Orbit-following Monte Carlo Code Research Articles

Analysis of high frequency Alfvén eigenmodes observed in ASDEX Upgrade plasmas in the presence of RF-accelerated NBI ions

High frequency Alfvén eigenmodes in the ion cyclotron frequency range are actively researched on the ASDEX Upgrade tokamak (AUG). The general properties of this particular mode type are: (a) the mode is beam-driven and, if excited, can persist for the entire duration of the beam-on time window; (b) the mode is sub-cyclotron with the frequency ω ∼0.5ω ci, where ωci corresponds to the on-axis cyclotron frequency of the beam ions; (c) the mode propagates in the counter-current/counter-injection direction; and (d) the field-aligned (∼toroidal) mode number is large: |n //| ∼50. It has been observed on AUG that radio frequency- (RF)-acceleration of beam-injected ions at the 3rd cyclotron harmonic significantly expands the number of excited modes. In this work we demonstrate how this observation is consistent with the global Alfvén eigenmode (GAE) behavior. The RF-driven fast ion population is modeled using a combination of an orbit-following Monte Carlo code (ASCOT-RFOF) and an electro-magnetic wave code (TORIC). The application of this code combination is a first to model beam-ion RF-acceleration at the 3rd cyclotron harmonic. The RF-accelerated fast ion distributions are then used to analytically calculate anisotropy-driven mode growth rates. We see that the region of positive (unstable) growth rates is expanded by RF-accelerated fast ions in both the frequency and the mode number directions for the GAEs, consistent with the measurements. Although the compressional Alfvén eigenmode growth rates are also positive for our particular fast ion distributions, the growth rate values are ∼3 orders of magnitude lower. The plasma conditions on AUG are more destabilizing to the GAEs. Overall, our results are consistent with the observation of similar modes on other conventional tokamaks, namely JT-60U and DIII-D.

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.

ASCOT orbit-following simulations of ion cyclotron heating with synthetic fast ion loss diagnostic: a first application to ASDEX Upgrade

The orbit-following Monte Carlo code ASCOT interfaced with the radiofrequency Monte Carlo library RFOF can simulate radiofrequency heating of ion populations using wave solutions from full-wave solvers such as TORIC. It is applied to the fundamental mode ion cyclotron resonant heating of hydrogen and 2nd harmonic frequency heating of neutral beam injected deuterium in ASDEX Upgrade discharge #33147 to validate the model against fast ion loss detector (FILD) measurements. In addition, for FILD signal simulations requiring enhanced resolution or scanning the effect of various perturbations such as magnetohydrodynamic phenomena near the plasma edge, a two-stage simulation scheme is presented where the fast ion population is first created by a full ASCOT-RFOF ion cyclotron heating simulation, and the resulting distribution is then used as an input to ASCOT’s distribution-sampling marker source module for more efficient simulation of the ICRH ion wall load and FILD signal. A satisfactory agreement with the experimentally observed FILD signal is found.

The effects of resonant magnetic perturbations and charge-exchange reactions on fast ion confinement and neutron emission in the Mega Amp Spherical Tokamak

The application of non-axisymmetric resonant magnetic perturbations (RMPs) to low current plasmas in the Mega Amp Spherical Tokamak (MAST) was found to be correlated with substantial drops in neutron production, suggesting a significant degradation of fast ion confinement. The effects of such perturbations on fast ions in MAST have been modelled using a revised version of a non-steady-state orbit-following Monte-Carlo code, in which the parametrization of fusion reaction rates has been updated and neutron rates have been recalculated. Losses of fast ions via charge-exchange (CX) with background neutrals and the subsequent reionization of fast neutrals due to collisions with bulk plasma particles have also been taken into account. The effects of the plasma response to externally-applied RMPs have been included in the modelling. The updated results show that computed neutron rates in the presence of RMPs with the plasma response and CX reactions taken into account agree very well with the experimental data throughout the analysis target time. CX reactions play an important role in determining the neutron rates, in particular before the onset of RMPs.

