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At least 973 records · Page 54

Macroscopic trends of linear tearing stability in cylindrical current profiles

Abstract The likelihood of realising tokamak power-plants will be greatly improved by the discovery of high-gain equilibria that resist the formation of small islands and hence avoid the disruptive neoclassical tearing mode. We propose a series of studies to understand how simple tokamak design can leverage aspects of tearing onset physics to maximise passive resistance to island formation. Here we investigate the variation that current profiles can bring about in preventing tearing onset through the cylindrical linear tearing stability parameter Δ ′ . A database of 159148 realistic pilot-plant current profiles was generated with Monte Carlo sampling, and the distribution of Δ ′ values was linked with interpretable profile characteristics. In agreement with prior theoretical and experimental studies, Δ ′ was found to be strongly correlated with the existence and steepness of a local toroidal current well or hill, with the former destabilising and the latter stabilising. In the absence of these two cases, the remaining Δ ′ values were linearly bounded by the toroidal current gradient at the rational surface.

Physics↗

Simultaneous control of the electron temperature and safety factor profiles in DIII-D using model-based optimal control techniques

Future tokamak power plants will likely operate using a single, well-defined plasma scenario, either in steady state or for very long pulse lengths. In order to enhance the robustness of the scenario, feedback controllers for a variety of plasma properties will be necessary to counteract any disturbances and ensure safe operation. However, only a limited set of actuators will be available to control many different quantities. Because of this, it is necessary to develop controllers that are able to regulate multiple plasma properties using a limited set of actuators. To this end, a controller has been developed for the simultaneous regulation of both the electron temperature and safety factor profiles in DIII-D. This algorithm uses a linear quadratic integral control synthesis approach based on a linearized model of the dynamics of the two profiles. Two neural network surrogate models, NubeamNet and MMMnet, are included to improve the fidelity of the model. Furthermore, the controller has been tested in simulation using COTSIM, and has demonstrated the ability to simultaneously track changes in both the electron temperature and safety factor targets, including changes in both the magnitude and the shape of the profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Zoomed high-resolution simulations of Multi-coupled Dark Energy: cored galaxy density profiles at high redshift

We perform for the first time high-resolution zoom-in re-simulations of individual halos in the context of the Multi-coupled Dark Energy (McDE) scenario, which is characterised by the existence of two distinct Dark Matter particle species with opposite couplings to a Dark Energy scalar field. We compare the structural properties of the simulated halos to the standard ΛCDM results. The zoomed-in initial conditions are set up using a specifically designed code called ZInCo that we publicly release along with the present paper. Our numerical results allow to investigate in detail and with unprecedented resolution the halo segregation process that characterises McDE cosmologies from its very early stages. In particular, we find that in contrast to what could be inferred from previous numerical analysis at lower resolution, the segregation process is already in place at redshifts as high as z ∼ 7. Most remarkably, we find that the subsequent evolution of the segregation leads to the formation of cored total matter density profiles with a core size that progressively increases in time. The shape of the cored profiles can be accurately predicted as the superposition of two NFW profiles with an increasing offset, thereby confirming the interpretation of the simulations results in terms of the segregation of the two dark matter components of the halo as a consequence of their different coupling to the Dark Energy field.

79 ASTRONOMY AND ASTROPHYSICS↗

Dependence of scrape-off layer profiles and turbulence on gas fuelling in high density H-mode regimes in TCV

A set of high density, highly shaped H-mode discharges has been performed in the TCV tokamak with the aim of assessing the effects of increasing divertor neutral recycling on the properties of upstream inter-ELM scrape-off layer (SOL) profiles and transport. An increase of divertor neutral pressure has been correlated with the evolution of separatrix properties and turbulence level. The latter has been quantified by means of the α t parameter introduced in (Eich 2020 Nucl. Fusion 60 056016), describing the contribution of resistive-interchange turbulence in the SOL relative to drift wave transport. The analysis reveals a general broadening of the upstream SOL profiles as α t increases, with the SOL power width measured by the vertical IR thermography system increasing significantly. In a similar way, the upstream density profile widens in the near SOL, whereas in the far SOL a density shoulder is observed to progressively form and increase in amplitude. This behaviour is associated with an enhancement of far SOL turbulent transport in the form of blob-filaments travelling radially faster across the far SOL and becoming bigger at higher α t . Finally, the detected filaments, evaluated from the fast reciprocating probe at the outer midplane, are determined to mostly belong to the resistive ballooning and resistive X-point regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energetic particle marginal stability profile for HL-2M integrated simulation based on neural network module

Abstract A critical gradient model is employed to develop a module of energetic particle (EP) marginal stability profiles in OMFIT integrated simulations for studying EP transport. Currently, each iteration of transport evolution is approximately 10 min in the integrated simulation, whereas, the EP marginal stability profile, which serves as an input in the integrated simulation could take much longer; the reason being a combination of the TGLFEP and EPtran codes is employed in our previous investigation. To reduce the simulation time, the critical gradient is predicted by a neural network instead of the TGLFEP code, and the EPtran code is revised with parallel computing, so that the running time of this module can be controlled to within 5 min. The predictions are in good agreement with previous approaches. The integrated simulation of HL-2M with Alfven eigenmodes transported by neutral beam EP profiles indicates that EP transport reduces the total pressure and current as expected, but could also under some conditions raise the safety factor in the core, which is favorable for reversed magnetic shear and high-performance plasmas.

