Fraction Of Trapped Particles Research Articles

The optimisation of the step electron cyclotron current drive concept

Abstract A fusion reactor based on the spherical tokamak is very likely to be completely non-inductive for the majority of the plasma ramp-up and steady-state phases, due to the limitations imposed on the central coil assemblies by the compact design. Efficiency gains from solenoid-driven current cannot be relied upon. It is also critical that an electricity-producing plant maximises the wall-plug efficiency of its heating and current drive (HCD) system, this being one of the largest consumers of recirculating power. It is therefore essential that the HCD system is well-optimised for current drive efficiency in order to meet the goal of net electricity production. The UK’s Spherical Tokamak for Energy Production (STEP) reactor design program has recently taken the decision to use exclusively microwave-based heating and current drive actuators for its reactor concepts. We present the optimisation of an electron cyclotron current drive scheme for a spherical tokamak reactor, based around the STEP concept, arriving at a solution which overcomes the limitations imposed by the spherical tokamak geometry in terms of microwave access and high trapped particle fraction. The solution uses high-field side absorption and a mix of fundamental and 2nd harmonic O mode, with overall power requirements reducing with increasing number of frequencies used. An additional fundamental frequency is also added to further boost the efficiency during non-inductive plasma ramp.

Plasma edge and scrape-off layer turbulence in gyrokinetic simulations of negative triangularity plasmas

Abstract Gyrokinetic simulations in the long-wavelength or drift-kinetic limit are carried out of DIII-D inner-wall-limited (IWL) plasmas to investigate the effect of triangularity on edge and scrape-off layer (SOL) turbulence. The effect of neutral interactions and triangularity on plasma blobs is explored due to the impact blobs can have in setting the SOL width or introducing impurities through interactions with plasma-facing components. Seeded blob simulations with neutrals in shaped SOL scenarios demonstrate that increasing elongation, triangularity, or Shafranov shift decreases radial blob velocities but neutral interactions have a minor effect. Fully turbulent simulations of DIII-D IWL plasmas include both open- and closed-field-line regions. The negative triangularity simulation has lower average core Te, lower normalized Te fluctuations, and lower fluxes, but a greater number of coherent structures (blobs) identified with increased size and velocity, on average. Density and electron temperature profiles are within a factor of 2 of experimental values. The increased trapped electron particle fraction in negative triangularity simulations is consistent with previous studies.

Trapping of deformable active particles by a periodic background potential.

The dynamic behaviors, specifically trapping and sorting, of active particles interacting with periodic substrates have garnered significant attention. This study investigates numerically the trapping of soft, deformable particles on a periodic potential substrate, which can be experimentally verified through optical tweezers. The research demonstrates that multiple factors, including the relative size of traps, self-propelled velocity, shape parameters, ratio of particles to traps, and translational diffusion, can influence the trapping effect. Within certain parameter boundaries, it is shown that all particles can be consistently trapped. The research reveals that stable trapping typically occurs at median values of the relative trap size. An increase in the self-propelled velocity, the shape parameter, and the translational diffusion coefficient tends to facilitate the escapement of the particles from the traps. It is noteworthy that particles with larger shape parameters can escape even when the restoring force exceeds the self-propelled force. In addition, as the ratio of particles to traps grows, the fraction of trapped particles steadily reduces. Notably, rigid particles are consistently divided and trapped by traps closely approximating an integer multiple of the particles' area, up until the ratio reaches the aforesaid integer value. These findings can potentially enhance the understanding of the interactive effects between active deformable particles and periodic substrates. Moreover, this work suggests a different experimental approach to sort active particles based on rigidity disparities.

Experimental validation of momentum transport theory in the core of H-mode plasmas in the ASDEX Upgrade tokamak

This study employs the established momentum transport analysis at ASDEX Upgrade [Zimmermann et al., Nucl. Fusion 63, 124003 (2023)] to investigate the parametric variations of the momentum transport coefficients in the core of H-mode plasmas. These experimental results are compared to a comprehensive database of gyrokinetic calculations. Generally, good agreement between predicted and measured diffusive and convective transport coefficients is found. The predicted and measured Prandtl numbers correlate most dominantly with the magnetically trapped particle fraction. The experimentally inferred pinch numbers strongly depend on the logarithmic density gradient and magnetic shear, consistent with the theoretical predictions of the Coriolis pinch. The intrinsic torque from residual stress in the inner core is small, scales with the local logarithmic density gradient, and the data indicate a possible sign reversal. In the outer periphery of the core, the intrinsic torque is always co-current-directed and scales with the pressure gradient. This is consistent with prior experimental findings and global, non-linear gyrokinetic predictions. It suggests that profile shearing effects generate the intrinsic torque in the inner core. Toward the outer core, most likely, effects from E×B-shearing become more influential. These results offer the first comprehensive picture of this transport channel in the core plasma and contribute to validating the corresponding theoretical understanding. The derived scaling laws are used to construct a reduced momentum transport model, which has been validated against an additional dataset. This demonstrates that the model captures the essential contributions to momentum transport in the core of H-mode plasmas.

