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This presentation examines the energetic particle transport induced by saturated kink modes and sawtooth crashes in JET deuterium plasmas. It is known that kink mode-resonant transport and phase-space redistribution from sawtooth crashes can drive strong fast ion transport with dependencies on particle pitch and energy. Measurements with JET’s Faraday cup fast ion loss detector array have shown that the internal kink growth phase preceding sawtooth crashes produces substantial fast ion losses. This report will numerically investigate the dominant energetic particle transport mechanism with a detailed examination of the fast ion phase-space dependencies, resonances, orbit topology changes, induced losses, and redistribution associated with the long-lived, resonant, kink mode and non-resonant sawtooth crash. The ORBIT-kick model forms the basis of the transport studies with realistic fast ion distributions produced from TRANSP. A recently created reduced model for sawtooth induced transport is used while the saturated kink modes are modeled with ideal magnetohydrodynamic codes. The simulations were further validated against experiment with a newly developed synthetic Faraday cup fast ion loss detector in addition to scintillator probe and neutron measurements.

Alfvénic instabilities (AEs) are well known to cause enhanced transport of energetic particles (EPs) in fusion devices. Most studies until now have focused on characterizing and understanding AE stability in single-species plasmas heated by neutral beams (NB), where deuterium is typically used as both main plasma species and NB fuel. As the fusion community moves toward fusion reactors that target burning plasma conditions, such as ITER, the single-species picture breaks down. Burning plasmas, which will use a mix of deuterium and tritium (DT) as main fuel, also feature the presence of several supra-thermal fusion products such as alpha particles, protons, helium isotopes and high-energy tritium ions. This work presents the extension of the EP transport kick model implemented in the TRANSP time-dependent tokamak transport code to study the combined effect of multiple EP species on AE stability and, in turn, the response of different EP species to plasma instabilities in terms of their redistribution and losses. Further validation of the enhanced model is planned based on experimental results expected from the JET DT campaign scheduled for 2021, in preparation for ITER plasmas and beyond.

An integrated energetic particle transport model has been constructed in JET plasmas constrained by experimental fast ion loss measurements. The model incorporates a synthetic fast ion loss detector identical to JET’s thin-foil Faraday cup fast ion loss detector array. The loss model combines analyses from the TRANSP and ORBIT-kick codes with enhanced features for producing the synthetic diagnostic. Extensions to the ORBIT code framework allow a full-orbit representation within the vacuum region that can map particles directly to an installed detector geometry. Since synthetic fast ion loss detectors are plagued by weak loss statistics, a novel reverse integration biasing scheme has been implemented to boost computational efficiency. The model is validated against experimental loss measurements induced by long-lived kink modes and is found to be in good agreement. This confirms the development of a fully integrated transport/loss model which can be quantitatively verified against experiment allowing for future validation and predictive studies. The model is particularly useful for more complicated plasma scenarios that involve multiple fast ion species such as JET’s 2021 DT-campaign.

In RFX-mod high current experiments the plasma frequently reaches the Single Helical Axis (SHAx) state, in which the core electron temperature assumes a helical shape and significant gradients appear. The plasma magnetic topology is strongly helical in the core while it is almost axisymmetric at the edge, thanks to the active control of the edge radial field. The weak helical field produced by the plasma profoundly affects the shape of the equilibrium going from 2D to 3D, therefore three-dimensional tools are being developed for the description of these states. On one hand the SHEq code, based on a perturbative approach, is used to determine the magnetic field topology. On the other hand, the VMEC code has been modified for the helical RFP, in order to describe the SHAx states by using tools developed by the Stellarator community. The effect of three-dimensional fields on transport is also being actively investigated. The magnetic shear is found to be correlated with regions with reduced transport: an investigation on the effect of 3D fields on transport mechanisms underlying such barriers is being performed by adopting several approaches.

The method of Kruskal-Newton diagrams for the solution of differential equations with boundary layers is shown to provide rapid intuitive understanding of layer scaling and can result in the conceptual simplification of some problems. The method is illustrated using equations arising in the theory of pattern formation and in plasma physics.

Recently reported numerical results for axisymmetric devices with low aspect ratio A found radial transport enhanced over the expected neoclassical value by a factor of 2 to 3. In this paper, we provide an explanation for this enhancement. Transport theory in toroidal devices usually assumes large A, and that the ratio B{sub p}/B{sub t} of the poloidal to the toroidal magnetic field is small. These assumptions result in transport which, in the low collision limit, is dominated by banana orbits, giving the largest collisionless excursion of a particle from an initial flux surface. However in a small aspect ratio device one may have B{sub p}/B{sub t} {approx} 1, and the gyroradius may be larger than the banana excursion. Here, we develop an approximate analytic transport theory valid for devices with arbitrary A. For low A, we find that the enhanced transport, referred to as omniclassical, is a combination of neoclassical and properly generalized classical effects, which become dominant in the low-A, B{sub p}/B{sub t} {approx} 1 regime. Good agreement of the analytic theory with numerical simulations is obtained.

