Session PO6: RF, Neutral Beams, Fast Particles and Diagnostics

RF Wave Propagation and Scattering in Tokamaks

The propagation, scattering and absorption of the lower hybrid and electron cyclotron RF waves used to control fusion plasmas is reviewed. Drift wave turbulence driven by the steep ion and electron temperature gradients in H-mode divertor tokamaks produces strong scattering of the RF waves used for heating and plasma currents drive Both the 3-5GHz lower-hybrid (LH) and the 170GHZ electron cyclotron (EC) waves experience scattering and diffraction as propagating through the statistically complex density of the plasma. Ray equations are used to calculate the spread of the rays and the associated change in the parallel phase, polarization and group velocity of the RF waves in the propagation through the fusion plasma. A Fokker Planck equation for the phase space of the RF plasmons is one method to describe the spread of the RF wave power in the complex geometry of a divertor tokamak using the ray tracing codes. The evolution of the electron distribution function from the resonant electron-wave interactions is summarized for several scenarios. The resulting X-ray spectrum is broaden giving better agreement with the measured X-ray spectrum than that calculated in the absence of the turbulent scattering of the RF waves. M. Goniche, et al. and Tore Supra Team, Phys. Plasmas 21, 2014.   

ECRH and ECCD Experiments at the Wendelstein7-X Stellarator

Plasmas in the first operation phase OP1.1 of W7-X were exclusively heated by ECRH. 6 gyrotrons with up to 4.3 MW power at 140 GHz and a quasi-optical transmission line generated plasma start-up, heating and wall conditioning with a very high reliability. The central ECRH power deposition enabled highly peaked electron temperature (Te) profiles with a peak Te above 8 keV, n$_{\mathrm{e}}$ of 4\textbullet 10$^{\mathrm{19}}$m$^{\mathrm{-3}}$ and flat ion temperatures profiles reaching 2 keV. By off-axis ECRH, the absence of core Te profile resilience in W7-X was demonstrated. With ECRH-power modulation heat waves for transport analysis have been generated on a regular basis. First ECCD experiments demonstrated a strong sensitivity of the confinement with sawtooth-like crashes of the central Te profile when central ECCD was applied. The high Te enabled successful demonstration of ECRH in O2-mode only. This scenario is foreseen for high-density operation above the X2-mode cut-off density in the next operation phase. The density control could be recovered by ECRH discharges in helium, which substituted glow discharge when the supra-conducting field coils were charged. The efficiency of ECRH absorption was monitored by diagnostics that measured the unabsorbed part of the ECRH. These also served as plasma interlock, preventing damages by unabsorbed ECRH power.   

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters.   

Toroidal Electromagnetic Particle-in-Cell Code with Gyro-kinetic Electron and Fully-kinetic ion

A kinetic simulation model has been developed using gyro-kinetic electron and fully-kinetic ion by removing fast gyro motion of electrons using the Lie-transform perturbation theory. A particle-in-cell kinetic code is developed based on this model in general magnetic flux coordinate systems, which is particularly suitable for simulations of toroidally confined plasma. Single particle motion and field solver are successfully verified respectively. Integrated electrostatic benchmark, for example the lower-hybrid wave (LHW) and ion Bernstein wave (IBW), shows a good agreement with theoretical results. Preliminary electromagnetic benchmark of fast wave at lower hybrid frequency range is also presented. This code can be a first-principal tool to investigate high frequency nonlinear phenomenon, such as parametric decay instability, during lower-hybrid current drive (LHCD) and ion cyclotron radio frequency heating (ICRF) with complex geometry effect included.   

The effect of density fluctuations on ECRH beam broadening and implications to NTM mitigation on ITER

We present state-of-the-art computations of propagation and absorption of electron cyclotron waves, retaining the effects of scattering due to density fluctuations. In ITER, injected microwaves are foreseen to suppress NTMs by driving current at the resonant surface(s). The good localization of the absorption profile can be spoiled by beam scattering and impair the NTM control capabilities. A novel tool based on the wave kinetic equation has been developed, which retains diffraction, an integral form of the scattering operator assuming the Born scattering approximation, full tokamak geometry and determination of the power absorption profile. This approach has been implemented in the code WKBeam, which has been benchmarked against the beam-tracing code TORBEAM and the full-wave code IPF-FDMC, in particular to verify usage of the Born approximation for ITER parameters. We show that in ITER the radiation transport is diffusive unlike in existing machines. Using WKBeam we demonstrate through parameter scans that the width of the deposition profile in ITER depends on the assumptions on the fluctuations and beam parameters: the effect can be of the order of 100%. A method to quantify mode-to-mode scattering induced by fluctuations has been developed and first results are presented.   