The effect of triangularity on predicted pedestals for the CFETR

In this work, the dominant unstable magnetohydrodynamic mode and its stable region in the pedestal of the China Fusion Engineering Test Reactor are studied by numerical modeling with the peeling-ballooning theory over a wide range of triangularities (δ) and collisionalities (υ*). A new accessible stable region is found at δ<−0.1 for large βN,ped and υ*. This new stable region expands toward lower βN,ped and υ* with decreasing δ and is totally covered by the peeling unstable region with δ=−0.5 because of the increasing trapped particle fraction (ft,eff). The sensitivity of this new stable region to the kinetic ballooning mode constraint and elongation is studied. For negative and low δ<0.1, the boundary of the first stable region is determined from the ballooning mode. For δ>0.1, the peeling mode becomes dominant as the boundary approaches low s with low υ*, while the ballooning mode is still dominant at the boundary with high υ*. When δ increases beyond 0.46, the first stable region is expanded, and access to the second stable region of the ballooning mode opens up. The entire newly connected region of the first and second stable regions keeps expanding with further increases in δ until δ=0.6. Beyond this value, the ballooning mode becomes more unstable with increasing δ, while the peeling mode is approximately unchanged with increasing δ in this range. The change in the dominant mode and the stable region with increasing δ can be explained by the trade-off between the stabilization effect from the deeper poloidal magnetic well and destabilization due to the enlarged drive term.

Analytical model for the combined effects of rotation and collisionality on neoclassical impurity transport

The influence of rotation, collisionality and trapped particle fraction on the magnitude and direction of neoclassical impurity transport in tokamaks is analyzed using an extensive database of drift-kinetic simulations with the NEO code. It is shown that an operational window opens at sufficiently high Mach number and low collisionality, where the magnitude of the temperature screening of impurities increases with higher rotation. If the collisionality increases, this effect is quickly lost and the temperature gradient then drives an inward impurity flux when rotation is present. The boundary between these two regimes is calculated as a function of the trapped particle fraction, and it is shown that plasma parameters achieved in recent JET experiments allow them to access the new beneficial regime, in accordance with observations of reduced tungsten accumulation. Applications to ASDEX Upgrade experiments where these effects become relevant are also presented, and the implications for ITER are discussed. A method for extracting the physically distinct Pfirsch–Schlüter (PS) and banana-plateau (BP) neoclassical flux components from the NEO output is introduced and employed to construct a model that describes them analytically at arbitrary rotation and collisionality. The beneficial behavior of the screening with rotation is found to be a BP effect, in contrast to the known detrimental role of rotation in the PS component. The new analytical model is able to reproduce the results of NEO when modeling radial profiles of transport coefficients from experimental kinetic profiles, with the added feature of isolating the BP and PS components for additional physical analysis, while remaining well suited for fast applications.

Analytical model for collisional impurity transport in tokamaks at arbitrary collisionality

The physics governing the collisional transport of impurities in tokamak plasmas can change significantly depending on four main parameters, namely the collisionality, the impurity charge and mass, and the trapped particle fraction, which can vary widely from the core to the edge of a fusion device. We present an analytical model for collisional impurity transport with a consistent dependence on broad scans in these four parameters, showing good agreement with the drift-kinetic code NEO. Radial profiles of collisional fluxes are calculated for different impurity species using ASDEX Upgrade experimental profiles as well as ITER simulated profiles, and they are also compared to NEO. This model is well suited for fast integrated modelling applications due to its low computational cost.

