Fast-ion Distribution Function Research Articles

Orbit tomography in constants-of-motion phase-space

Tomographic reconstructions of a 3D fast-ion constants-of-motion phase-space distribution function are computed by inverting synthetic signals based on projected velocities of the fast ions along the diagnostic lines of sight. A spectrum of projected velocities is a key element of the spectrum formation in fast-ion D-alpha spectroscopy, collective Thomson scattering, and gamma-ray and neutron emission spectroscopy, and it can hence serve as a proxy for any of these. The fast-ion distribution functions are parameterised by three constants of motion, the kinetic energy, the magnetic moment and the toroidal canonical angular momentum. The reconstructions are computed using both zeroth-order and first-order Tikhonov regularisation expressed in terms of Bayesian inference to allow uncertainty quantification. In addition to this, a discontinuity appears to be present in the solution across the trapped-passing boundary surface in the three-dimensional phase space due to a singularity in the Jacobian of the transformation from position and velocity space to phase space. A method to allow for this apparent discontinuity while simultaneously penalising large gradients in the solution is demonstrated. Finally, we use our new methods to optimise the diagnostic performance of a set of six fans of sightlines by finding where the detectors contribute most complementary diagnostic information for the future COMPASS-Upgrade tokamak.

Velocity-space distribution function of fast ions in a sawtoothing plasma

This study explores the influence of sawtooth oscillations on the velocity space distribution of fast ions in tokamak plasma discharges. The relevant Fokker–Planck equation for fast ions is solved analytically. Two distinct effects arising from the temperature drop associated with a sawtooth crash and their impact on the distribution function of fast ions are considered. The first effect involves the modulation of the fusion alpha particle source on the timescale of the sawtooth period, linked to the drop in fusion yield resulting from the sawtooth temperature relaxations. The second effect is tied to the increase of the slowing-down time during the sawtooth ramp, causing particles born later in the sawtooth cycle to experience reduced slowing down compared to those born right after the crash, creating an accumulation-like mechanism at higher energies. In regimes where the sawtooth period is shorter than the fast ion slowing-down time, the combined influence of these effects gives rise to fast ion distribution functions that transiently exhibit positive slopes in velocity space.

The research progress of an E//B neutral particle analyzer

An // neutral particle analyzer (NPA) has been designed and is under development at Sichuan University and Southwestern Institute of Physics. The main purpose of the // NPA is to measure the distribution function of fast ions in the HL-2A/3 tokamak. The // NPA contains three main units, i.e. the stripping unit, the analyzing unit and the detection unit. A gas stripping chamber was adopted as the stripping unit. The results of the simulations and beam tests for the stripping chamber are presented. Parallel electric and magnetic fields provided by a NdFeB permanent magnet and two parallel electric plates were designed and constructed for the analyzing unit. The calibration of the magnetic and electric fields was performed using a 50 kV electron cyclotron resonance ion source (ECRIS) platform. The detection unit consists of 32 lutetium-yttrium oxyorthosilicate (LYSO) detector modules arranged in two rows. The response functions of , hydrogen ions ( , and ) and for a detector module were measured with Am, Cs and Eu sources together with the 50 kV ECRIS platform. The overall results indicate that the designed // NPA device is capable of measuring the intensity of neutral hydrogen and deuteron atoms with energy higher than 20 keV.

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Commissioning of the imaging neutral particle analyser for the ASDEX Upgrade tokamak

An imaging neutral particle analyser (INPA) diagnostic has been installed and commissioned at the ASDEX Upgrade (AUG) tokamak. The AUG INPA diagnostic provides energy and radially resolved measurements of the fast-ion (FI) distribution, complementing the existing set of diagnostic which measure the confined FI population. To this end, it analyses charge exchange (CX) neutrals produced in reactions between FI and neutrals injected by a neutral beam injector. These CX neutrals are ionised by a 20 nm carbon foil and deflected towards a scintillator by the machine magnetic field. The use of a scintillator as active component allows us to cover the whole plasma radial range with an energy resolution of 9 keV and a spatial of 3 cm for 93 keV deuterons. First measurements demonstrate the high sensitivity of the INPA diagnostic to different AUG fast-ion distribution functions, from NBI and ion-cyclotron resonance heating origin, and show good agreement with the synthetic diagnostic.