Application of a non-steady-state orbit-following Monte-Carlo code to neutron modeling in the MAST spherical tokamak

As part of the verification and validation of a newly developed non-steady-state orbit-following Monte-Carlo code, application studies of time dependent neutron rates have been made for a specific shot in the Mega Amp Spherical Tokamak (MAST) using 3D fields representing vacuum resonant magnetic perturbations (RMPs) and toroidal field (TF) ripples. The time evolution of density, temperature and rotation rate in the application of the code to MAST are taken directly from experiment. The calculation results approximately agree with the experimental data. It is also found that a full orbit-following scheme is essential to reproduce the neutron rates in MAST.

Synthetic Fast Ion Diagnostics in Tokamaks: Comparing the Monte Carlo Test Particle Code ASCOT against Experiments

Measuring fast ions, most notably fusion alphas, in ITER and future reactors remains an issue that still lacks an adequate solution. Numerical simulations are invaluable in testing the potential and limitations of various proposed diagnostics. However, the validity of the numerical tools first has to be checked against results from existing tokamaks. In this contribution, various synthetic diagnostics for fast ions (collective Thomson scattering, neutral particle analyzer, neutron camera, infrared measurements, fast ion loss detector, and activation probe) from the orbit-following Monte Carlo code ASCOT are compared to measurements from several tokamaks (ASDEX Upgrade, DIII-D, and JET). Within the limitations of the physics included in the numerical model and availability of input data from experiments, the agreement between synthetic data and measurements is found to be quite good.

Effects of the radial electric field on the confinement of fast ions in ITER

The effects of a radial electric field (EF) on the losses of alpha particles and neutral beam injection (NBI) fast ions in typical ITER operation scenarios for both error fields due to test blanket modules (TBMs) and toroidal field (TF) ripple were evaluated using an iterative method to execute an orbit-following Monte-Carlo code and a one-dimensional transport code. The EF effect on the loss of fast ions strongly depends on the operation scenario as well as on the error field. The electric field is very significant in the loss of fast ions in a 9 MA ITER operation scenario with a higher safety factor and in the error field associated with TBMs. The EF effect in the error field of TF ripple is very small in any operation scenario. The electric field is much more significant for the loss of NBI fast ions than for that of alpha particles. The radial electric field changes the toroidal precession of fast ions and consequently alters their condition of resonance with the error field, which may account for the EF effect on the loss of fast ions in ITER with TBMs.

Power loads to ITER first wall structures due to fusion alphas in a non-axisymmetric magnetic field including the presence of MHD modes

We use the orbit-following Monte Carlo code ASCOT to calculate the wall power loads in ITER caused by fusion alphas. The simulations are carried out for a realistic 3D magnetic field that includes the effect of both ferritic inserts and the test blanket modules, both causing aberrations in the magnetic field structure, particularly at the edge. In addition to an magnetohydrodynamic (MHD)-quiescent plasma we now also address the power loads in the presence of relevant MHD events: both neoclassical tearing modes (NTMs) and toroidal Alfvén eigenmodes (TAEs) are included in the simulation model. In the case of NTMs, the total power load to the wall is found to depend on the perturbation amplitude. Even with the strongest perturbation, however, the power load density stays within the design limit of the ITER wall materials. In the case of TAEs, while the wall power load density stays at the MHD-quiescent level, significant redistribution of alphas inside the plasma was observed. This was also found to affect the alpha heating profile.

Development of the transport-code framework for self-consistent predictions of rotation and the radial electric field

A toroidal momentum solver, which calculates the evolution of the toroidal angular momentum density summed over thermal species, is modelled and integrated into the 1.5D integrated transport code TOPICS. A non-iterative scheme to uniquely determine the radial electric field Er is developed. It is also used to compute the parallel and toroidal flows for each species based on the neoclassical transport theory. The combination of TOPICS and the orbit-following Monte Carlo code OFMC enables us to self-consistently predict the evolution of not only the density, temperature and safety factor but also the toroidal momentum and Er. The framework developed has been tested against JT-60U experiments and showed the predictive capability of toroidal rotation. Several time-dependent simulations in which toroidal rotation and Er play an important role are carried out, showing that the H-mode confinement considerably depends on the direction of toroidal rotation via the change in Er, as observed in JT-60U. Rapid toroidal rotation can be hardly expected in ITER if rotation is solely driven by neutral beam (NB) injection, whereas the residual stress may potentially generate the torque comparable to or greater than that by NBs.