Gyrokinetic Particle Simulation of Fast Electron Driven Beta-induced Alfven Eigenmodes

The fast electron driven beta induced Alfven eigenmode (e-BAE) has been routinely observed in HL-2A tokamak. We study e-BAE for the first time using global gyrokinetic GTC simulation, where the fast electrons are described by the drift kinetic model. Frequency chirping is observed in nonlinear simulations in the absence of sources and sinks, which provide a new nonlinear paradigm beyond the standard ``bump-on-tail'' model. For weakly driven case, nonlinear frequency is observed to be in phase with particle flux, and nonlinear mode structure is almost the same as linear stage. In the strongly driven case, BAAE is also unstable and co-exists with BAE after the BAE saturation. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the fast electron phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phrase space islands in the canonical variables. Zonal fields are found to affect wave-particle resonance in the nonlinear e-BAE simulations.   

Self-consistent long-time simulation of chirping energetic particle modes and abrupt large events in beam-driven JT-60U tokamak plasmas

Recurring bursts of chirping Alfv\'{e}n modes as well as so-called Abrupt Large Events (ALE) that were observed in JT-60U tokamak plasmas driven by negative-ion-based neutral beams (N-NB) are reproduced in first-principle simulations performed with an extended version of the hybrid code MEGA. This code simulates the interactions between gyrokinetic fast ions and magnetohydrodynamic (MHD) modes in the presence of a realistic fast ion source and collisions, so that it self-consistently captures dynamics across a wide range of time scales (0.01--100 ms). Detailed comparisons with experimental measurements are performed. On the long time scale (10--100 ms) the simulation reproduces ALEs with the associated avalanche-like transport of fast ions. ALEs are shown to occur when multiple modes with toroidal mode numbers $n=1,2,3$ are excited to large amplitudes. On the meso time scale (1--10 ms), bursts of chirping modes are reproduced, which are shown to be $n=1$ energetic particle modes (EPM). On the short time scale (0.01--0.1 ms), pulsations and phase jumps are reproduced, which we interpret as the result of beating between multiple resonant wave packets.   

Comparison and prediction of chirping in NSTX and DIII-D

We present an explanation of why frequency chirping of Alfven waves is ubiquitous in NSTX and rarely observed in DIII-D. A time-delayed cubic nonlinear equation [1,2] is employed for the study of the onset of nonlinear phase-space structures. Its explosive solutions are chirping precursors. We employ NOVA and NOVA-K codes to provide consistent Alfvenic eigenmodes and weighted physical contributions from all regions of phase space. In addition, TRANSP is employed to determine the diffusivity needed to fulfill power balance. Though background micro-turbulence is usually unimportant in determining the energetic particle spatial profile, it may still be important with regard to whether chirping structures likely form. We show that the energetic particle micro-turbulent induced scattering often competes with collisional pitch-angle scattering. This competition explains the tendency for NSTX, where micro-turbulence is weak, to exhibit Alfv\'{e}nic chirping, whereas in DIII-D turbulent diffusion usually dominates and chirping is not observed except when micro-turbulence markedly reduces. [1]~F. J. Hickernell, \textit{J. Fluid Mech.} \textbf{142}, 431 (1984). [2]~H. L. Berk, B. N. Breizman and M. Pekker, \textit{Phys. Rev. Lett.} \textbf{76}, 1256 (1996).   

Influence of energetic ions on neoclassical tearing modes

In addition to their effect on the linear stability of tearing modes, energetic particles can influence the nonlinear evolution of a magnetic island through an uncompensated cross field current due to the charge separation effect when energetic particle orbit width is much larger than the island width. The corresponding return parallel current may compensate the loss of bootstrap current in the magnetic island. This nonlinear effect depends on the island propagation frequency, the density gradient of energetic ions and magnetic shear. If the island propagation frequency is positive, the effect of the uncompensated current plays a stable role on neoclassical tearing modes. When the magnetic shear is sufficiently small, this effect becomes significant and can partially cancels or even overcome the destabilizing effect of the perturbed bootstrap current. In ITER this provides a possibility of suppressing neoclassical tearing mode by energetic ions for the steady state operation scenario with weak magnetic shear.   

