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NASA NTRS1995

Prediction and measurement of blade-vortex interaction loading

An extensive quantity of airload measurements was obtained for a pressure-instrumented model of the BO-105 main rotor for a large number of higher-harmonic control (HHC) settings at Duits-Nederlandse Wind Tunnel (DNW). The wake geometry, vortex strength, and vortex core size were also measured through a laser light sheet technique and LDV. These results are used to verify the BVI airload prediction methodologies developed by AFDD, DLR, NASA Langley, and ONERA. The comparisons show that an accurate prediction of the blade motion and the wake geometry is the most important aspect of the BVI airload predictions.

Tung, Chee↗

NASA NTRS1984

Electron-cyclotron maser emission - Relative growth and damping rates for different modes and harmonics

The temporal growth rate and the number of e-folding growths are calculated and compared for the following wave modes due to a loss-cone-driven cyclotron maser: fundamental x, o, and z modes and second harmonic x and o modes. The dominant mode of the maser should be the fastest growing mode for a saturated maser and should be the mode with the greatest number of e-folding growths for an unsaturated maser; this mode is the fundamental x mode) for a plasma frequency to cyclotron frequency ratio of less than about 0.3; it is the z mode (or perhaps the fundamental o mode) for ratios between 0.3 and 1.0, and the z mode (or perhaps the second harmonic x mode) for ratios between 1.0 and 1.3. Two main points are made: the dominance of the z mode over the range of ratios considered and the very weak effect of cyclotron damping. Electron-cyclotron maser emission is seen as responsible for auroral kilometric radiation, decametric radio emission from Jupiter and Saturn, solar microwave spike bursts, and microwave emission from some flare stars.

Melrose, D. B.↗

NASA NTRS1992

Multi-wave interaction theory for wind-generated surface gravity waves

Consistently employing the assumption of localness of wave-wave interactions in the wavenumber space, the Kolmogorov treatment of the energy cascade is applied to the case of wind-generated surface gravity waves. The effective number v of resonantly interacting wave harmonics is not limited to four but is found as a solution of a coupled system of equations expressing: (i) the dependence of the spectrum shape on the degree of the wave nonlinearity, and (ii) the continuity of the wave action flux through the spectrum given a continuous positive input from wind. The latter is specified in a Miles-type fashion, and a simple scaling relationship based on the concept of the turnover time is derived in place of the kinetic equation. The mathematical problem is reduced to an ordinary differential equation of first order. The exponent in the 'power law' for the spectral density of the wave potential energy and the effective number of resonantly interacting wave harmonics are found as functions of the wave frequency and of external factors of wind-wave interaction. The solution is close to the Zakharov-Filonenko spectrum at low frequencies and low wind input while approaching the Phillips spectrum at high frequencies and sufficiently high wind.

Glazman, Roman E.↗

NASA NTRSDate not supplied

Pressure Fluctuations due to ‘Trapped Waves’ in Heated Jets

An experimental study was conducted to investigate the presence and characteristics of ‘trapped waves’ in the near field of a small axisymmetric jet at heated conditions. Trapped waves occur within the potential core of compressible jets and manifest as distinct peaks in the unsteady pressure spectra measured just outside the jet near the nozzle exit. The existence and properties of the trapped wave spectral peaks in round and rectangular jets of various sizes in subsonic and supersonic conditions were studied in our recent experiments, at cold conditions [7]. The current work extends the study to heated jets. Pressure fluctuation spectra near the nozzle exit are analyzed for a small (D = 6.35 mm) axisymmetric jet at stagnation temperature ratios up to 1.6. It is shown that trapped waves continue to persist in heated jets. At sufficiently high Mach numbers, one of the trapped wave harmonics emerges as screech tone, a behavior consistent with that observed in cold jets. For a given Mach number, the frequencies of both trapped waves and screech increase with jet temperature with no significant change occurring in their amplitudes. The Strouhal numbers based on jet diameter for the trapped waves and screech continue to follow similar scaling laws as observed previously with cold jets.

