High Harmonic Fast Wave Research Articles

Numerical Studies and Simulation of the Lower Hybrid Waves Current Drive by using Fokker – Planck Equation in NSST and HT-7 Tokamaks

Recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. The spherical tours (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as NSTX and higher toroidal beta regimes and improves the design of a power plant. To support the ST development path, one option of a Next Step Spherical Torus (NSST) device has been examined .NSST is a performance extension stage ST with a plasma current of 5-10 MA, R=1.5m, Bt<2.7T with flexible physics. The baseline heating and current device system for NSST is the 30MW NBI system and a 10 MW of ion cyclotron range of frequency (ICRF) and high harmonic fast wave (HHFW) system. In this work, we investigated lower hybrid wave interaction in the NSST reactor and found an optimal lower hybrid wave power and frequency for it. Finally, we compared the lower optimal hybrid waves and NSST spherical tokamak with HT-7 tokamak. Our results indicated that the use of lower hybrid waves in improved spherical tokamak NSST, as compared to the HT-7, was much better and more efficient.

Overview of physics results from the conclusive operation of the National Spherical Torus Experiment

Research on the National Spherical Torus Experiment, NSTX, targets physics understanding needed for extrapolation to a steady-state ST Fusion Nuclear Science Facility, pilot plant, or DEMO. The unique ST operational space is leveraged to test physics theories for next-step tokamak operation, including ITER. Present research also examines implications for the coming device upgrade, NSTX-U. An energy confinement time, τE, scaling unified for varied wall conditions exhibits a strong improvement of BTτE with decreased electron collisionality, accentuated by lithium (Li) wall conditioning. This result is consistent with nonlinear microtearing simulations that match the experimental electron diffusivity quantitatively and predict reduced electron heat transport at lower collisionality. Beam-emission spectroscopy measurements in the steep gradient region of the pedestal indicate the poloidal correlation length of turbulence of about ten ion gyroradii increases at higher electron density gradient and lower Ti gradient, consistent with turbulence caused by trapped electron instabilities. Density fluctuations in the pedestal top region indicate ion-scale microturbulence compatible with ion temperature gradient and/or kinetic ballooning mode instabilities. Plasma characteristics change nearly continuously with increasing Li evaporation and edge localized modes (ELMs) stabilize due to edge density gradient alteration. Global mode stability studies show stabilizing resonant kinetic effects are enhanced at lower collisionality, but in stark contrast have almost no dependence on collisionality when the plasma is off-resonance. Combined resistive wall mode radial and poloidal field sensor feedback was used to control n = 1 perturbations and improve stability. The disruption probability due to unstable resistive wall modes (RWMs) was surprisingly reduced at very high βN/li > 10 consistent with low frequency magnetohydrodynamic spectroscopy measurements of mode stability. Greater instability seen at intermediate βN is consistent with decreased kinetic RWM stabilization. A model-based RWM state-space controller produced long-pulse discharges exceeding βN = 6.4 and βN/li = 13. Precursor analysis shows 96.3% of disruptions can be predicted with 10 ms warning and a false positive rate of only 2.8%. Disruption halo currents rotate toroidally and can have significant toroidal asymmetry. Global kinks cause measured fast ion redistribution, with full-orbit calculations showing redistribution from the core outward and towards V∥/V = 1 where destabilizing compressional Alfvén eigenmode resonances are expected. Applied 3D fields altered global Alfvén eigenmode characteristics. High-harmonic fast-wave (HHFW) power couples to field lines across the entire width of the scrape-off layer, showing the importance of the inclusion of this phenomenon in designing future RF systems. The snowflake divertor configuration enhanced by radiative detachment showed large reductions in both steady-state and ELM heat fluxes (ELMing peak values down from 19 MW m−2 to less than 1.5 MW m−2). Toroidal asymmetry of heat deposition was observed during ELMs or by 3D fields. The heating power required for accessing H-mode decreased by 30% as the triangularity was decreased by moving the X-point to larger radius, consistent with calculations of the dependence of E × B shear in the edge region on ion heat flux and X-point radius. Co-axial helicity injection reduced the inductive start-up flux, with plasmas ramped to 1 MA requiring 35% less inductive flux. Non-inductive current fraction (NICF) up to 65% is reached experimentally with neutral beam injection at plasma current Ip = 0.7 MA and between 70–100% with HHFW application at Ip = 0.3 MA. NSTX-U scenario development calculations project 100% NICF for a large range of 0.6 < Ip(MA) < 1.35.