Diagnostic weight functions in constants-of-motion phase-space

The fast-ion phase-space distribution function in axisymmetric tokamak plasmas is completely described by the three constants of motion: energy, magnetic moment and toroidal canonical angular momentum. In this work, the observable regions of constants-of-motion phase-space, given a diagnostic setup, are identified and explained using projected velocities of the fast ions along the diagnostic lines-of-sight as a proxy for several fast-ion diagnostics, such as fast-ion Dα spectroscopy, collective Thomson scattering, neutron emission spectroscopy and gamma-ray spectroscopy. The observable region in constants-of-motion space is given by a position condition and a velocity condition, and the diagnostic sensitivity is given by a gyro-orbit and a drift-orbit weighting. As a practical example, 3D orbit weight functions quantifying the diagnostic sensitivity to each point in phase-space are computed and investigated for the future COMPASS-Upgrade and MAST-Upgrade tokamaks.

Experimental characterization of the active and passive fast-ion H-alpha emission in W7-X using FIDASIM

This paper presents the first results from the analysis of Balmer-alpha spectra at Wendelstein 7-X which contain the broad charge exchange emission from fast-ions. The measured spectra are compared to synthetic spectra predicted by the FIDASIM code, which has been supplied with the 3D magnetic fields from VMEC, 5D fast-ion distribution functions from ASCOT, and a realistic Neutral Beam Injection geometry including beam particle blocking elements. Detailed modeling of the beam emission shows excellent agreement between measured beam emission spectra and predictions. In contrast, modeling of beam halo radiation and Fast-Ion H-Alpha signals (FIDA) is more challenging due to strong passive contributions. While about 50% of the halo radiation can be attributed to passive signals from edge neutrals, the FIDA emission—in particular for an edge-localized line of sights—is dominated by passive emission. This is in part explained by high neutral densities in the plasma edge and in part by edge-born fast-ion populations as demonstrated by detailed modeling of the edge fast-ion distribution.

Synthetic Diagnostic of Spectra of Charge-Exchange Atoms for Analysis of Influence of the MHD Instability on Fast-Particle Confinement in Spherical Tokamaks Globus-M/M2

Absorbed power of the neutral-injection beam in spherical tokamaks Globus-M/M2 is estimatednumerically. Deceleration of fast particles is simulated by means of the NUBEAM code. The signal of analyzerof charge-exchange atoms is simulated by means of the FIDASIM code using the distribution functionof fast ions calculated by means of the NUBEAM code. Comparison of calculated and experimental signalsallowed determining the degree of influence of instabilities on confinement of fast particles along withabsorbed beam power.

Interpretation of ion cyclotron emission from sub-Alfvénic beam-injected ions heated plasmas soon after L-H mode transition in EAST

Ion cyclotron emission (ICE) at deuterium ion cyclotron harmonics, driven by sub-Alfvénic beam-injected deuterium ions, has been observed by the high-frequency B-dot probe in the EAST tokamak. The origin of ICE shifts from the plasma core to the plasma edge soon after an L-H mode transition, where the beam-injected deuterium ions have a relatively peak bump-on tail structure in the energy direction and a very intense pitch angle anisotropy. Based on the fast ion distribution function obtained from the TRANSP/NUBEAM code, together with a linear analysis theory of magnetoacoustic cyclotron instability (MCI), the growth rates of MCI could be calculated. It is shown that MCI, resulting in the generation of obliquely propagating fast Alfvén waves at deuterium ion cyclotron harmonics, can occur under such conditions. And the temporal evolution of the MCI growth rate closely follows that of the observed ICE amplitude in the EAST.