Physics↗

Density and temperature profiles after low-Z and high-Z shattered pellet injections on DIII-D

Abstract In this work we utilize the recently upgraded Thomson scattering diagnostic to resolve density and temperature plasma profiles after pure deuterium and mixed neon/deuterium shattered pellet injections (SPIs) on DIII-D. This allows us to study individual components of the staggered scheme proposed for disruption mitigation on ITER, consisting of a low-Z material SPI followed by a delayed high-Z SPI. Obtained spatio-temporal density profiles exhibit very different dynamics after dominantly neon and pure deuterium SPIs. The neon SPI causes a fast radiative plasma collapse in a few milliseconds and results in almost flat density profile once the impurity mixes with the plasma during and after the thermal quench (TQ). The deuterium SPI leads to a disruption delayed by ten and more milliseconds, but very limited core fueling can be observed before the disruption. Even during and after the TQ, the edge deuterium density significantly exceeds the core density. 1D transport modeling suggests that this poor core fueling can be explained by strong outward grad-B-induced drift of the injected deuterium. Preliminary simulations show that larger pellet shards and greater injected quantity can be used to improve the penetration of the low-Z material into the core. These results call for optimization and further evaluation of the staggered SPI on ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Machine learning-based real-time kinetic profile reconstruction in DIII-D

Abstract Kinetic equilibrium reconstruction plays a vital role in the physical analysis of plasma stability and control in fusion tokamaks. However, the traditional approach is subjective and prone to human biases. To address this, the consistent automatic kinetic equilibrium reconstruction (CAKE) method was introduced, providing objective results. Nonetheless, its offline nature limits its application in real-time plasma control systems (PCSs). To address this limitation, we present RTCAKENN, a machine learning model that approximates 7 CAKE-level output profiles, namely pressure, inverse q , toroidal current density, electron temperature and density, carbon ion impurity temperature and rotation profiles, using real-time available inputs. The deep neural network consists of an encoder layer, where the scalars and interdependent inputs such as plasma boundary coordinates and motional Stark effect data are encoded using multi-layer perceptrons (MLPs), while profile inputs are encoded by 1D convolutional layers. The encoded data is passed through a MLP for latent feature extraction, before being decoded in the decoding layers, which consist of upsampling and convolutional layers. RTCAKENN has been implemented in the DIII-D PCS and our model achieves accuracy comparable to CAKE and surpasses existing real-time alternatives. Through clever dropout training, RTCAKENN exhibits robustness and can operate even in the absence of Thomson scattering data or charge exchange recombination data. It executes in under 8 ms in the real-time environment, enabling future application in real-time control and analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The effect of plasma shaping on high density H-mode SOL profiles and fluctuations in TCV

Abstract The impact of plasma shaping on the properties of high density H-mode scrape-off layer (SOL) profiles and transport at the outer midplane has been investigated on Tokamakà configuration variable. The experimental dataset has been acquired by evolving the upper triangularity while keeping the other parameters constant. The scan comprises δ u p values between 0.0 and 0.6, excluding negative triangularity scenarios. Within this study, a transition from type-I edge localised modes to the quasi-continuous exhaust regime takes place from low to high δ u p . The modification of the upstream SOL profiles has been assessed, in terms of separatrix quantities, within the α t turbulence control parameter theoretical framework (Eich et al 2020 Nucl. Fusion 60 056016). The target parallel heat load and the upstream near-SOL density profiles have been shown to broaden significantly for increasing α t . Correspondingly, in the far SOL a density shoulder formation is observed when moving from low to high δ u p . These behaviours have been correlated with an enhancement of the SOL fluctuation level, as registered by wall-mounted Langmuir probes as well as the thermal helium beam diagnostic. Specifically, both the background and the filamentary-induced fluctuating parts of the first wall ion saturation current signal are larger at higher δ u p , with filaments being ejected more frequently into the SOL. Comparison of two pulses at the extremes of the δ u p scan range, but with otherwise same input parameters, shows that the midplane neutral pressure does not change much during the H-mode phase of the discharge. This indicates that indirect effects of the change in geometry, linked to first wall recycling sources, should not play a significant role. The total core radiation increases at high δ u p , on account of a stronger plasma–wall interaction and resulting larger carbon impurity intake from the first wall. This is likely associated to the enhanced first wall fluctuations, as well as a smaller outer gap and the close-to-double-null magnetic topology at high shaping.