Calculations of collisional thermal and particle diffusivities in toroidal magnetic plasma confinement devices order the toroidal gyroradius to be small relative to the poloidal gyroradius. This ordering is central to what is usually referred to as neoclassical transport theory. This ordering is incorrect at low aspect ratio, where it can often be the case that the toroidal gyroradius is larger than the poloidal gyroradius. We calculate the correction to the particle and thermal diffusivities at low aspect ratio by comparing the diffusivities as determined by a full orbit code (which we refer to as omni-classical diffusion) with those from a gyroaveraged orbit code (neoclassical diffusion). In typical low aspect ratio devices the omni-classical diffusion can be up to 2.5 times the calculated neoclassical value. We discuss the implications of this work on the analysis of collisional transport in low aspect ratio magnetic confinement experiments.

We have started to examine the reactor potential of quasi-axisymmetric (QA) stellarators with an integrated approach that includes systems evaluation, engineering considerations, and plasma and coil optimizations. In this paper, we summarize the progress made so far in developing QA configurations with reduced alpha losses while retaining good MHD stability properties. The minimization of alpha losses is achieved by directly targeting the collisionless orbits to prolong the average resident times. Configurations with an overall energy loss rate of {approx}10% or less, including collisional contributions, have been found. To allow remotely maintaining coils and machine components in a reactor environment, there is a desire to simplify to the extent possible the coil design. To this end, finding a configuration that is optimized not only for the alpha confinement and MHD stability but also for the good coil and reactor performance, remains to be a challenging task.

Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The 3-D plasma shape can be designed to enhance the MHD stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low-aspect ratio, high beta-limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation of approximately 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for beta > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at beta = 4% (the rest is from the coils), thus the equilibrium is much less nonlinear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of ''reversed'' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks.more » Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.« less

Absorption of fast Alfven waves by the minority fundamental ion-cyclotron resonance, coupled with finite banana width physics, generates torque distributions and ultimately rotational shear layers in the bulk plasma, even when the toroidal wavenumber k(subscript ''phi'') = n/R of the fast wave vanishes (n=0) and cyclotron absorption introduces no angular momentum nor canonical angular momentum [F.W. Perkins, R.B. White, P.T. Bonoli, and V.S. Chan, Phys. Plasmas 8 (2001) 2181]. The present work extends these results to travelling waves with non-zero n where heating directly introduces angular momentum. Since tokamak fast-wave antennas have approximately one wavelength per toroidal field coil, the toroidal mode number n lies in the range n = 10-20, independent of machine size. A zero-dimensional analysis shows that the rotation rate arising from direct torque is comparable to that of the rotational shear layer and has the same scaling. Nondimensional rotation profiles for n = (-10, 10) show modest changes from the n = 0 case in the expected direction. For a balanced antenna spectrum, the nondimensional rotational profile (averaged over n = -10, 10) lies quite close to the n = 0 profile.

A general method for including various collisional effects, such as the drag and diffusion of test particles due to background plasmas, the effect of particle source and sink, and the like-particle Coulomb collisions, is presented. The marker density g is generally unknown along the particle trajectory, and its evaluation depends on the way particles are initially loaded and new particles are injected into the simulation. The method is demonstrated for the problem of the nonlinear evolution of the Toroidicity Induced Alfven eigenmode, driven by energetic {alpha} particles. The saturation amplitude is found to scale with the collision rate in a way as predicted by theory.

In recent Deuterium-Tritium experiments on the Tokamak Fusion Test Reactor (TFTR), both the Pellet Charge Exchange (PCX) and the alpha Charge Exchange Recombination Spectroscopy ({alpha}-CHERS) diagnostics indicate that sawtooth oscillations can cause significant broadening of the fusion alpha radial density profile. The authors investigate this sawtooth mixing phenomenon by applying a Hamiltonian guiding center approach. A model of time evolution of the Kadomtsev-type sawtooth is constructed. The presence of more than one mode in the nonlinear stage of the sawtooth crash is necessary to cause significant broadening of the alpha density profile. Use of numerical equilibria allows us to perform detailed comparisons with TFTR experimental data. The results are in reasonable agreement with {alpha}-CHERS and show a broadening of alpha particles similar to that seen in PCX measurements.

The threshold for stochastic transport of high energy trapped particles in a tokamak due to toroidal field ripple is calculated by explicit construction of primary resonances, and a numerical examination of the route to chaos. Critical field ripple amplitude is determined for loss. The expression is given in magnetic coordinates and makes no assumptions regarding shape or up-down symmetry. An algorithm is developed including the effects of prompt axisymmetric orbit loss, ripple trapping, convective banana flow, and stochastic ripple loss, which gives accurate ripple loss predictions for representative Tokamak Fusion Test Reactor and International Thermonuclear Experimental Reactor equilibria. The algorithm is extended to include the effects of collisions and drag, allowing rapid estimation of alpha particle loss in tokamaks.

This report discusses the following topics: toroidal Alfven eigenmode induced ripple trapping, and high-{beta} disruption in TFTR.