Heating of ions by high frequency electromagnetic waves in magnetized plasmas

The heating of ions by high frequency electrostatic waves in magnetically confined plasmas has been a paradigm for studying nonlinear wave-particle interactions. The frequency of the waves is assumed to be much higher than the ion cyclotron frequency and the waves are taken to propagate across the magnetic field. In fusion type plasmas, electrostatic waves, like the lower hybrid wave, cannot access the core of the plasma. That is a domain for high harmonic fast waves or electron cyclotron waves—these are primarily electromagnetic waves. Previous studies on heating of ions by two or more electrostatic waves are extended to two electromagnetic waves that propagate directly across the confining magnetic field. While the ratio of the frequency of each wave to the ion cyclotron frequency is large, the frequency difference is assumed to be near the ion cyclotron frequency. The nonlinear wave-particle interaction is studied analytically using a two time-scale canonical perturbation theory. The theory elucidates the effects of various parameters on the gain in energy by the ions—parameters such as the amplitudes and polarizations of the waves, the ratio of the wave frequencies to the cyclotron frequency, the difference in the frequency of the two waves, and the wave numbers associated with the waves. For example, the ratio of the phase velocity of the envelope formed by the two waves to the phase velocity of the carrier wave is important for energization of ions. For a positive ratio, the energy range is much larger than for a negative ratio. So waves like the lower hybrid waves will impart very little energy to ions. The theoretical results are found to be in good agreement with numerical simulations of the exact dynamical equations. The analytical results are used to construct mapping equations, simplifying the derivation of the motion of ions, which are, subsequently, used to follow the evolution of an ion distribution function. The heating of ions can then be properly quantified in terms of the wave parameters and can be conveniently used to find ideal conditions needed to heat ions by high frequency electromagnetic waves.

A description of the full-particle-orbit-following SPIRAL code for simulating fast-ion experiments in tokamaks

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared with measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared with measured neutron signals. Magnetohydrodynamic (MHD) activity such as tearing modes and toroidicity-induced Alfvén eigenmodes (TAEs) have a profound effect on the fast-ion content of tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between ion cyclotron range of frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.

High-Harmonic Fast-Wave Power Flow along Magnetic Field Lines in the Scrape-Off Layer of NSTX

A significant fraction of high-harmonic fast-wave (HHFW) power applied to NSTX can be lost to the scrape-off layer (SOL) and deposited in bright and hot spirals on the divertor rather than in the core plasma. We show that the HHFW power flows to these spirals along magnetic field lines passing through the SOL in front of the antenna, implying that the HHFW power couples across the entire width of the SOL rather than mostly at the antenna face. This result will help guide future efforts to understand and minimize these edge losses in order to maximize fast-wave heating and current drive.

High non-inductive fraction H-mode discharges generated by high-harmonic fast wave heating and current drive in the National Spherical Torus Experiment

A deuterium H-mode discharge with a plasma current of 300 kA, an axial toroidal magnetic field of 0.55 T, and a calculated non-inductive plasma current fraction of 0.7–1 has been generated in the National Spherical Torus Experiment by 1.4 MW of 30 MHz high-harmonic fast wave (HHFW) heating and current drive. Seventy-five percent of the non-inductive current was generated inside an internal transport barrier that formed at a normalized minor radius ∼0.4. Three quarters of the non-inductive current was bootstrap current, and the remaining non-inductive current was generated directly by HHFW power inside a normalized minor radius ∼0.2.

