Negative Triangularity Research Articles

Extended Solov'ev type equilibria for rotating plasmas with positive and negative triangularity

The Solov'ev ansatz is employed to solve the equilibrium equation for plasmas rotating in the toroidal direction. The plasma shape can be controlled by fixing the values of the aspect ratio, elongation, triangularity, and curvature at the equatorial points. In addition, it is possible to set the values of the plasma current, total β, and Mach number. Analytic expressions for the shape coefficients and examples of equilibria with positive and negative triangularity are presented.

Modelling of RFX-mod2 tokamak equilibria with DEMO-like shape conditions and negative triangularity

In this paper, DEMO-like shaped plasma equilibria are defined for RFX-mod2 tokamak operations by using the Inverse Equilibrium Tool (IET code). IET allows for the computation of the coil currents needed to obtain a predetermined plasma shape with well defined plasma global parameters (i.e. total plasma current and total poloidal magnetic flux at the boundary) by solving a constrained minimization problem. The new shape conditions would allow achieving higher plasma current and plasma density values at the same toroidal magnetic field and safety factor limits of previous RFX-mod tokamak operations. The feasibility of these new equilibria is explored in terms of coil current requirements and vertical stability analysis. This study shows that RFX-mod2 is a flexible device, able to perform DEMO-like shaped tokamak operations with low requirements on both magnitude and distribution of active coil currents.

Analytical formula for pellet fuel source density in toroidal plasma configurations based on an areal deposition model

An analytical formula for the fuel source density averaged over a magnetic flux surface following pellet injection is derived. During pellet motion the ablated and ionized fuel will be initially deposited nearby the pellet, prior to subsequent homogenization within the magnetic flux surfaces. In this paper, it is assumed that the deposition area projected normal to the magnetic field is on the order of the cross-sectional area of the ionized ablation column whose axis is aligned with the magnetic field. Previous pellet deposition codes (Houlberg et al 1979) employed a point source deposition approximation, which overpredicts the surface-averaged density, particularly when the obliquity between the pellet trajectory and the flux surface normal approaches 90 degrees. A key finding of this study is that as the obliquity approaches 90 degrees, grazing trajectory, the areal model predicts a well behaved , and removes the unphysical divergence stemming from the point model. To highlight the difference exhibited between areal and point models for near grazing trajectories, we considered vertical pellet injection into a CFETR-like tokamak with a negative triangularity plasma cross section using a pellet ablation/deposition module.

The design and optimisation of tokamak poloidal field systems in the BLUEPRINT framework

Abstract As part of our aim to develop a reactor design framework, we present here our approach to the optimisation of plasma equilibria and tokamak poloidal field systems. A 2-D, free boundary, ideal magneto-hydrodynamic plasma equilibrium solver is described. We use it within the BLUEPRINT reactor design framework to design plasma equilibria and poloidal field coilsets for future fusion reactors in an integrated way. Plasma shape parameters (R0, A, δ, κ) and integral parameters (Ip, βp, li) are controlled for. Constrained optimisation procedures for the positions and currents of the poloidal field coils are presented; these account for current, field, force, and positional constraints on the coils. A pulse length constraint is incorporated in the optimisation procedure in the case of pulsed reactors. We demonstrate our approach on three different reactor concepts: single-null, double-null and negative triangularity tokamaks.

DEMO physics challenges beyond ITER

Abstract For electricity producing tokamak fusion reactors like EU-DEMO, it is prudent to choose a plasma scenario close to the ITER baseline, where the largest amount of experimental evidence is available. Nevertheless, there are some aspects in which ITER and EU-DEMO have to differ, as the simple exercise of up-scaling from ITER to a larger device is constrained both by physical nonlinearities and by technological limits. In this work, relevant differences between ITER and the current EU-DEMO baseline in terms of plasma scenario are discussed. Firstly, EU-DEMO is assumed to operate with a very large amount of radiative power originating both from the scrape-off layer and, markedly, from the core. This radiation level is obtained by means of seeded impurities, whose presence significantly affects many aspects of the scenario itself, especially in terms of transient control. Secondly, because of the need of breeding tritium, the EU-DEMO wall is less robust than the ITER one. This implies that every off-normal interruption of the plasma discharge, for example in presence of a divertor reattachment, cannot rely on fast-shutdown procedures finally triggering a loss of plasma control at high current, but other strategies need to be developed. Thirdly, the ITER method for the control of the so-called sawteeth (ST) has been shown to be too expensive in terms of auxiliary power requirements, thus other solutions have to be explored. Finally, the problem of actively mitigating, or suppressing, the Edge Localised Modes (ELMs) has recently increased the interest on naturally ELM-free regimes (like QH-mode, I-mode, and also negative triangularity) for EU-DEMO, thus increasing the needs for ELM mitigation or suppression with respect to the approach adopted in ITER.