aeroacoustics↗

NASA NTRS1992

Radiated noise of ducted fans

The differences in the radiated acoustic fields of ducted and unducted propellers of the same thrust operating under similar conditions are investigated. An FEM model is created for the generation, propagation, and radiation of steady, rotor alone noise and exit guide vane interaction noise of a ducted fan. For a specified number of blades, angular mode harmonic, and rotor angular velocity, the acoustic field is described in a cylindrical coordinate system reduced to only the axial and radial directions. It is found that, contrary to the usual understanding of the Tyler and Sofrin (1962) result, supersonic tip speed rotor noise can be cut off if the tip Mach number is only slightly in excess of unity and if the number of blades is relatively small. If there are many blades, the fundamental angular mode number is large, and the Tyler and Sofrin result for thin annuli becomes more relevant. Shrouding of subsonic tip speed propellers is a very effective means of controlling rotor alone noise.

Eversman, Walter↗

DOE OSTI2020

DC Link Voltage Balancing of the Active Front-End for the Extreme Fast Charging Stations

One of the most important challenges of the extreme fast charging (XFC) stations is to balance the DC link voltages of the active front-end (AFE). The multilevel cascaded H-bridge (CHB) converter is a great topology for the AFE applications due to the high power density, low total harmonic distortion (THD), and a low number of active and passive components. In this paper, a technique is proposed for balancing DC-link capacitor voltages of a three-phase CHB converter, when a phase shiftPWM modulation technique is used on all cells of the converter. To reach this goal, the redundant states of the CHB converters are used for generating different AC voltage levels by sorting the voltages of the converters. The proposed voltage balancing technique uses the principles that are employed for the DC link voltage balancing of the low-frequency modulation techniques to balance the DC link voltages of the CHB converter. As shown in this paper, the DC link voltages of the CHB converter can accurately be balanced very fast without using PI controllers, which are used in the conventional DC link voltage balancing techniques. A controller also is proposed which will be used to control the dq currents of the CHB converter. To verify the advantages of the proposed technique, the simulation results of the proposed technique will be carried out in a three-phase 7-cell CHB AFE.

Grid-tied converters, cascaded H-bridge, DC link v↗

DOE OSTI2024

Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

Abstract It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage V L on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage V L at 2 MHz varies from 0 to 700 V while the HF voltage V H at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. V L = 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as V L increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher V L , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔEbecomes wider with the increase of V L . The IEDF at the radial center of the powered electrode exhibits a broader ΔEthan that at the edge. For the IADF, an increased V L results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

Physics↗

DOE OSTI2020

Magnetic reconnection in 3D fusion devices: non-linear reduced equations and linear current-driven instabilities

Abstract Magnetic reconnection in 3D fusion devices is investigated. With the use of Boozer co-ordinates, we reduce the non-linear resistive magnetohydrodynamic equations in the limit of large aspect ratio and finite pressure fluctuations, to obtain a set of non-linear equations suitable for magnetic reconnection studies in stellarators. Magnetic flux unfreezing due to a finite electron mass is also considered. Equations that govern the linear regime and some of their general properties are given. We emphasise the role of magnetic geometry and identify how some aspects of stellarator optimisation could have an impact on reconnecting instabilities, in particular by exacerbating those enabled by electron inertia. The effect of 3D coupling on the linear reconnection rates and the mode structure is quantitatively addressed in the case in which the equilibrium rotational transform has one specific resonant location for which one mode can reconnect while coupled to an arbitrary number of non-resonant harmonics. The full problem is rigorously reduced to an equivalent cylindrical one, by introducing some geometrically modified plasma inertial and dissipative scales. The 3D scalings for the growth rates of reconnection instabilities and their destabilisation criteria are given.