Simulation of High-Harmonic Fast-Wave Heating on the National Spherical Tokamak Experiment

Images associated with radio-frequency heating of low-confinement mode plasmas in the National Spherical Tokamak Experiment, as calculated by computer simulation, are presented. The AORSA code has been extended to simulate the whole antenna-to-plasma heating system by including both the kinetic physics of the well-confined core plasma and a poorly confined scrape-off plasma and vacuum vessel structure. The images presented show the 3-D electric wave field amplitude for various antenna phasings. Visualization of the simulation results in 3-D makes clear that -30° phasing excites kilo-volt per meter coaxial standing modes in the scrape-off plasma and shows magnetic-field-aligned whispering-gallery type modes localized to the plasma edge.

Overview of physics results from NSTX

In the last two experimental campaigns, the low aspect ratio NSTX has explored physics issues critical to both toroidal confinement physics and ITER. Experiments have made extensive use of lithium coatings for wall conditioning, correction of non-axisymmetric field errors and control of n = 1 resistive wall modes (RWMs) to produce high-performance neutral-beam heated discharges extending to 1.7 s in duration with non-inductive current fractions up to 0.7. The RWM control coils have been used to trigger repetitive ELMs with high reliability, and they have also contributed to an improved understanding of both neoclassical tearing mode and RWM stabilization physics, including the interplay between rotation and kinetic effects on stability. High harmonic fast wave (HHFW) heating has produced plasmas with central electron temperatures exceeding 6 keV. The HHFW heating was used to show that there was a 20–40% higher power threshold for the L–H transition for helium than for deuterium plasmas. A new diagnostic showed a depletion of the fast-ion density profile over a broad spatial region as a result of toroidicity-induced Alfvén eigenmodes (TAEs) and energetic-particle modes (EPMs) bursts. In addition, it was observed that other modes (e.g. global Alfvén eigenmodes) can trigger TAE and EPM bursts, suggesting that fast ions are redistributed by high-frequency AEs. The momentum pinch velocity determined by a perturbative technique decreased as the collisionality was reduced, although the pinch to diffusion ratio, Vpinch/χϕ, remained approximately constant. The mechanisms of deuterium retention by graphite and lithium-coated graphite plasma-facing components have been investigated. To reduce divertor heat flux, a novel divertor configuration, the ‘snowflake’ divertor, was tested in NSTX and many beneficial aspects were found. A reduction in the required central solenoid flux has been realized in NSTX when discharges initiated by coaxial helicity injection were ramped in current using induction. The resulting plasmas have characteristics needed to meet the objectives of the non-inductive start-up and ramp-up program of NSTX.

Use of the Far Infrared Tangential Interferometer/Polarimeter diagnostic for the study of rf driven plasma waves on NSTX

A rf detection system for waves in the 30 MHz range has been constructed for the Far Infrared Tangential Interferometer/Polarimeter on National Spherical Torus Experiment (NSTX). It is aimed at monitoring high frequency density fluctuations driven by 30 MHz high harmonic fast wave fields. The levels of density fluctuations at various radial chords and antenna phase angles can be estimated using the electric field calculated by TORIC code and linearized continuity equation for the electron density. In this paper, the experimental arrangement for the detection of rf signal and preliminary results of simulation will be discussed.

Advances in high-harmonic fast wave physics in the National Spherical Torus Experiment

Improved core high-harmonic fast wave (HHFW) heating at longer wavelengths and during start-up and plasma current ramp-up has now been obtained by lowering the edge density with lithium wall conditioning, thereby moving the critical density for perpendicular fast-wave propagation away from the vessel wall. Lithium conditioning allowed significant HHFW core electron heating of deuterium neutral beam injection (NBI) fuelled H-mode plasmas to be observed for the first time. Large edge localized modes were observed immediately after the termination of rf power. Visible and infrared camera images show that fast wave interactions can deposit considerable rf energy on the outboard divertor. HHFW-generated parametric decay instabilities were observed to heat ions in the plasma edge and may be the cause for a measured drag on edge toroidal rotation during HHFW heating. A significant enhancement in neutron rate and fast-ion profile was measured in NBI-fuelled plasmas when HHFW heating was applied.