4D and 5D phase-space tomography using slowing-down physics regularization

We compute reconstructions of 4D and 5D fast-ion phase-space distribution functions in fusion plasmas from synthetic projections of these functions. The fast-ion phase-space distribution functions originating from neutral beam injection (NBI) at TCV and Wendelstein 7-X (W7-X) at full, half, and one-third injection energies can be distinguished and particle densities of each component inferred based on 20 synthetic spectra of projected velocities at TCV and 680 at W7-X. Further, we demonstrate that an expansion into a basis of slowing-down distribution functions is equivalent to regularization using slowing-down physics as prior information. Using this technique in a Tikhonov formulation, we infer the particle density fractions for each NBI energy for each NBI beam from synthetic measurements, resulting in six unknowns at TCV and 24 unknowns at W7-X. Additionally, we show that installing 40 LOS in each of 17 ports at W7-X, providing full beam coverage and almost full angle coverage, produces the highest quality reconstructions.

3D simulation of orbit loss and heat load on limiters of ICRF-NBI synergy induced fast ions on EAST

Fast ions synergy induced by ion-cyclotron range of frequency (ICRF) and neutral beam injection (NBI) are of interest not only because of their advantage of heating the plasma and drive currents, but also because of their disadvantage of damaging plasma surface components and driving MHD instabilities. In this paper, we calculate the fast ion loss and the deposition distribution of the lost particles on the limiters in EAST under the synergistic effect of the ripple field and collisions with the full-orbit-following simulation program ISSDE for the first time. The previous models to study the NBI fast ion loss by the action of ICRF are relatively simple and consider fewer influencing factors. Most studies on fast ion loss have used toroidal uniform boundaries. In this work, we consider the distribution of ICRF-NBI synergy induced fast ions with different minority H concentrations. After setting the limiter boundary, we consider the prompt fast ion loss caused by the equilibrium field and the fast ion loss caused by the ripple field and collision. Under the action of minority-ion ion-cyclotron resonant heating, the NBI fast ion distribution function has spread in the high-energy part, especially for the minority H concentration of 1%, and the fast ions show each anisotropic distribution near the resonance band on the poloidal dimension. The synergistic loss caused by the ripple field and collision will first be greater than the loss caused by either factor, and then reach a final loss fraction of 3.8%. The heat load power density of the lost fast ions on different limiters is not uniform, as well as on each limiter, which is related to the distance from the limiter to the plasma, the relative position between the limiters and the parallel direction of most fast ions. Once the study of ICRF-NBI synergy induced fast ion loss caused by the action of ripple and collision has been done, we can do optimization in a targeted manner. Such as adding ferromagnetic inserts to reduce the ripple loss and optimizing the limiters’ position to reduce or control the generation of impurities.

Tomography of fast ion distribution function under neutral beam injection and ion cyclotron resonance heating on EAST

In magnetic confinement fusion devices, velocity-space tomography of fast-ion velocity distribution function is crucial for investigating fast-ion distribution and transport. In the neutral beam injection (NBI) and ion cyclotron resonance heating (ICRF) synergistic heating experiments in Experimental Advanced Superconducting Tokamak (EAST), high-energy particles with energy exceeding the particle energy in NBI are observed. Simulations of synergistic effect on fast-ion velocity distribution function given by TRANSP also show the existence of particles with energy higher than the particle energy in NBI. To investigate the behaviors of fast ion distribution and calculate the velocity distribution functions under different heating conditions, the first-order Tikhonov regularization tomographic inversion method with higher inversion accuracy is introduced by comparing various regularization techniques. The limitations of the dual-view fast-ion D<sub>α</sub> (FIDA) diagnostic measurements in velocity space are addressed by incorporating prior information such as null measurement and the known peaks and effectively mitigate the occurrence of artifacts. This method is first employed in the case of NBI heating. The NBI peak is successfully reconstructed at the expected location in velocity space, which shows significant improvement in the inversion results. In order to further validate the synergistic effect of NBI-ICRF heating and study the mechanism of fast ion distribution under synergistic heating, the combination of FIDA and neutron emission spectrometer (NES) is applied to the first-order Tikhonov regularization tomographic inversion method for enhancing the coverage of velocity space, through which the issue of artifacts in the inversion results is significantly improved, and thus the precision of the obtained fast-ion velocity distribution functions is enhanced. Based on the benefit described above, the method of combining NES diagnosis and FIDA diagnosis is used to obtain fast-ion velocity distribution functions in the NBI and ICRF synergistic heating discharge. The synergistic heating effect is manifested in the fast-ion velocity distribution. The availability of this inversion method in reconstructing fast-ion velocity distribution functions during high-performance operation of NBI-ICRF synergistic heating in the EAST experiment is confirmed. In the next-step EAST research, high performance discharge will demand more efficiency NBI and ICRF synergistic heating, the present work builds the stage for investigating the underlying mechanism of synergistic heating and the intricate behaviors associated with fast ion distribution and transport.