Physics↗

DOE OSTI2026

MHD-induced SOL filaments and divertor heat flux striations in NSTX

Magnetohydrodynamic (MHD) activity in NSTX has been found to induce striated heat flux patterns at the divertor. These striated heat fluxes were previously interpreted as strike-point splitting caused by stochastic magnetic lobes near the X-point. Recent analysis indicates that MHD can directly generate filaments in the scrape-off layer (SOL), and the MHD-related filaments are consistent with the rotation and the frequency of the MHD. Magnetic field line tracing from the mid-plane of the MHD-related filaments to the divertor is consistent with the location of striated heat fluxes on the divertor. Additionally, gas puff imaging (GPI) diagnostic data shows the generation of regular blobs following each edge harmonic oscillation (EHO) toroidal mode number n = 1 perturbation, which indicates that the MHD perturbation directly drives the blobs. These blobs are responsible for the divertor heat flux striations. Here, this finding provides a new framework for understanding MHD-induced edge transport and has important implications for heat-load control in NSTX-U and future spherical tokamaks.

MHD↗

DOE OSTI2021

Global gyrokinetic simulation with kinetic electron for collisionless damping of zonal flow in stellarators

Global gyrokinetic simulations with kinetic electrons for collisionless damping of zonal flows in LHD and W7-X stellarators show that the helical components of the equilibrium magnetic field responsible for helically trapped particles have significant impacts on zonal flow. Kinetic electrons reduce zonal flow residue and increase the frequency of low frequency oscillation (LFO). Here, the LFO is induced by dominant helical harmonics of magnetic field strength. Furthermore, linear toroidal coupling of multiple toroidal n-harmonics barely affects the zonal flows, but can generate long wavelength toroidal harmonics with the same toroidal number as the helical magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

encore : an O ( N g2) estimator for galaxy N -point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1992

Flap-lag damping in hover and forward flight with a three-dimensional wake

Prediction of lag damping is difficult owing to the delicate balance of drag, induced drag and Coriolis forces in the in-plane direction. Moreover, induced drag is sensitive to dynamic wake, both shed and trailing components, and thus its prediction requires adequate unsteady-wake representation. Accordingly, rigid-blade flap-lag equations are coupled with a three-dimensional finite-state wake model; three isolated rotor configurations with three, four and five blades are treated over a range of thrust levels, Lock numbers, lag frequencies and advance ratios. The investigation includes convergence characteristics of damping with respect to the number of shape functions and harmonics of the wake model for multiblade modes of low frequency (less than 1/rev.) to high frequency (greater than l/rev.). Predicted flap and lag damping levels are then compared with similar predictions with (1) rigid wake (no unsteady induced flow), (2) Loewy lift deficiency, and (3) dynamic inflow.

Manjunath, A. R.↗

NASA NTRS1999

A magnetostatic-coupling based remote query sensor for environmental monitoring

A new type of in situ, remotely monitored magnetism-based sensor is presented that is comprised of an array of magnetically soft, magnetostatically-coupled ferromagnetic thin-film elements or particles combined with a chemically responsive material that swells or shrinks in response to the analyte of interest. As the chemically responsive material changes size the distance between the ferromagnetic elements changes, altering the inter-element magnetostatic coupling. This in turn changes the coercive force of the sensor, the amplitude of the voltage spikes detected in nearby pick-up coils upon magnetization reversal and the number of higher-order harmonics generated by the flux reversal. Since the sensor is monitored through changes in magnetic flux, no physical connections such as wires or cables are needed to obtain sensor information, nor is line of sight alignment required as with laser telemetry; the sensors can be detected from within sealed, opaque or thin metallic enclosures.

NASA Discipline Life Sciences Technologies↗

NASA NTRS1984

Standing hydromagnetic oscillations in the magnetosphere

The mechanisms for generating Alfven waves in the magnetosphere are determined, on the basis of a comprehensive survey of satellite magnetometer data. The mechanisms are classified in terms of the physical properties of standing Alfven waves such as the direction of the major axis of polarization, harmonic mode, and the azimuthal wave number. In an analysis of the statistical organization of the pulsations, it is shown that the most common transverse waves seem to be azimuthally polarized waves involving the fundamental and several harmonics, with radially polarized waves excited at the second harmonic. The former are probably driven externally, while the latter are likely to be excited internally through particle-wave interactions.