Profiles of fast ions that are accelerated by high harmonic fast waves in the National Spherical Torus Experiment

Combined neutral beam injection and high-harmonic fast-wave (HHFW) heating accelerate deuterium fast ions in the National Spherical Torus Experiment (NSTX). With 1.1 MW of HHFW power, the neutron emission rate is about three times larger than in the comparison discharge without HHFW heating. Acceleration of fast ions above the beam injection energy is evident on an E||B type neutral particle analyzer (NPA), a 4-chord solid state neutral particle analyzer (SSNPA) array and a 16-channel fast-ion D-alpha (FIDA) diagnostic. The accelerated fast ions observed by the NPA and SSNPA diagnostics mainly come from passive charge exchange reactions at the edge due to the NPA/SSNPA localization in phase space. The spatial profile of accelerated fast ions that is measured by the FIDA diagnostic is much broader than in conventional tokamaks because of the multiple resonance layers and large orbits in NSTX. The fast-ion distribution function calculated by the CQL3D Fokker–Planck code differs from the measured spatial profile, presumably because the current version of CQL3D uses a zero-banana-width model. In addition, compressional Alfven eigenmode activity is stronger during the HHFW heating and it may affect the fast-ion spatial profile.

Direct Measurements of High Harmonic Fast Wave Profile in the UTST Spherical Tokamak Plasma

The spatial distribution of the radiofrequency (RF) magnetic field associated with a high harmonic fast wave (HHFW) was measured using an array of magnetic probes in the plasma inside the University of Tokyo Spherical Tokamak (UTST). Data obtained from 25 probes (19 locations for toroidal polarization and 6 locations for vertical polarization) distributed along the poloidal cross section were analyzed. The RF magnetic field is polarized in the toroidal direction, indicating that the HHFW is excited in the plasma. The RF field is weak on the inboard side. Analysis of the group delay suggests that the waves travel long distances in the plasma, probably because of poor absorption. No indication of parametric decay was observed up to 80 kW of injected RF power.

Overview of results from the National Spherical Torus Experiment (NSTX)

The mission of the National Spherical Torus Experiment (NSTX) is the demonstration of the physics basis required to extrapolate to the next steps for the spherical torus (ST), such as a plasma facing component test facility (NHTX) or an ST based component test facility (ST-CTF), and to support ITER. Key issues for the ST are transport, and steady state high β operation. To better understand electron transport, a new high-k scattering diagnostic was used extensively to investigate electron gyro-scale fluctuations with varying electron temperature gradient scale length. Results from n = 3 braking studies are consistent with the flow shear dependence of ion transport. New results from electron Bernstein wave emission measurements from plasmas with lithium wall coating applied indicate transmission efficiencies near 70% in H-mode as a result of reduced collisionality. Improved coupling of high harmonic fast-waves has been achieved by reducing the edge density relative to the critical density for surface wave coupling. In order to achieve high bootstrap current fraction, future ST designs envision running at very high elongation. Plasmas have been maintained on NSTX at very low internal inductance li ∼ 0.4 with strong shaping (κ ∼ 2.7, δ ∼ 0.8) with βN approaching the with-wall β-limit for several energy confinement times. By operating at lower collisionality in this regime, NSTX has achieved record non-inductive current drive fraction fNI ∼ 71%. Instabilities driven by super-Alfvénic ions will be an important issue for all burning plasmas, including ITER. Fast ions from NBI on NSTX are super-Alfvénic. Linear toroidal Alfvén eigenmode thresholds and appreciable fast ion loss during multi-mode bursts are measured and these results are compared with theory. The impact of n > 1 error fields on stability is an important result for ITER. Resistive wall mode/resonant field amplification feedback combined with n = 3 error field control was used on NSTX to maintain plasma rotation with β above the no-wall limit. Other highlights are results of lithium coating experiments, momentum confinement studies, scrape-off layer width scaling, demonstration of divertor heat load mitigation in strongly shaped plasmas and coupling of coaxial helicity injection plasmas to ohmic heating ramp-up. These results advance the ST towards next step fusion energy devices such as NHTX and ST-CTF.