Shaping effects on scrape-off layer plasma turbulence: A rigorous validation of three-dimensional simulations against TCV measurements

The effect of plasma shaping on scrape-off layer (SOL) plasma turbulence is investigated through a rigorous validation exercise. Two- and three-dimensional simulations of the SOL plasma dynamics in three TCV limited discharges are carried out with the GBS code. These discharges realize an almost circular magnetic equilibrium, an elongated equilibrium, and an elongated equilibrium with negative triangularity. For the three plasma discharges, three simulations are performed, considering (i) a three-dimensional model with an explicit dependence on elongation, triangularity, and the inverse aspect ratio; (ii) a circular three-dimensional model in the infinite aspect ratio limit; and (iii) a two-dimensional model, which assumes a circular magnetic equilibrium in the infinite aspect ratio limit, cold ions, and interchange driven turbulence in the sheath limited regime. Ten validation observables common to simulations and experimental measurements from a reciprocating probe located at the TCV outer midplane are identified, and the agreement between experimental and numerical results relative to each observable is evaluated. The composite metric introduced by Ricci et al. [Phys. Plasmas 18, 032109 (2011)] is then used to assess the overall agreement between simulations and experimental measurements. It is found that the shaping model implemented in GBS improves the description of SOL plasma turbulence, taking into account the impact of elongation and triangularity.

Computational analysis of ion orbital loss in diverted positive- and negative-triangularity tokamaks

The mechanism of ion orbital loss in diverted negative-triangularity (NT) tokamaks is significantly different from that of positive-triangularity (PT) tokamaks. The orbital loss from the edge of NT tokamaks can be quite large, because the separatrix X-point is located on the outboard side, meaning that trapped ions crossing the separatrix are lost to the inboard divertor plate after a mirror reflection on the side of the strong magnetic field. NT tokamaks have difficulties in building up steep pressure gradients in the edge regions. In contrast, the majority of trapped ions crossing the separatrix in PT tokamaks survive (through complete banana motions) without reaching the X-point region. For NT tokamaks, topological changes in the trapped ion trajectories can be achieved in the presence of the radial electric field, thus reducing the orbital loss, whereas for PT tokamaks, the orbital loss is relatively insensitive to the radial electric field.

Effects of collisionality and Te/Ti on fluctuations in positive and negative δ tokamak plasmas

The effects of negative triangularity () on confinement and fluctuations in plasmas covering a large range of parameters were investigated on the tokamak à configuration variable (TCV). The conditions explored in this paper include discharges where neutral beam (NB) heating was employed to obtain an electron-ion temperature ratio across a large fraction of the plasma profile. This significantly extended the range of negative plasmas studied on TCV towards conditions more relevant to future reactor-like tokamaks. Negative triangularity was found to improve confinement over the full range of collisionality studied () and (). The amplitude of radiative temperature fluctuations, measured using a correlation electron cyclotron emission diagnostic over the range , was found to be reduced, in negative with respect to positive plasmas, for all combinations of parameters explored. This was, in particular, verified for a pair of positive and negative plasmas with comparable density and under different conditions of NB heating. Linear gyrokinetic simulations found the dominant turbulence regime, in the strongly NB heated discharges, to be a mixture of trapped electron modes (TEMs) and ion temperature gradient driven modes. This is in contrast to ohmic or electron cyclotron heated discharges, for which the dominant turbulence regime was found to be pure TEM. Negative triangularity was found to lead to partial stabilization of the most unstable modes for low wavenumbers in both turbulence regimes. These findings demonstrate that negative triangularity could provide significant confinement improvement over a large range of parameters, that include conditions closer to future reactor-like machines (, low collisionality).