Numerical studies of fast ion slowing down rates in cool magnetized plasma using LSP

In MFE devices, rapid transport of fusion products from the core into the scrape-off layer (SOL) could perform the dual roles of energy and ash removal. The first-orbit trajectories of most fusion products from small field-reversed configuration (FRC) devices will traverse the SOL, allowing those particles to deposit their energy in the SOL and be exhausted along the open field lines. Thus, the fast ion slowing-down time should affect the energy balance of an FRC reactor and its neutron emissions. However, the dynamics of fast ion energy loss processes under the conditions expected in the FRC SOL (with $\rho_{e}<\lambda_{De}$) are analytically complex, and not yet fully understood. We use LSP, a 3D electromagnetic PIC code, to examine the effects of SOL density and background B-field on the slowing-down time of fast ions in a cool plasma. As we use explicit algorithms, these simulations must spatially resolve both $\rho_{e}$ and $\lambda_{De}$, as well as temporally resolve both $\Omega_{e}$ and $\omega_{pe}$, increasing computation time. Scaling studies of the fast ion charge (Z) and background plasma density are in good agreement with unmagnetized slowing down theory. Notably, Z-scaling represents a viable way to dramatically reduce the required CPU time for each simulation.   

Development of a disruption precursor based on rotating mhd instabilities and its application to JET H-mode plasma scenario.

Magneto-hydrodynamic activity often precedes disruption events in tokamaks, being either the root cause for disruption or one of the last symptoms of plasma deterioration due to a different root cause. Often a locked mode is detected before the plasma termination, with a warning time useful to trigger mitigation strategies but not enough for recovery, i.e. to act to avoid the disruption. In this work we present a study of disruption precursors derived from the Singular Value Decomposition analysis of the signals of a 3-d array of pick-up coils. Such signals are sensitive to rotating magneto-hydrodynamic activity before the locking phase. The analysis has been applied to the dataset of H-mode plasma scenario being developed at JET in preparation of the DT campaign. It is shown that using this technique a reasonable good rate of right/false alarms (81{\%}/16{\%}) can be obtained with an extended warning time (4-7s). Moreover, since such precursors are based on the phase analysis of normalized signals they are rather insensitive to calibration problems and show a potential for more general application..   

Design of geometric phase measurement in EAST Tokamak

The aim of this work is to propose the optimum scheme for geometric phase measurement in EAST Tokamak. On the one hand, the experimental observation of geometric phase in plasma systems is an essential verification of the geometric phase theory by a new experimental technique. On the other hand, the measurement of geometric phase confirms geometric effect as a new system error in the existing diagnostics. The geometric phase in Faraday rotation angle for linearly polarized electromagnetic waves propagating in non-uniform magnetized plasmas is a good candidate for the first identification of geometric phase in plasma. In this work, the theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Several schemes are proposed for the measurement of the geometric phase in POINT system by amplifying the geometric phase and enhancing the diagnostic resolution. To reach the conditions of the designed scheme for geometric phase measurement, the feasibility of replacing individual retro reflectors (RRs) with retro reflector array (RRA) in POINT system is verified experimentally. Corresponding results are beneficial for geometric phase measurement in EAST Tokamak.   

Low-noise superheterodyne receiver array for ECEI and MIR

Superheterodyne receiver array has been widely used in ECEI and MIR to extract the temperature and plasma density fluctuation, respectively. The system downconverts RF signals to a much lower IF for easy filtering and processing. The current system employs Schottky diode as the mixing element, which is mounted directly on the antenna. The LO and RF signals illuminate the antenna simultaneously to produce desired IF signals. One big drawback is that the system generates large amount of noise due to the lack of low-noise amplifier (LNA) before the mixer. It also requires complicated lens system in order to facilitate simultaneous RF and LO illumination. Additionally, it's difficult to shield the circuits from stray heating power and interfering signals. New receivers are developed for improving the signal quality as well as the ease of measurement. The new circuit consists of compact GaAs MMICs integrated on low-loss liquid crystal polymer substrate. Low noise and high gain GaAs LNAs, mixers and even complete receivers are available as off-the-shelf chips for V and W band applications. Employing MMICs in plasma diagnostics not only dramatically improves signal integrity, the on-board LO signal supply also eliminates the lenses for simultaneous RF and LO illumination. Additionally, the new receiver employs horn antennas, which produces directive radiation and strong interference attenuation.