Takahashi, K.↗

DOE OSTI2022

Virtual Dynamic Grid Impedance and Its Impacts on Harmonics and Stability of Inverter Based Resources Plant

Nowadays, a large number of inverter-based resources (IBRs) are integrated into the grid at a single connection point as an IBR plant. In this article, a virtual dynamic grid impedance concept is introduced to evaluate the harmonics and stability for grid integration of an IBR plant containing multiple IBRs. First, a detailed theoretical study is conducted to build a foundation of the virtual grid impedance concept, which is a dynamic impedance that changes with the number of IBRs added into an IBR plant. Then, based on the new virtual dynamic grid impedance concept, frequency spectrum analysis is performed to explore harmonic impact at the interconnection point for an IBR plant with IBRs having L, LC, and LCL filters, respectively. An electromagnetic transient (EMT) simulation model of a grid-connected IBR plant is developed to explore the harmonics and stability of the IBR plant connected to the grid as well as the reliable operation of IBRs within the plant from the novel virtual equivalent dynamic grid impedance point of view. Hardware experiments are conducted to validate the EMT simulation evaluation. The results show that the number of IBRs added into an IBR plant influences the grid impedance, i.e., grid strength, and the grid impedance variation has multiple impacts on the IBR plant and IBRs within the plant depending on the grid-connected filters of the IBRs.

grid impedance↗

DOE OSTI2023

Scalable self attraction and loading calculations for unstructured ocean tide models

Self attraction and earth-loading effects are important for accurately modeling global tides. A common approach of handling this forcing is to expand mass anomalies into spherical harmonics, which are scaled by load Love numbers to account for elastic earth deformation. We investigate two different approaches to perform these calculations for ocean models that employ unstructured meshes and distributed memory parallelization. The first approach leverages a highly efficient spherical harmonics library, but requires all-to-one and one-to-all communications and interpolation operations between the unstructured and a structured mesh. This approach is compared to a parallel algorithm that computes the spherical harmonic transformations directly on the unstructured mesh with an all-reduce communication. Here, our results show that although the unstructured mesh calculations are more expensive, the scalability of the unstructured mesh approach allows for more efficient spherical harmonics transforms for high-resolution meshes and large processor counts. This methodology enables the efficient inclusion of tidal dynamics large-scale Earth system model simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