Role of convective amplification of n = 1 energetic particle modes for N-NB ion dynamics in JT-60U

The hybrid code MEGA is used to simulate an abrupt large-amplitude event (ALE) in JT-60U shot E039672 that was strongly driven by a pair of negative-ion-based neutral beams (N-NBs). This configuration is known to be unstable to energetic particle modes (EPMs) with toroidal mode number n = 1. The purpose of this study is to look for a threshold with respect to the on-axis fast ion beta value, βh0, beyond which the EPM undergoes convective amplification (CA) and causes significant fast ion transport. This is motivated by the hypothesis that such a threshold may work as a trigger mechanism for relaxation events, such as ALE. In order to facilitate quantitative comparisons with the experiment, a realistic geometry and bulk pressure is used. Furthermore, MEGA is initialized with a fast ion distribution computed for JT-60U by an orbit-following Monte-Carlo code, and a passive vacuum region allows particles to travel without encountering artificial loss boundaries. Consistently with the experiment, the simulation predicts a burst time of about 0.3 ms and peak magnetic fluctuation levels around δBϑ/B < 10−3 at the plasma boundary. As βh0 is increased, a gradual increase in the CA of the EPM and in the convective transport of both resonant and nonresonant particles is found. The absence of a sharp transition between low- and high-amplitude fluctuations leads to the conclusion that the onset of CA does not suffice as a trigger mechanism for ALE.

Fast ion power loads on ITER first wall structures in the presence of NTMs and microturbulence

The level and distribution of the wall power flux of energetic ions in ITER have to be known accurately in order to ensure the integrity of the first wall. Until now, most quantitative estimates have been based on the assumption that fast ion transport is dictated by neoclassical effects only. However, in ITER, the fast ion distribution is likely to be affected by various MHD effects and probably also by microturbulence. We have now upgraded our orbit-following Monte Carlo code ASCOT so that it has simple, theory-based models for neoclassical tearing mode (NTM)-type islands as well as for turbulent diffusion. ASCOT also allows for full-orbit following, which is important close to the material surfaces and, possibly, also when strong toroidal inhomogeneities are present in the magnetic field. Here we introduce the new models, preliminary results obtained with them, and how these models could be made more realistic in the future. The simulations are carried out for thermonuclear alpha particles in ITER scenario 2 plasma, because we consider this combination to be most critical for the successful operation of ITER. Neither the turbulent transport nor NTM-type islands are found to introduce alarming changes in the wall loads. However, at this stage it was not possible to combine the island structures with the non-axisymmetric magnetic field of ITER, and it remains to be seen what the combined effect of drift islands together with the toroidal ripple and local field aberrations, such as those due to test blanket modules and resonant magnetic perturbations will be.

Alpha particle-driven toroidal rotation in burning plasmas

The mechanism of a torque intrinsically produced by alpha particles and the subsequent possibility to create significant toroidal rotation and shear are numerically investigated. In steady-state DEMO plasmas, regardless of the magnetic configuration, the orbit-following Monte Carlo code OFMC predicts that co-directed collisional torque and a counter-directed torque always emerge due to the gradient of the source profile of alpha particles and both of them virtually cancel each other out, as analytically predicted earlier. The magnitude of each torque is enhanced in the reversed shear configuration compared with the normal shear configuration, provided that the source gradient is finite and similar in both cases. The resultant rotation velocity estimated by the TASK/TX transport code is far below the threshold to stabilize resistive wall modes (RWMs) through intrinsic alpha-driven torque alone. It is estimated that a neutral beam injection at a moderate power level may be capable of producing toroidal rotation sufficient to stabilize RWMs.