The role of noise in PIC and Vlasov simulations of the Buneman instability

The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the Buneman instability in unmagnetized plasmas are studied. It is found that, in the regime of low drift velocity, the linear stage of the instability in PIC simulations differs significantly from the theoretical predictions, whereas in the Vlasov simulations it does not. A series of highly resolved PIC simulations with increasingly large numbers of macroparticles per cell is performed using a number of different PIC codes. All the simulations predict highly similar growth rates that are several times larger than those calculated from the linear theory. As a result, we find that the true convergence of the PIC simulations in the linear regime is elusive to achieve in practice and can easily be misidentified. The discrepancy between the theoretical and the observed growth rates is attributed to the initial noise inherently present in PIC simulations, but not in Vlasov simulations, that causes particle trapping even though the fraction of trapped particles is low. We show analytically that even weak distortions of the electron velocity distribution function (such as flattening due to particle trapping) result in significant modifications of the growth rates. It is also found that the common quiet-start method for PIC simulations leads to more accurate growth rates but only if the maximum growth rate mode is perturbed initially. We demonstrate that the quiet-start method does not completely remedy the noise problem because the simulations generally exhibit inconsistencies with the linear theory.

Ion cyclotron resonance heating with shifted separatrix

Ion cyclotron resonance heating, which we refer to as ICRH-SS, with the quasilinear (QL) separatrix (i.e., the separatrix in the space of QL routes of ion acceleration) located in the region of passing particles is studied. The aim of ICRH-SS is to minimize the fraction of trapped particles (particles with small longitudinal velocities) in the population of fast ions. The basic idea of ICRH-SS—shifting the separatrix to the region of passing particles—was advanced in the paper (Kolesnichenko et al 2017 Nuclear Fusion 57 066004). In this work, new features of ICRH-SS are revealed. The 3D QL routes of the particle acceleration and effects of Coulomb collisions are studied. A QL equation for distribution function of neutral beam injection (NBI) ions, which is convenient for analysis, is derived. Conditions for QL flux prevailing over collisional flux caused by pitch scattering are obtained. Numerical simulations using the SCENIC package are carried out for a JET plasma with NBI ions that are accelerated by RF field in the core region. A JET pulse designed as a demonstration of the so called ‘three ions’ scheme, which also complies with the criteria of ICRH-SS scheme, was selected. The numerical results show that in the considered example most accelerated ions have larger longitudinal velocities and fast particle orbits are passing during ICRH-SS, whereas, ‘conventional’ ICRH (defined as ICRH with the separatrix in the region of trapped particles) produces accelerated ions with banana orbits. Numerical results also show an increase in fast ion generation and core plasma heating performance for ICRH-SS as compared to the conventional ICRH.

Mechanical trapping of particles in granular media.

Mechanical trapping of fine particles in the pores of granular materials is an essential mechanism in a wide variety of natural and industrial filtration processes. The progress of invading particles is primarily limited by the network of pore throats and connected pathways encountered by the particles during their motion through the porous medium. Trapping of invading particles is limited to a depth defined by the size, shape, and distribution of the invading particles with respect to the size, shape, and distribution of the host porous matrix. Therefore, the trapping process, in principle, can be used to obtain information about geometrical properties, such as pore throat and particle size, of the underlying host matrix. A numerical framework is developed to simulate the mechanical trapping of fine particles in porous granular media with prescribed host particle size, shape, and distribution. The trapping of invading particles is systematically modeled in host packings with different host particle distributions: monodisperse, bidisperse, and polydisperse distributions of host particle sizes. Our simulation results show quantitatively and qualitatively to what extent trapping behavior is different in the generated monodisperse, bidisperse, and polydisperse packings of spherical particles. Depending on host particle size and distribution, the information about extreme estimates of minimal pore throat sizes of the connected pathways in the underlying host matrix can be inferred from trapping features, such as the fraction of trapped particles as a function of invading particle size. The presence of connected pathways with minimum and maximum of minimal pore throat diameters can be directly obtained from trapping features. This limited information about the extreme estimates of pore throat sizes of the connected pathways in the host granular media inferred from our numerical simulations is consistent with simple geometrical estimates of extreme value of pore and throat sizes of the densest structural arrangements of spherical particles and geometrical Delaunay tessellation analysis of the pore space of host granular media. Our results suggest simple relations between the host particle size and trapping features. These relationships can be potentially used to describe both the dynamics of the mechanical trapping process and the geometrical properties of the host granular media.