Turbulent transport in TCV plasmas with positive and negative triangularity

Local gyrokinetic simulations with the GENE code are used to investigate the turbulent transport for different levels of neutral beam injection heating power in the Tokamak à Configuration Variable (TCV) for plasmas with both positive and negative edge triangularity. The sensitivity of the heat fluxes with respect to the main plasma parameters, including background gradients, impurity content, and electron temperature, is systematically studied. The experimentally measured transport levels are recovered with variations of profiles compatible with experimental error bars. When considering experimental conditions, trapped electron modes are the dominant instabilities for all heating powers and both types of shapes, whereas ion temperature gradients (ITGs) are not found. A numerical experiment, considering plasma profiles that strongly destabilize ITG modes, is thus performed. Negative triangularity is found to reduce the transport level also in this regime.

Magnetic shear due to localized toroidal flow shear in tokamaks

We investigate the impact of toroidal rotation on axisymmetric MHD equilibria analytically and numerically, with a focus on the change of the safety factor and magnetic shear induced by the flow. When the toroidal rotation is radially localized by an external momentum source, the pressure due to the flow can change the magnetic configuration and the safety factor significantly, even for subsonic flows. Specifically, when the radial profile of the safety factor is not conserved throughout a discharge, toroidal flow can lead to magnetic shear reversal for the equilibrium magnetic field, and we find that the magnitude of the negative shear is amplified for cross sections with large negative triangularity. This has implications for both magnetohydrodynamic stability and anomalous transport. Furthermore, even when the magnetic flux is conserved and the radial magnetic shear profile does not change, the toroidal flow can modify the local magnetic shear. The poloidal variations of the local magnetic shear due to the flow can stabilize magnetohydrodynamic ballooning modes.

Physics research on the TCV tokamak facility: from conventional to alternative scenarios and beyond

The research program of the TCV tokamak ranges from conventional to advanced-tokamak scenarios and alternative divertor configurations, to exploratory plasmas driven by theoretical insight, exploiting the device’s unique shaping capabilities. Disruption avoidance by real-time locked mode prevention or unlocking with electron-cyclotron resonance heating (ECRH) was thoroughly documented, using magnetic and radiation triggers. Runaway generation with high-Z noble-gas injection and runaway dissipation by subsequent Ne or Ar injection were studied for model validation. The new 1 MW neutral beam injector has expanded the parameter range, now encompassing ELMy H-modes in an ITER-like shape and nearly non-inductive H-mode discharges sustained by electron cyclotron and neutral beam current drive. In the H-mode, the pedestal pressure increases modestly with nitrogen seeding while fueling moves the density pedestal outwards, but the plasma stored energy is largely uncorrelated to either seeding or fueling. High fueling at high triangularity is key to accessing the attractive small edge-localized mode (type-II) regime. Turbulence is reduced in the core at negative triangularity, consistent with increased confinement and in accord with global gyrokinetic simulations. The geodesic acoustic mode, possibly coupled with avalanche events, has been linked with particle flow to the wall in diverted plasmas. Detachment, scrape-off layer transport, and turbulence were studied in L- and H-modes in both standard and alternative configurations (snowflake, super-X, and beyond). The detachment process is caused by power ‘starvation’ reducing the ionization source, with volume recombination playing only a minor role. Partial detachment in the H-mode is obtained with impurity seeding and has shown little dependence on flux expansion in standard single-null geometry. In the attached L-mode phase, increasing the outer connection length reduces the in–out heat-flow asymmetry. A doublet plasma, featuring an internal X-point, was achieved successfully, and a transport barrier was observed in the mantle just outside the internal separatrix. In the near future variable-configuration baffles and possibly divertor pumping will be introduced to investigate the effect of divertor closure on exhaust and performance, and 3.5 MW ECRH and 1 MW neutral beam injection heating will be added.