The interaction of high energy particles with an Alfven eigenmode is investigated self-consistently by using a realistic kinetic dispersion relation. All important poloidal mode numbers and their radial mode profiles as calculated with the NOVA-K code are included. A Hamiltonian guiding center code is used to simulate the alpha particle motion. The numerical simulations include particle orbit width, nonlinear particle dynamics and the effects of the modes on the particles. Modification of the particle distribution leading to mode saturation is observed. Particle loss is limited to devices in which the alpha particle gyro radius is a significant fraction of the minor radius.

The interaction of alpha particles with a toroidicity induced Alfven eigenmode is investigated self-consistently by using a kinetic dispersion relation. All important poloidal harmonics and their radial mode profiles are included. A Hamiltonian guiding center code is used to simulate the alpha particle motion. The simulations include particle orbit width, nonlinear particle dynamics and the effects of the modes on the particles. Modification of the particle distribution leading to mode saturation is observed. There is no significant alpha particle loss.

Transport in a magnetic field configuration near stochastic threshold is investigated. The waiting time distribution near magnetic islands, and the size distribution of these islands are identified as the two fundamental functions which determine both the short time subdiffusive behavior, and the regular diffusive regime. These time and length distributions are studied, the mean square displacement is expressed in terms of these functions, and the result is compared to direct numerical simulation.

This report discusses long-wavelength microinstabilities in toroidal plasmas and alpha particle destabilization of TAE modes in TFTR DT Experiments.

Heat transport in a stochastic magnetic field configuration is shown to be nonlocal. Collisional transport processes, in such a disordered media, cannot always be reduced to a standard diffusion process, and the concept of a diffusion coefficient is meaningless for a wide range of typical tokamak parameters. In the nonlocal regime the relaxation of a gradient is described by an integral equation, involving a nonlocal propagator. This propagator is calculated, and the relation to previous results is elucidated. 15 refs.

A graphics robot simulator designed for an IBM PC/XT/AT or PS/2 personal computer is presented. The simulator is a terminate-and-stay resident (TSR) program that runs in the background and intercepts commands that would normally go to the robot controller through the COM1 serial communication device. With the use of the simulator, students can develop and test robot control programs offline without a physical robot present, using the language of their choice. The status of the simulated robot is available through a 3-D graphics display and a one-line text window, each of which can be activated from the keyboard or from within a user program. Data files are used to specify the robot to be simulated and the environment or workcell within which it is to operate. Currently supported robots include the Rhino XR-3 educational robot and the Adept One and Inteledex 660 industrial robots. The workcell features an overhead camera and objects that can be sensed by the camera and manipulated by the robot. >

The solution of ordinary differential equations by the means of Phase Integral Methods is eminently suited for an interactive computational system with real time graphics: We describe a code devised for this purpose and illustrate its use.

Coherent magnetohydrodynamic modes have been observed during neutral beam injection in TFTR and JET. Periodic bursts of oscillations were detected with several plasma diagnostics, and Fokker-Planck calculations show that the populations of trapped particles in both tokamaks are sufficient to account for fishbone destabilization. Estimates of mode parameters are in reasonable agreement with the experiments, and they indicate that the fishbone mode may continue to affect the performance of intensely heated tokamaks. 13 refs., 1 fig., 1 tab.

The presence of energetic particles is shown to qualitatively modify the stability properties of ideal as well as resistive magnetohydrodynamic (MHD) modes in tokamaks. Specifically, we demonstrate that, consistent with highpower ICRF heating experiments in JET, high energy trapped particles can effectively stabilize the sawtooth mode, providing a possible route to stable high current tokamak operation. An alternative stabilization scheme employing barely circulating energetic particles is also proposed. Finally, we present analytical and numerical studies on the excitations of high-n MHD modes via transit resonances with circulating alpha particles. 14 refs., 3 figs.

Two-dimensional, low ..beta.. (..beta.. = plasma pressure/magnetic field pressure) plasma equilibria have been examined for stability to symmetry breaking, current driven ideal MHD perturbations. In particular, the helically symmetric equilibria which arise in two-dimensional nonlinear studies of tearing modes in cylindrical columns are shown to be unstable to perturbations which tend to reduce the numbers of islands, when the wavevector of the perturbation in the equilibrium symmetry direction is sufficiently small. However, in applying these results to a small inverse aspect ratio torus, we find that to satisfy periodicity requirements in the torus, the minimum wavevector of the perturbation along the symmetry direction of the island equilibrium is too large for instability.

It is shown that, in present-day large-size tokamaks, finite resistivity modifies qualitatively the stability properties of magnetohydrodynamic instabilities resonantly excited by the unfavorable processional drift of energetic-trapped particles, i.e., the so-called ''fishbone''-type instabilities. Specifically, it is found that (1) the n = 1 energetic-trapped particle-induced internal kink (''fishbone'') instability is strongly stabilized by resistive dissipation and (2) finite resistivity lowers considerably the threshold conditions for resonant excitations of high-n ballooning/interchange modes. The possibility of exciting fishbones by alpha particles in ignition experiments is also considered.