Neoclassical, semi-collisional tearing mode theory in an axisymmetric torus

A set of layer equations for determining the stability of semi-collisional tearing modes in an axisymmetric torus, incorporating neoclassical physics, in the small ion Larmor radius limit, is provided. These can be used as an inner layer module for inclusion in numerical codes that asymptotically match the layer to toroidal calculations of the tearing mode stability index, $\unicode[STIX]{x1D6E5}^{\prime }$. They are more complete than in earlier work and comprise equations for the perturbed electron density and temperature, the ion temperature, Ampère’s law and the vorticity equation, amounting to a twelvth-order set of radial differential equations. While the toroidal geometry is kept quite general when treating the classical and Pfirsch–Schlüter transport, parallel bootstrap current and semi-collisional physics, it is assumed that the fraction of trapped particles is small for the banana regime contribution. This is to justify the use of a model collision term when acting on the localised (in velocity space) solutions that remain after the Spitzer solutions have been exploited to account for the bulk of the passing distributions. In this respect, unlike standard neoclassical transport theory, the calculation involves the second Spitzer solution connected with a parallel temperature gradient, because this stability problem involves parallel temperature gradients that cannot occur in equilibrium toroidal transport theory. Furthermore, a calculation of the linearised neoclassical radial transport of toroidal momentum for general geometry is required to complete the vorticity equation. The solutions of the resulting set of equations do not match properly to the ideal magnetohydrodynamic (MHD) equations at large distances from the layer, and a further, intermediate layer involving ion corrections to the electrical conductivity and ion parallel thermal transport is invoked to achieve this matching and allow one to correctly calculate the layer $\unicode[STIX]{x1D6E5}^{\prime }$.

Density gradient driven microinstabilities and turbulence in ASDEX Upgrade pellet fuelled plasmas

ASDEX Upgrade plasmas fuelled by pellets in the H-mode confinement regime are analyzed. The gyrokinetic code GKW is applied to calculate the microinstabilities which are predicted to be unstable in these plasmas. Two types of density gradient driven modes are found, outside and inside the pellet deposition location. The first mode is driven by a negative radial density gradient, and corresponds to the usual density gradient driven trapped electron mode instability, producing a large diffusive particle flux directed outwards, and becomes more unstable with increasing trapped particle fraction and with decreasing collisionality. The second is driven by a positive radial density gradient (that is, a locally hollow density profile) and is identified for the first time in this work. The instability is located in the proximity of the high field side of the poloidal cross section, and drives a diffusive particle flux directed inward. It is mainly produced by the non-adiabatic response of passing particles with low parallel velocities at high collisionality and it becomes more unstable with increasing passing particle fraction and increasing collision frequency. Nonlinear gyrokinetic turbulence simulations show that these instabilities can lead to saturated turbulence and produce particle diffusion at experimentally relevant levels. In contrast to the usual behavior of the turbulent fields in tokamak plasmas, which have largest fluctuations on the low field side, locally hollow density profiles are prediced to lead to turbulent electrostatic potential and density fluctuations which are maximum on the high field side of the torus.

The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code**supported by National Special Research Program of China for ITER (Nos. 2013GB111000 and 2014GB107004), China Scholarship Council (No. 2011601098), U.S. DOE Grants DE-SC0010416 and DE-FG02-07ER54916

The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code (GTC). The ion and electron density profiles become partially flattened inside the islands. The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side, which do not move along the perturbed magnetic field lines. When the fraction of trapped particles decreases, the density profile at the low field becomes more flattened.

Electrodeposition of Ni–Fe and Ni–Fe-(nano Al2O3) multilayer coatings

In this study, production of multilayer (ML) coatings of Ni–Fe–Al2O3 has been carried out by using the pulse electrodeposition. The substrate was low carbon steel and the number of consecutively deposited layers was in eight layers. At the first step of investigation, the eight consecutive layers were deposited one after another on the surface with frequency of 100 and 6400 Hz at constant duty cycle of 88%. At the second step, the frequency was constant and the duty cycles of 11% and 88% were considered in order to electrodeposit eight layers from a bath. The results of EDS the exhibited that the variation of frequency had no significant effect either on the adsorption of nanoparticles or on the contents of Ni and Fe. In contrast, the changing of the duty cycle has been led to the coatings with different contents of Fe and nanoparticles. The deposited layers with duty cycles of 88% and 11% contained 15 wt.% and 37 wt.% Fe respectively. The fraction of trapped particles also is further in the deposited layers with duty cycle of 11%. The potentiodynamic and wear tests were performed on the alloy and nanocomposite coatings. Comparing the results of the ML coatings electrodeposited by two above methods showed that the corrosion and wear resistance are greater in the coatings which its consecutive layers have been deposited with the continuous changing of frequency between two values of 100 and 6400 Hz.