Alfvén eigenmodes and fast ion transport in negative triangularity DIII-D plasmas

The first energetic particle experiments in negative triangularity tokamak plasmas have been carried out on DIII-D. Alfvén eigenmode (AE) activity and associated fast ion transport comparable to that in positive triangularity is observed during the current ramp portion of all plasmas with early beam heating indicating negative triangularity does not confer a special advantage with respect to AE induced transport. In these discharges, a range of mode activity driven by the sub-Alfvénic () 80 kV neutral beams is found including beta induced Alfvén acoustic eigenmodes, beta induced Alfvén eigenmodes, reversed shear Alfvén eigenmodes (RSAEs) and toroidicity induced Alfvén eigenmodes (TAEs). Mode intermittency and possibly chirping appears to be more common than comparable positive triangularity and/or oval discharges but overall, the unstable spectra and mode amplitudes observed on magnetics, CO2 interferometry, and electron cyclotron emission in a set of matched positive and negative triangularity cases at moderate beam power is similar. Large levels of Alfvén eigenmode induced fast ion transport are found in both positive and negative triangularity with up to central fast ion pressure deficits relative to classical predictions early during the current ramp phase for discharges with 3 MW injected 80 kV neutral beam power. The deficit in both cases is reduced toward zero as the current penetrates and eventually reaches classical levels during current flattop with . Fast ion transport in negative triangularity plasmas measured using a beam modulation technique show very similar levels to those measured in oval plasmas over the range of tested beam powers (–7 MW). This similarity is found despite quite different unstable spectra in the highest beam power case where a mixture of coherent and quasi-coherent modes in the TAE frequency range are observed in negative triangularity and a spectrum of more typical narrowband TAEs and RSAEs is observed for the oval plasmas.

Central ion cyclotron emission in the DIII-D tokamak

Collective ion cyclotron emission (ICE) at the ion cyclotron frequency and its harmonics is a potential passive diagnostic of the fast-ion distribution in fusion reactors. ICE is observed in most plasmas in the DIII-D tokamak and is most strongly excited by the fast ions from neutral beam injection. The conventional outboard-edge ICE is detected in H-mode plasmas. However, weaker centrally-localized ICE is measured in L-mode plasmas, including those with negative triangularity shapes. Similar ICE spectra are found with both ICE diagnostics systems, the dedicated magnetic probes and the instrumented antenna straps. Many differences in the behavior of this central ICE are generated by varying the deuterium beam injection angle into deuterium plasmas. The co-current ‘near-perpendicular’ beam excites the most central ICE from the co-current beams, with this emission detected from the fundamental to the fifth ICE harmonic. However, the counter-current ‘near-tangential’ beam destabilizes the highest amounts of centrally-localized ICE. This emission is spectrally broader than that driven by the co-current beams and is observed up to its seventh ICE harmonic. The central ICE excited by this co-current beam correlated strongly on the local electron density and related parameters (plasma current and neutron rate) and increased with deeper fast-ion loss boundaries towards the magnetic axis. This was also the case with second harmonic ICE driven by the counter-current beam but not with its stronger third harmonic emission. The central ICE harmonics destabilized by both beams are observed to have different temporal dynamics. The central ICE amplitude responds rapidly to transient MHD events; it dropped and recovered in less than a millisecond at each sawtooth event. ICE frequency splitting is triggered by both the co-current and counter-current ‘near-tangential’ beams. The data presented in this paper provide opportunities to test and validate models of excitation of ICE by energetic ions.

L-mode-edge negative triangularity tokamak reactor

The negative triangularity tokamak (NTT) is a unique reactor concept based on ‘power-handling-first’ philosophy with the heat exhaust problem as the leading concern. The present paper exposes a reactor concept using L-mode edge based on NTT configuration, providing merits of no (or very weak) edge-localized modes, larger particle flux and large major radius for power handling. It is shown that a reasonably compact (Rp from 9 m to 7 m) NTT reactor is possible by achieving higher confinement improvement (HH = 1.5) and/or by utilizing reasonably higher magnetic field (Bmax = 15.5 T). Current physics basis and critical issues on its scientific and technical feasibility are discussed.

H-mode grade confinement in L-mode edge plasmas at negative triangularity on DIII-D

Plasmas with a negative triangularity shape have been created on the DIII-D tokamak that, despite maintaining standard L-mode edge radial profiles, reach volume averaged pressure levels typical of H-mode scenarios. Within the auxiliary power available for these experiments, plasmas exhibit near-zero power degradation while sustaining βN = 2.7 and H98,y2 = 1.2 for several energy confinement times. Detailed comparison with matched discharges at positive triangularity indicates that Trapped Electron Modes are weakened at negative triangularity, consistent with increased confinement and reduced intensity of fluctuations in electron density, electron temperature, and ion density. These results indicate that a negative triangularity plasma operating without an edge pedestal might provide an attractive scenario for operations in future reactors.