CORPSE model with litter decomposition parameters derived from the LIDET dataset

This is a version of the CORPSE model (Carbon, Organisms, Rhizosphere and Protection in the Soil Environment, Sulman et al. 2014) that uses litter decomposition parameters derived from a modified Monte Carlo simulation using the LIDET litter decomposition dataset (Long-term Intersite Decomposition Experiment Team, Harmon 2013). The code also includes the Baseline parameters, and the eight other best parameter sets identified in a modified Monte Carlo simulation. Related publication:Juice, S.M., Ridgeway, J.R., Hartman, M.D., Parton, W.J., Berardi, D.M., Sulman, B.N., Allen, K.E., & Brzostek, E.R. Reparameterizing litter decomposition using a simplified Monte Carlo method improves litter decay simulated by a microbial model and alters bioenergy soil carbon estimates. Description of files:The folder "Input Files" contains one folder for each LIDET site with data necessary to run the model. Note that "(site)" in the filenames below indicates where the LIDET site code appears (see Table 1 for site codes). Data streams include: CORPSE_full_spinup_litter.csv, CORPSE_full_spinup_rhizo.csv, CORPSE_full_spinup_bulk.csv, litterbag_init_100g_6spp.csv: initial C and N (kg C or N/m2) pool values for each soil layer, the litterbag_init_100_6spp.csv file is for the litterbag layer and is the same file for all sites. All initial C and N files have the same columns (Column - Description - Units) uFastC - Unprotected fast decomposing carbon - kg carbon/m2 uSlowC - Unprotected slow decomposing carbon - kg carbon/m2 uNecroC - Unprotected necromass carbon - kg carbon/m2 pFastC - Protected fast decomposing carbon - kg carbon/m2 pSlowC - Protected slow decomposing carbon - kg carbon/m2 pNecroC - Protected necromass carbon - kg carbon/m2 livingMicrobeC - Carbon in living microbial biomass - kg carbon/m2 uFastN - Unprotected fast decomposing nitrogen - kg nitrogen/m2 uSlowN - Unprotected slow decomposing nitrogen - kg nitrogen/m2 uNecroN - Unprotected necromass nitrogen - kg nitrogen/m2 pFastN - Protected fast decomposing nitrogen - kg nitrogen/m2 pSlowN - Protected slow decomposing nitrogen - kg nitrogen/m2 pNecroN - Protected necromass nitrogen - kg nitrogen/m2 inorganicN - Inorganic nitrogen - kg nitrogen/m2 CO2 - Carbon in carbon dioxide - kg carbon/m2 livingMicrobeN - Nitrogen in living microbial biomass - kg nitrogen/m2 soilT (site) DOY274start.csv: Average daily soil temperature (oC) interpolated from previously calculated monthly values used in DayCent LIDET simulations (Bonan et al., 2013). soilT (site) DOY274start.csv: Average daily soil volumetric water content (VWC) scalar interpolated from previously calculated monthly values used in DayCent LIDET simulations (Bonan et al., 2013). litter production.csv: Average daily litter production values for each site, data sources listed in Table S3 of related publication. litter (site) CN.csv: C:N ratio for each species from LIDET dataset (Table 2, Harmon 2013). (site).csv: Table indicating number of observations for each species decomposed at each site. Instructions: Save the model code ("CORPSE_LIDET.R") and "Input Files" folder in the same folder. Also make a folder for the model output (e.g., "results_Baseline") in the same folder. Set the working directory (setwd) in the model code to the folder with the files saved in step #1. Select the parameter set to use for the litter and litterbag compartments, comment out all other parameter sets. Run code. Output will be saved in the folder made in step 1. Output destination can be changed as necessary in code section called "Running the model." Table 1 LIDET sites and site codes used in model files. Site Code - Site AND - H.J. Andrews Experimental Forest BNZ - Bonanza Creek Experimental Forest BSF - Blodgett Research Forest CDR - Cedar Creek Natural History Area CPR - Central Plains Experimental Range HBR - Hubbard Brook Experimental Forest HFR - Harvard Forest JUN - Juneau KBS - Kellogg Biological Station KNZ - Konza Prairie Research Natural Area NWT - Niwot Ridge/Green Lakes Valley OLY - Olympic National Park OLY Conifer forest SEV - Sevilleta National Wildlife Refuge SMR - Santa Margarita Ecological Reserve UFL - University of Florida VCR - Virginia Coast Reserve Table 2 LIDET species and species codes used in model files (6 common species). Species - Species Code Sugar maple (Acer saccharum) - ACSA Drypetes (Drypetes glauca) - DRGL Red pine (Pinus resinosa) - PIRE Chestnut oak (Quercus prinus) - QUPR Western redcedar (Thuja plicata) - THPL Wheat (Triticum aestivum) - TRAE References:Bonan, G. B., Hartman, M. D., Parton, W. J., & Wieder, W. R. (2013). Evaluating litter decomposition in earth system models with long-term litterbag experiments: an example using the Community Land Model version 4 (CLM4). Global Change Biology, 19(3), 957-974. https://doi.org/https://doi.org/10.1111/gcb.12031 Harmon, M. (2013). LTER Intersite Fine Litter Decomposition Experiment (LIDET), 1990 to 2002. Long-Term Ecological Research. Forest Science Data Bank, Corvallis, OR. [Data set]. Accessed http://andlter.forestry.oregonstate.edu/data/abstract.aspx?dbcode=TD023. https://doi.org/10.6073/pasta/f35f56bea52d78b6a1ecf1952b4889c5. Sulman, B. N., Phillips, R. P., Oishi, A. C., Shevliakova, E., & Pacala, S. W. (2014). Microbe-driven turnover offsets mineral-mediated storage of soil carbon under elevated CO2. Nature Climate Change, 4, 1099 - 1102. https://doi.org/10.1038/nclimate2436

Juice, Stephanie↗

DOE OSTI2022

Non-linear MHD modelling of edge localized modes suppression by resonant magnetic perturbations in ITER

Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. In this study, the main aim was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ~5 MW m ₋2 to ~1 MW m ₋2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