The residual zonal flow in tokamak plasmas rotating toroidally at sonic speed

The residual zonal flow, initially driven by ion-temperature-gradient turbulence, is investigated for a tokamak plasma rotating in the toroidal direction at sonic speed. The general expression of the residual zonal flow is the same as that of the static case but the numerical result is different due to the difference in the evaluation of the particle orbit average, the fraction of trapped particles and the non-uniformity of density on magnetic surfaces. For rotations at sonic speed, the value of residual zonal flows is approximately one third of that for static cases. The result is important in the fluid simulation of turbulence for rotating tokamak plasmas.

Microtearing modes at the top of the pedestal

Microtearing modes (MTMs) are unstable in the shallow gradient region just inside the top of the pedestal in the spherical tokamak experiment MAST, and may play an important role in the pedestal evolution. The linear properties of these instabilities are compared with MTMs deeper inside the core, and further detailed investigations in s–α geometry expose the basic drive mechanism, which is not well described by existing theories. In particular, the growth rate of the dominant edge MTM does not peak at a finite collision frequency, as frequently reported for MTMs further into the core. Our study suggests that the edge MTM is driven by a collisionless trapped particle mechanism that is sensitive to magnetic drifts. This drive is enhanced in the outer region of MAST at high magnetic shear and high trapped particle fraction. Observations of similar modes in conventional aspect ratio devices suggest this drive mechanism may be somewhat ubiquitous towards the edge of current day and future hot tokamaks.

Fast particle modifications to equilibria and resulting changes to Alfvén wave modes in tokamaks

We quantify the impact of poloidal and toroidal rotation, anisotropy and energetic particle pressure produced by neutral beam injected energetic particles on the magnetic configuration and wave modes in tokamaks. Specifically, we focus on the class of spherical tokamaks, for which the impact of neutral beam heating is larger due to the relatively low toroidal field and large trapped particle fraction. Recently, (Hole et al 2011 Plasma Phys. Control. Fusion 53 074021) we have used Bayesian inference techniques to compute rotating MAST equilibria, and thereby compute toroidal and poloidal Mach numbers and their uncertainties, as well as computed MAST anisotropic equilibria in the presence of neutral beam heating. Motivated by this work, we compute the impact of rotation and anisotropy on magnetohydrodynamic (MHD) waves of the plasma. Specifically, we determine how a change in q profile due to rotation and anisotropy could affect frequency scalings of the Alfvén continuum, Alfvén gap modes and compressional Alfvén eigenmodes. We also use Bayesian inference to infer energetic particle pressure, and compare the result with the inferred pressure from high-fidelity TRANSP simulations.

Inverse free electron laser accelerator for advanced light sources

We discuss the inverse free electron laser (IFEL) scheme as a compact high gradient accelerator solution for driving advanced light sources such as a soft x-ray free electron laser amplifier or an inverse Compton scattering based gamma-ray source. In particular, we present a series of new developments aimed at improving the design of future IFEL accelerators. These include a new procedure to optimize the choice of the undulator tapering, a new concept for prebunching which greatly improves the fraction of trapped particles and the final energy spread, and a self-consistent study of beam loading effects which leads to an energy-efficient high laser-to-beam power conversion.

The monoenergetic approximation in stellarator neoclassical calculations

In ‘monoenergetic’ stellarator neoclassical calculations, to expedite computation, ad hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction. The error in the trapped ion fraction can be of order unity for large but experimentally realizable values of the radial electric field, suggesting some results of these codes may be unreliable in this regime. This inaccuracy is independent of any errors introduced by approximation of the collision operator.

Orbit-averaged quasilinear diffusion operator in the ion-cyclotron range of frequencies

The absorption of radio-frequency waves in the ion-cyclotron range of frequencies (ICRF) in fusion plasmas is adequately described in the frame of the quasilinear theory. A peculiarity of ICRF heating is to increase the fraction of trapped particles, whose the guiding-center trajectories are typically banana orbits with finite width. One possible way to properly account for the effects due to the finite-width orbits is provided by the orbit-averaged quasilinear theory. Here, we propose a routine for the evaluation of the orbit-averaged quasilinear diffusion tensor, given the the wave fields from the full wave code TORIC. Particular care is taken in the evaluation of the contribution of each wave-particle resonance as well as for the transition between the two regimes of correlated and uncorrelated resonances along the orbit. We discuss the quasilinear diffusion coefficient thus obtained and validate the result by comparing the power deposition profile computed from the orbit-averaged quasilinear operator with the one determined by TORIC. For future applications, a novel algorithm for the calculation of the corresponding Monte Carlo operators is also presented.