periodicity of the RMP coil configuration. Positions of maximum heat loads are closely related to the coil phasing of RMPs. These mean that the magnetic topology of RMPs is responsible for the toroidal distribution of heat loads.

Tomography of the positive-pitch fast-ion velocity distribution in DIII-D plasmas with Alfvén eigenmodes and neoclassical tearing modes

Understanding the effect of Alfvén eigenmodes (AEs) and neoclassical tearing modes (NTMs) on fast ions is highly important for fusion reactors due to potentially strong resonant interactions between the fast ions and the modes. Here, we use the four-view fast-ion D-alpha (FIDA) diagnostic installed in the DIII-D tokamak to reconstruct the fast-ion velocity distribution at two radial positions during two sequential discharges with strong and weak mode activity, respectively. The velocity-space coverage of the diagnostics, however, only allows reliable reconstructions of fast ions with positive pitches. Therefore, we suggest new tomographic inversion methods relying on prior information outside the well-diagnosed region. We find that within the population of fast ions with positive pitches, ions, at all energies, are transported away from the measurement volumes. Comparisons between the reconstructions and kick model simulations, where the mode activity is considered, reveal that low-frequency modes such as the NTMs and low-frequency AEs contribute significantly to the positive-pitch fast-ion transport in the central measurement volume, whereas TAEs and EAEs become important farther out and are responsible for decreased fast-ion confinement.

Collective Thomson Scattering Diagnostic for Wendelstein 7-X at 175 GHz

The Collective Thomson Scattering (CTS) diagnostic measures the scattering spectrum of incident radiation off collective fluctuations in plasmas. In Wendelstein 7-X (W7-X) the diagnostic uses a 140 GHz heating gyrotron as a source of the probing radiation. At this frequency, the CTS spectra are heavily affected by the electron cyclotron emission, and the microwave beam propagation is restricted at typical W7-X plasma parameters. The diagnostic was successfully commissioned in the last experimental campaign and demonstrated ion temperature measurements. However, the signal-to-noise ratio was too low for measuring other quantities such as the fast-ion velocity distribution function or the fuel ion ratio. Currently, the W7-X CTS diagnostic is undergoing an upgrade to a frequency of 175 GHz. This will increase the sensitivity of the diagnostic, since the noise due to electron cyclotron emission will be reduced, and it will relax the constraints on microwave beam propagation in W7-X. Here we present the salient features of the upgraded CTS system and discuss its prospects for both thermal-ion and fast-ion measurements.

Influence of energy losses on charge distribution of fast ions passing through solid matter

The charge distribution of fast multicharged ions passing through a matter is studied taking ion energy losses into account. Within the framework of the proposed method, we show that the changes in the charge exchange cross-sections, caused by the decreasing of ion energy, affect the process of the formation of the equilibrium ion charge distribution. The target thickness, required for obtaining the equilibrium ion charge distribution, reaches the maximum value for ions without electrons and hydrogen-like ions. The equilibrium target thickness increases with increasing in ion nuclear charge and energy and for fast heavy ions becomes comparable with their range.

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfvén eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co- and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Moreover, previous results in the very narrow beam case are corrected and generalized to retain all terms in ω/ωci and |k∥/k⊥|, which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs.

Collective Thomson scattering with 77, 154, and 300 GHz sources in LHD

Collective Thomson scattering (CTS) is one of attractive diagnostics for measuring locally and directly the fuel temperature and the velocity distribution of fast ions in fusion plasmas. A mega-watt class source of millimeter or sub-millimeter waves is required to detect a weak scattered radiation superimposed on background radiation owing to electron cyclotron emissions (ECEs) from plasmas. Based on electron cyclotron resonance heating (ECRH) system with the frequencies of 77 GHz and 154 GHz in the Large Helical Device (LHD), the CTS diagnostic system has been developed to measure bulk ion temperatures from a few keV to ∼10 keV and fast ions originated from 180 keV-neutral beam injection in the LHD. The measured CTS spectra and their time evolutions are analyzed with the electrostatic scattering theory. The bulk ion temperatures obtained from CTS spectra increase with the neutral beam injections and decrease with the heating terminated. The velocity map of simulated fast ions explains that the bumps on tail of measured CTS spectra are caused by the co- and counter- fast ions. A new prescription for anisotropic velocity distribution function is proposed. As for 154 GHz bands, the CTS spectrum broadenings for D and H plasmas are distinguished reasonably at the same temperature, and its ion temperatures are comparable to those of the charge exchange recombination spectroscopy. As reactor-relevant diagnostics, a 300 GHz gyrotron and a corresponding receiver system have been implemented in LHD to access high density plasmas with low background ECEs. The recent progress for CTS diagnostics and their spectrum analysis with the probe frequencies of 77 GHz, 154 GHz, and 300 GHz in the LHD experiments is described.

Controlling energy distribution of fast ions and X-ray emission via target reliefs in ultrafast and relativistic laser plasma interaction

Secondary emission from laser produced plasma is governed by the electron distribution function. Therefore, its control is of utmost importance to steer the emission, e.g., of ultrashort bursts of high energy photons and ions for decisive application. Maximum gain is achieved if the laser light absorption by plasma is also maximized. In our theoretical analysis including comparison to recent experiments, we follow this route and study how the energy is transferred from a short laser pulse to the energy of fast ions and X-rays. We make use of ion and K-α emissions, which respond differently to branches of the electron distribution function when we optimize the laser light absorption via structuring of the target surface. Our investigation comprises laser intensities up to 5 × 1020 W/cm2 produced with femtosecond near infrared laser pulses and titanium foil targets of a few micrometer thicknesses. In particular, we reveal an energy relaxation process of hot electrons, which determines the observed laser intensity dependence of secondary emission and points to the benefit of target surface structuring in different optimization scenarios.

Modification of classical electron transport due to collisions between electrons and fast ions

A Fokker-Planck model for the interaction of fast ions with the thermal electrons in a quasineutral plasma is developed. When the fast ion population has a net flux (i.e., the distribution of fast ions is anisotropic in velocity space), the electron distribution function is perturbed from Maxwellian by collisions with the fast ions, even if the fast ion density is orders of magnitude smaller than the electron density. The Fokker-Planck model is used to derive classical electron transport equations (a generalized Ohm's law and a heat flow equation) that include the effects of the electron-fast ion collisions. It is found that these collisions result in a collisionally induced current term in the transport equations which can be significant. The new transport equations are analyzed in the context of a number of scenarios including α particle heating in inertial confinement fusion and magnetoinertial fusion plasmas as well as ion beam heating of dense plasmas.