Spectral effects on fast wave core heating and current drive

Recent results obtained with high harmonic fast wave (HHFW) heating and current drive (CD) on NSTX strongly support the hypothesis that the onset of perpendicular fast wave propagation right at or very near the launcher is a primary cause for a reduction in core heating efficiency at long wavelengths that is also observed in ICRF heating experiments in numerous tokamaks. A dramatic increase in core heating efficiency was first achieved in NSTX L-mode helium majority plasmas when the onset for perpendicular wave propagation was moved away from the antenna and nearby vessel structures. Efficient core heating in deuterium majority L-mode and H-mode discharges, in which the edge density is typically higher than in comparable helium majority plasmas, was then accomplished by reducing the edge density in front of the launcher with lithium conditioning and avoiding operational points prone to instabilities. These results indicate that careful tailoring of the edge density profiles in ITER should be considered to limit radio frequency (rf) power losses to the antenna and plasma facing materials. Finally, in plasmas with reduced rf power losses in the edge regions, the first direct measurements of HHFW CD were obtained with the motional Stark effect (MSE) diagnostic. The location and radial dependence of HHFW CD measured by MSE are in reasonable agreement with predictions from both full wave and ray tracing simulations.

Parametric decay instability during high harmonic fast wave heating experiments on the TST-2 spherical tokamak

A degradation of heating efficiency was observed during high harmonic fast wave (HHFW) heating of spherical tokamak plasmas when parametric decay instability (PDI) occurred. Suppression of PDI is necessary to make HHFW a reliable heating and current drive tool in high β plasmas. In order to understand PDI, measurements were made using a radially movable electrostatic probe (ion saturation current and floating potential), arrays of RF magnetic probes distributed both toroidally and poloidally, microwave reflectometry and fast optical diagnostics in TST-2. The frequency spectrum usually exhibits ion-cyclotron harmonic sidebands f0 ± nfci and low-frequency ion-cyclotron quasi-modes (ICQMs) nfci. PDI becomes stronger at lower densities, and much weaker when the plasma is far away from the antenna. The lower sideband power was found to increase quadratically with the local pump wave power. The lower sideband power relative to the local pump wave power was larger for reflectometer compared with either electrostatic or magnetic probes. The radial decay of the pump wave amplitude in the SOL was much faster for the ion saturation current than for the floating potential. These results are consistent with the HHFW pump wave decaying into the HHFW or ion Bernstein wave (IBW) sideband and the low-frequency (ICQM). Two additional peaks were discovered between the fundamental lower sideband and the pump wave in hydrogen plasmas. The frequency differences of these peaks from the pump wave increase with the magnetic field. These decay modes may involve molecular ions or partially ionized impurity ions.

Internal transport barriers in the National Spherical Torus Experiment

In the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)], internal transport barriers (ITBs) are observed in reversed (negative) shear discharges where diffusivities for electron and ion thermal channels and momentum are reduced. While neutral beam heating can produce ITBs in both electron and ion channels, high harmonic fast wave heating can also produce electron ITBs (e-ITBs) under reversed magnetic shear conditions without momentum input. Interestingly, the location of the e-ITB does not necessarily match that of the ion ITB (i-ITB). The e-ITB location correlates best with the magnetic shear minima location determined by motional Stark effect constrained equilibria, whereas the i-ITB location better correlates with the location of maximum E×B shearing rate. Measured electron temperature gradients in the e-ITB can exceed critical gradients for the onset of electron thermal gradient microinstabilities calculated by linear gyrokinetic codes. A high-k microwave scattering diagnostic shows locally reduced density fluctuations at wave numbers characteristic of electron turbulence for discharges with strongly negative magnetic shear versus weakly negative or positive magnetic shear. Reductions in fluctuation amplitude are found to be correlated with the local value of magnetic shear. These results are consistent with nonlinear gyrokinetic simulations predicting a reduction in electron turbulence under negative magnetic shear conditions despite exceeding critical gradients.