Hot VDE investigation of the negative triangularity plasmas based on HL-2M tokamak

Heating loads on the divertor has been the major issue for the tokamak operation. The innovative negative triangularity plasmas are considered to be of the favorable property for the power handling. Investigating the hot-plasma vertical displacement events of the negative triangularity plasma has an important significance for the future fusion reactors. In this paper, the hot-plasma vertical displacement event of the negative triangularity plasmas are investigated by the DINA code, based on the new medium-sized copper conducting tokamak HL-2M. Simulation results show that: (i) The initial vertical instability, of the negative triangularity configuration, develops much more faster than that of the positive triangularity configurations; (ii) During the hot VDE, larger absolute value of the negative triangularity causes speeder development of the initial vertical instability and severer mechanical loads; (iii) During the hot VDE of the negative triangularity plasma, the most non-uniform distribution of the electromagnetic force almost occurs in the outer part of the vacuum vessel. Therefore, an arc design of this part is recommended; (iv) The initial vertical instability, as well as the electromagnetic loads, can be mitigated, by further optimizing the magnetic structure around the divertor region.

Achievement of Reactor-Relevant Performance in Negative Triangularity Shape in the DIII-D Tokamak.

Plasma discharges with a negative triangularity (δ=-0.4) shape have been created in the DIII-D tokamak with a significant normalized beta (β_{N}=2.7) and confinement characteristic of the high confinement mode (H_{98y2}=1.2) despite the absence of an edge pressure pedestal and no edge localized modes (ELMs). These inner-wall-limited plasmas have a similar global performance as a positive triangularity (δ=+0.4) ELMing H-mode discharge with the same plasma current, elongation and cross sectional area. For cases both of dominant electron cyclotron heating with T_{e}/T_{i}>1 and dominant neutral beam injection heating with T_{e}/T_{i}=1, turbulent fluctuations over radii 0.5<ρ<0.9 were reduced by 10-50% in the negative triangularity shape compared to the matching positive triangularity shape, depending on the radius and conditions.

Dependence of density fluctuations on shape and collisionality in positive- and negative-triangularity tokamak plasmas

The effects of plasma shaping, in particular of the triangularity δ, on plasma turbulence, in terms of relative density fluctuations, have been studied in the TCV tokamak. It has been found that for inner wall limited L-mode plasmas, negative triangularity leads to a substantial reduction of turbulence amplitude, as well as of the spectral index and correlation length, consistent with the beneficial effect on energy confinement. Crucially, this reduction extends deep in the core, where the local triangularity becomes vanishingly small. A stabilizing effect of effective collisionality on trapped electron mode turbulence was also observed. These observations are consistent with previous experimental results on the effects of triangularity and collisionality on electron heat transport, as well as with global gyrokinetic GENE simulation results.

Feedback stabilization of ideal kink and resistive wall modes in tokamak plasmas with negative triangularity

Active control of the ideal external kink mode and the resistive wall mode (RWM) is numerically investigated using the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), for a reactor relevant tokamak plasma shaped with negative triangularity (NTR). Magnetic coils are used as the actuators of the control system. An ideal feedback system (i.e. with no time delays), located inside the vacuum vessel, is shown to be capable of stabilizing the external kink mode and moderately increasing the ideal-wall beta limit by up to 10%. Despite the rather different plasma boundary shape as compared to the conventional D-shaped plasma, the optimal poloidal location of the active coils is still the low-field-side of the torus. The eddy currents in the wall may enhance or cancel the control field produced by active coils depending on the poloidal location of the active coils, thus improving or deteriorating the feedback performance. For a single row of active coils, the optimal poloidal width is about 50° for the RWM stabilization, for the NTR plasmas considered in this study. With two rows of coils, optimization of the feedback gain phasing helps to substantially improve the RWM control. The control performance experiences jumps as the radial location of the active coils is shifted across the poloidal sensor location, as shown in both MARS-F computations and by an analytic model.

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A twofold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.