Initial operation of perpendicular line-of-sight compact neutron emission spectrometer in the large helical device.

The perpendicular line-of-sight compact neutron emission spectrometer (perpendicular CNES) was newly installed to understand the helically trapped fast-ion behavior through deuterium-deuterium (D-D) neutron energy spectrum measurement in the Large Helical Device (LHD). The energy calibration of the EJ-301 liquid scintillation detector system for perpendicular CNES was performed on an accelerator-based D-D neutron source. We installed two EJ-301 liquid scintillation detectors, which view the LHD plasma vertically from the lower side through the multichannel collimator. The D-D neutron energy spectrum was measured in a deuterium perpendicular-neutral-beam-heated deuterium plasma. By the derivative unfolding technique, it was found that the D-D neutron energy spectrum had a double-humped shape with peaks at ∼2.33 and ∼2.65MeV. D-D neutron energy spectrum was calculated based on the fast ion distribution function using guiding center orbit-following models considering the detector's energy resolution. The calculated peak energies in the D-D neutron energy spectrum almost match the experiment. In addition, a feasibility study toward the measurement of the energy distribution of ion-cyclotron-range-of-frequency-wave-accelerated beam ions was performed.

ASCOT5 simulations of neutral beam heating and current drive in the TJ-II stellarator

The TJ-II stellarator neutral-beam injection (NBI) system, vacuum vessel and magnetic configuration have been included in the orbit-following Monte Carlo code ASCOT5 to simulate neutral-beam heating and current drive for high-density NBI plasmas. Co- and counter-injection beams are simulated separately. A scan in both electron density and temperature is carried out within the range of values corresponding to realistic high-density NBI plasmas, for which a low level of fast-ion losses due to charge-exchange reactions is expected, since the version of ASCOT5 used in the paper does not include such processes. The rest of the kinetic profiles (ion temperature, radial electric field and effective charge) are kept fixed. The initial distribution of markers shows that the amount of available power in the plasma carried by the beam ions depends slightly on the electron temperature and on the injection direction (co/counter). The steady-state fast-ion distribution function is obtained and used to calculate the three-dimensional fast-ion density, the neutral-beam driven current and the amount of power deposited to the plasma in the two injection scenarios. These three quantities are higher in the counter-injected case due to a lower amount of promptly lost particles. The neutral-beam current drive (NBCD) has been calculated using the fast-ion beam current given by ASCOT5 and the electron return current, which is computed with the analytic solution of the drift kinetic equation for electrons in the presence of fast ions in the low-collisionality regime. Neither the calculated fast-ion density nor the NBCD are flux functions, in consistency with the fact that fast-ion drift surfaces and flux surfaces are generally not aligned.

Orbit tomography of energetic particle distribution functions

Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics’ velocity-space weight functions, i.e. velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present orbit tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy, pitch, r, z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX upgrade using FIDA measurements. Finally, a comparison between the orbit tomography and velocity-space tomography is shown.