Validation of on- and off-axis neutral beam current drive against experiment in DIII-D

Neutral beam current drive (NBCD) experiments in DIII-D using vertically shifted plasmas to move the current drive away from the axis have clearly demonstrated robust off-axis NBCD. Time-dependent measurements of magnetic field pitch angles by the motional Stark effect diagnostic are used to obtain the evolution of the poloidal magnetic flux, which indicates a broad off-axis NBCD profile with a peak at about half the plasma minor radius. In most cases, the measured off-axis NBCD profile is consistent with calculations using an orbit-following Monte Carlo code for the beam ion slowing down including finite-orbit effects provided there is no large-scale magnetohydrodynamic activity such as Alfvén eigenmodes modes or sawteeth. An alternative analysis method shows good agreement between the measured pitch angles and those from simulations using transport-equilibrium codes. Two-dimensional image of Doppler-shifted fast ion Dα light emitted by neutralized energetic ions shows clear evidence for a hollow profile of beam ion density, consistent with classical beam ion slowing down. The magnitude of off-axis NBCD is sensitive to the alignment of the beam injection relative to the helical pitch of the magnetic field lines. If the signs of toroidal magnetic field and plasma current yield the proper helicity, both measurement and calculation indicate that the efficiency is as good as on-axis NBCD because the increased fraction of trapped electrons reduces the electron shielding of the injected ion current, in contrast with electron current drive schemes where the trapping of electrons degrades the efficiency. The measured off-axis NBCD increases approximately linearly with the injection power, although a modest amount of fast ion diffusion is needed to explain an observed difference in the NBCD profile between the measurement and the calculation at high injection power.

Self-consistent simulation of torque generation by radial current due to fast particles

The generation of toroidal rotation due to the radial current torque induced by the charge separation is studied by using the one-dimensional multi-fluid transport code TASK/TX. Owing to the effect of the drift motion, the charge separation occurs as long as fast neutrals, typically from near-perpendicular NBI, are ionized. Coupling the TASK/TX code with the orbit-following Monte Carlo code (OFMC), we have shown that the toroidal rotation is driven due to the generation of the radial current jbulk flowing in the bulk plasma with the near-perpendicular NBI. The simulations have clarified that the NB on the equatorial plane drives the toroidal rotation most efficiently from the aspects of the collisional and jbulk × B torques. The jbulk × B torque becomes a major driver of the rotation in a high density plasma, replacing the collisional torque. In a steady state, the toroidal rotation driven by the jbulk × B torque is determined by the balance among the torque, the viscosity, the convection, the friction with neutrals and the loss of momentum due to charge exchange.

Numerical Study of the Ripple Resonance Diffusion of Alpha Particles in Tokamaks

The energy dependence of the diffusion coefficients of α particles in rippled fields of tokamaks is numerically investigated with an orbit-following Monte Carlo code. The diffusion coefficients are enhanced around the ripple resonance energy while they are not so much enhanced in the neighborhood of it. Consequently, they have a local minimum near the resonance energy, and hence they have an M-shaped energy dependence. Ripple resonance is caused by a radial change of the toroidal precession of banana particles, and creates islands in (Nφ, ψ) phase space. Since particles outside the separatrix are the main contributors to diffusion enhancement, the M-shaped energy dependence is explained by the co-existence of open and closed orbits in the phase space. Ripple resonance diffusion is dominant for fusion-produced α particles since the resonance energy width occupies a large portion of the energy range in their slowing-down processes.

Ripple Loss of Alpha Particles in a Low-Aspect Ratio Tokamak Reactor

Studies on the loss of fusion produced alpha particles enhanced by toroidal field (TF) ripple in a low-aspect-ratio tokamak reactor (VECTOR) have been made by using an orbit-following Monte-Carlo code. In actual TF coil systems, the ripple loss of alpha particles is strongly reduced as the aspect ratio becomes low (the power loss is proportional to A8.8 for A>˜2.5) and the reduction of the number of TF coils results in a large amount of ripple losses even in a low-aspect-ratio tokamak. Judging from the allowable peak heat load on the first wall (≈1MW/m2) due to loss particles, the number of TF coils of VECTOR can be reduced fro 12 to 10 without changing the coil size, and in addition, the number can be reduced to 8 with ferrite plates. To reduce the number of TF coils from 12 to 6, about 40% of coil size enlargement is necessary. By using ferrite plates, the coil size enlargement for N=6 can be reduced to about 15%.