Study of turbulent fluctuations driven by the electron temperature gradient in the National Spherical Torus Experiment

Various theories and numerical simulations support the conjecture that the ubiquitous problem of anomalous electron transport in tokamaks may arise from a short-scale turbulence driven by the electron temperature gradient. To check whether this turbulence is present in plasmas of the National Spherical Torus Experiment, measurements of turbulent fluctuations were performed with coherent scattering of electromagnetic waves. Results from plasmas heated by high harmonic fast waves show the existence of density fluctuations in the range of wave numbers k⊥ρe = 0.1–0.4, corresponding to a turbulence scale length of the order of the collisionless skin depth. Experimental observations and agreement with numerical results from the linear gyro-kinetic GS2 code indicate that the observed turbulence is driven by the electron temperature gradient. These turbulent fluctuations were not observed at the location of an internal transport barrier driven by a negative magnetic shear.

Detection of a new parametric decay instability branch in TST-2 during high harmonic fast wave heating

Parametric decay instability (PDI) is often observed in the TST-2 spherical tokamak during high harmonic fast wave heating by rf pickup probes. The frequency spectrum exhibits lower and upper sideband peaks in addition to the pump wave at f(0)=21 MHz. Two types of PDI are observed. One is the well-known decay into the ion-cyclotron quasimode (nf(ci)) and the ion Bernstein wave (f(0)-nf(ci)). The other is a newly found decay with the sideband frequency between f(0) and f(0)-f(ci). The frequency difference between this sideband and the pump increases in proportion to B(t). Moreover, high-speed visible light measuring systems with photomultiplier tubes or hybrid photodetectors viewing the plasma core detected oscillation of light emission at around f(0).

The observation of nonlinear ion cyclotron wave excitation during high-harmonic fast wave heating in the large helical device

A wave detector, a newly designed magnetic probe, is installed in the large helical device (LHD). This wave detector is a 100-turn loop coil with electrostatic shield. Comparing a one-loop coil to this detector, this detector has roughly constant power coupling in the lower frequency range of 40 MHz, and it can easily detect magnetic wave in the frequency of a few megahertz. During high-harmonic fast wave heating, lower frequency waves (<10 MHz) were observed in the LHD for the first time, and for the power density threshold of lower frequency wave excitation (7.5 MHz) the power density of excited pumped wave (38.47 MHz) was approximately -46 dBmHz. These lower frequencies are kept constant for electron density and high energy particle distribution, and these lower frequency waves seem to be ion cyclotron waves caused by nonlinear wave-particle interaction, for example, parametric decay instability.

High harmonic fast wave heating efficiency enhancement and current drive at longer wavelength on the National Spherical Torus Experiment

High harmonic fast wave heating and current drive (CD) are being developed on the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)] for supporting startup and sustainment of the spherical torus plasma. Considerable enhancement of the core heating efficiency (η) from 44% to 65% has been obtained for CD phasing of the antenna (strap-to-strap ϕ=−90°, kϕ=−8m−1) by increasing the magnetic field from 4.5to5.5kG. This increase in efficiency is strongly correlated to moving the location of the onset density for perpendicular fast wave propagation (nonset∝B×k∥2∕ω) away from the antenna face and wall, and hence reducing the propagating surface wave fields. Radio frequency (RF) waves propagating close to the wall at lower B and k∥ can enhance power losses from both the parametric decay instability (PDI) and wave dissipation in sheaths and structures around the machine. The improved efficiency found here is attributed to a reduction in the latter, as PDI losses are little changed at the higher magnetic field. Under these conditions of higher coupling efficiency, initial measurements of localized CD effects have been made and compared with advanced RF code simulations.