Feasibility of neutral particle analysis for fast-ion measurements at W7-X

A preliminary study investigating capabilities of a planned but not yet installed neutral particle analyzer (NPA) [1,2] system combined with a diagnostic neutral beam at Wendelstein 7-X (W7-X) [3] is presented. Additionally two NPAs viewing the neutral beam injection (NBI) [4] source 8 beam and using it as neutral source are studied. The main focus is laid on what information about NBI fast-ion slowing down distributions can be inferred from active NPA measurements when altering the magnetic configuration, plasma β, density, electron temperature or radial electric field. For an order of magnitude estimation of the passive signal a model for penetration of neutral hydrogen recycling from the first wall is implemented. For the active signal a diagnostic neutral beam injector was simulated using FIDASIM [5]. The fast-ion slowing down distributions were calculated with ASCOT [6]. The synthetic NPA signal is found in general to be sensitive to changes in the fast-ion distribution function. Distinct features can be seen in the high energy active signal in the high-mirror configuration when changing β, especially, when looking at deeply trapped fast particles. However, for the initially planned installation geometry of the NPA diagnostic most fast-ion distributions exhibit only small differences in the magnitude and especially shape. In a high density case in the standard magnetic configuration with a central β of 8%, the fast-ion density in the core region is too low to provide a measurable flux of charge exchanged neutrals. The passive signal from the inner plasma regions is found to be negligible compared to the active signal.

Development of a reduced model for energetic particle transport by sawteeth in tokamaks

The sawtooth instability is known for inducing transport and loss of energetic particles (EPs), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a pre-processor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on EPs. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast-ion distribution function and its evolution over time.

Verification and validation of the high-performance Lorentz-orbit code for use in stellarators and tokamaks (LOCUST)

A novel high-performance computing algorithm, developed in response to the next generation of computational challenges associated with burning plasma regimes in ITER-scale tokamak devices, has been tested and is described herein. The Lorentz-orbit code for use in stellarators and tokamaks (LOCUST) is designed for computationally scalable modelling of fast-ion dynamics, in the presence of detailed first wall geometries and fine 3D magnetic field structures. It achieves this through multiple levels of single instruction, multiple thread parallelism and by leveraging general-purpose graphics processing units. This enables LOCUST to rapidly track the full-orbit trajectories of kinetic Monte Carlo markers to deliver high-resolution fast-ion distribution functions and plasma-facing component power loads. LOCUST has been tested against the prominent NUBEAM and ASCOT fast-ion codes. All codes were compared for collisional plasmas in both high and low-aspect ratio toroidal geometries, with full-orbit and guiding-centre tracking. LOCUST produces statistically consistent results in line with acceptable theoretical and Monte Carlo uncertainties. Synthetic fast-ion D-α diagnostics produced by LOCUST are also compared to experiment using FIDASIM and show good agreement.

Determining 1D fast-ion velocity distribution functions from ion cyclotron emission data using deep neural networks

The relationship between simulated ion cyclotron emission (ICE) signals s and the corresponding 1D velocity distribution function fv⊥ of the fast ions triggering the ICE is modeled using a two-layer deep neural network. The network architecture (number of layers and number of computational nodes in each layer) and hyperparameters (learning rate and number of learning iterations) are fine-tuned using a bottom-up approach based on cross-validation. Thus, the optimal mapping gs;θ of the neural network in terms of the number of nodes, the number of layers, and the values of the hyperparameters, where θ is the learned model parameters, is determined by comparing many different configurations of the network on the same training and test set and choosing the best one based on its average test error. The training and test sets are generated by computing random ICE velocity distribution functions f and their corresponding ICE signals s by modeling the relationship as the linear matrix equation Wf = s. The simulated ICE signals are modeled as edge ICE signals at LHD. The network predictions for f based on ICE signals s are on many simulated ICE signal examples closer to the true velocity distribution function than that obtained by 0th-order Tikhonov regularization, although there might be qualitative differences in which features one technique is better at predicting than the other. Additionally, the network computations are much faster. Adapted versions of the network can be applied to future experimental ICE data to infer fast-ion velocity distribution functions.

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.