Effects of ferromagnetic components on energetic ion confinement in ITER

By using a fully three dimensional magnetic field orbit-following Monte-Carlo code, the energetic ion confinement was investigated for the current conceptual design of the ferromagnetic components in ITER which will be employed for reducing the toroidal magnetic field (TF) ripple. The ferromagnetic insert is effective in the reference standard scenario with Q = 10 (Scenario No. 2) and steady state scenario with Q = 5 (Scenario No. 4) to improve the energetic ion confinement. Over-compensation appears at half of the full toroidal magnetic field and its effect becomes stronger when the quantity of the ferromagnetic insert is increased in order to more reduce the TF ripple at the full toroidal magnetic field. Though the current design is acceptable, whether to increase the ferromagnetic insert to achieve lower TF ripple amplitude at the full field operation depends on how prospected are possibilities of lower field operations. Planned test blanket modules do not induce large loss (<1%) at the full field in Scenario No. 4. At the half field, however, the loss reaches ∼10% for the alpha particles due to localized large TF ripple.

Simulation studies on alpha-particle-driven current in tokamak reactors

An asymmetry particle trapping caused by the finite banana width of alpha particles and a current produced by the resulting imbalance between transit particles with positive and negative velocities parallel to the magnetic field line (simply referred to as transit current) are numerically demonstrated by using an orbit-following Monte-Carlo code. The transit current is considerably enhanced by a collaborative effect of the finite-banana-width and a non-uniformity of the alpha particle source. The pitch-angle scattering is also very important for it. Banana-trapped particles drive a substantially negative current in the central region. Consequently, the positive transit current is degraded by the negative banana current and the net alpha current is almost flat near the plasma centre. The net alpha-driven total currents in an ITER-like normal aspect-ratio system (aspect ratio = 3.17) and in a low aspect-ratio system VECTOR (aspect ratio = 1.98) estimated with a conventional electron screening effect are about 0.4 MA and 1 MA, respectively. A low-aspect-ratio tokamak has an advantage over a normal or a large-aspect-ratio system in driving current by fusion-produced alpha particles.

Effect of radial electric field and ripple on edge neutral beam ion distribution in ASDEX Upgrade

The neutral beam injected fast ion distribution at the ASDEX Upgrade edge region is studied focusing on the difference between co- and counter-injected neutral beams. The slowing-down distribution of beam ions is simulated using the orbit-following Monte Carlo code ASCOT. The edge fast ion density and its gradient are higher for counter-injection than for co-injection. Also the distribution in the velocity space is different: for co-injection, there exists a population of untrapped particles which for counter-injection is found only when the effect of a non-constant, experimentally obtained quiescent H-mode radial electric field is included in the simulation. Toroidal ripple removes ions having small particle pitch, thereby reducing the density and density gradient, whereas the radial electric field has the opposite effect. Including simultaneously the effects of both ripple and the radial electric field restores the distribution close to the ideal case where both of them are neglected. The radial electric field is found to squeeze the orbit of a counter-injected neutral beam ion but to widen the orbit of a co-injected ion, and to cause transitions in the orbit topologies which are reflected in the fast ion distribution.

Surface loads and edge fast ion distribution for co- and counter-injection in ASDEX Upgrade

The fast particle flux onto the material surfaces and the fast ion edge distribution are compared between ASDEX Upgrade H-mode and quiescent H-mode (QH-mode) in the presence of toroidal ripple and radial electric field Er by using the orbit-following Monte Carlo code ASCOT. So far, the QH-mode has been obtained only with counter-injection of the neutral beams. The wall load caused by co-injected beams in H-mode is small and without ripple it is negligible. With counter-injection (QH-mode case), the wall load is substantial even without the ripple. The ripple always increases the wall load, but the divertor load is either decreased or is unchanged. The effect of Er alone is small, but it boosts the ripple-trapping of beam particles near the location of its maximum absolute value on the horizontal midplane. The fast ion density and its gradient in the pedestal region are higher for counter-injected than for co-injected particles. The ripple decreases the density gradient in both the cases. To make a connection with the experiment, the flux of high-energy tritons from beam–plasma interactions onto the surfaces is evaluated. The simulated flux of tritons impinging on the material surfaces is in qualitative agreement with the measured tritium distribution on the wall and divertor.