Stagni, A. (ORCID:0000000180841544)↗

Investigating the role of edge neutrals in exciting tearing mode activity and achieving flat temperature profiles in LTX-β

Abstract We present observations, numerical simulations, and analysis from experiments in the Lithium Tokamak Experiment-Beta (LTX- β ) in which the electron temperature profile ( T e ( r )) shifts from flat to peaked and a tearing mode is also destabilized when the average density ( n e ave ) exceeds ∼10 19 m −3 . Flat T e ( r ) is obtained routinely in LTX- β , with a lithium coated, low-recycling first wall, once the external fueling is stopped and density decays [Boyle et al 2023 Nucl. Fusion 63 056020]. In the present experiment, flat T e profiles can be sustained while maintaining constant n e ave below a line averaged density threshold ( n e ave th ) of ∼10 19 m −3 . Above n e ave th , T e ( r ) shifts from flat to peaked and a tearing mode is destabilized. Due to low recycling, the achieved n e ave can be controlled precisely by external fueling and hence, a certain threshold of the edge neutral inventory from the external fueling is experimentally manifested through n e ave th . The goal of the present work is to investigate the role of edge neutrals in determining T e ( r ) and MHD stability in the unique low-recycling regime of LTX- β . Our hypothesis is that the peaking of T e ( r ) beyond n e ave th is due ultimately to the edge cooling by the cold neutrals beyond a critical fueling flux. At lower fueling flux, flat T e ( r ) results in broader pressure profile and lower resistivity, which in turn stabilizes the tearing mode. This hypothesis is supported by edge neutral density estimation by DEGAS 2 code. Mode analysis by singular value decomposition confirms the tearing mode structure to be m / n = 2/1 ( m and n being the poloidal and toroidal mode numbers). Linear tearing stability analysis with M3D-C1 predicts that plasmas with n e ave > 10 19 are highly susceptible to a n = 1 tearing mode. ORBIT simulations, however, confirmed that the tearing modes do not contribute to the loss of fast ions from neutral beam injection. This study shows for the first time that the neutral inventory at the edge could be one of the deciding factors for the achievability of the unique operation regime of flat T e ( r ) and the excitation of tearing activity that could be disruptive for the plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Combining physics-based and data-driven models for quantitatively accurate plasma profile prediction that extrapolates well; with application to DIII-D, AUG, and ITER tokamaks

For design, scenario planning, and control, ITER and all other envisioned tokamaks rely on a variety of statistical and physics-based models to extrapolate to unseen regimes; most notably from low plasma current to high. A 'meta-learning' methodology for combining the accuracy of data-driven models with the generalizability of physics-based models is described and tested, yielding a 5–10 percent improvement in performance beyond either alone for the task of extrapolating time-dependent plasma profile prediction from low- to high- plasma current DIII-D tokamak discharges. Meanwhile, it is shown that both machine learning models extrapolated far-distribution and state-of-the-art 'physics-based' profile predictors fare worse than merely assuming plasma profiles do not change from their initial values. Finally, a variety of other mechanisms for helping data-driven models generalize—transfer learning, adding contextual information from physics simulators, and adding data from the ASDEX Upgrade tokamak—are attempted for similar extrapolation tasks but, in the methodology used in this paper, yield no significant improvement beyond simple data-driven models. Results are summarized in figures 15 and 16.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Real-time breath analysis towards a healthy human breath profile

Abstract The direct analysis of molecules contained within human breath has had significant implications for clinical and diagnostic applications in recent decades. However, attempts to compare one study to another or to reproduce previous work are hampered by: variability between sampling methodologies, human phenotypic variability, complex interactions between compounds within breath, and confounding signals from comorbidities. Towards this end, we have endeavored to create an averaged healthy human ‘profile’ against which follow-on studies might be compared. Through the use of direct secondary electrospray ionization combined with a high-resolution mass spectrometry and in-house bioinformatics pipeline, we seek to curate an average healthy human profile for breath and use this model to distinguish differences inter- and intra-day for human volunteers. Breath samples were significantly different in PERMANOVA analysis and ANOSIM analysis based on Time of Day, Participant ID, Date of Sample, Sex of Participant, and Age of Participant ( p < 0.001). Optimal binning analysis identify strong associations between specific features and variables. These include 227 breath features identified as unique identifiers for 28 of the 31 participants. Four signals were identified to be strongly associated with female participants and one with male participants. A total of 37 signals were identified to be strongly associated with the time-of-day samples were taken. Threshold indicator taxa analysis indicated a shift in significant breath features across the age gradient of participants with peak disruption of breath metabolites occurring at around age 32. Forty-eight features were identified after filtering from which a healthy human breath profile for all participants was created.

60 APPLIED LIFE SCIENCES↗

Elastic full-waveform inversion and parameterization analysis applied to walk-away vertical seismic profile data for unconventional (heavy oil) reservoir characterization

We report seismic full-waveform inversion (FWI) methods hold strong potential to recover multiple subsurface elastic properties for hydrocarbon reservoir characterization. Simultaneously updating multiple physical parameters introduces the problem of interparameter tradeoff, arising from the covariance between different physical parameters, which increases nonlinearity and uncertainty of multiparameter FWI. The coupling effects of different physical parameters are significantly influenced by model parameterization and acquisition arrangement. An appropriate choice of model parameterization is critical to successful field data applications of multiparameter FWI. The objective of this paper is to examine the performance of various model parameterizations in isotropic-elastic FWI with walk-away vertical seismic profile (W-VSP) dataset for unconventional heavy oil reservoir characterization. Six model parameterizations are considered: velocity-density (α, β and ρ'), modulus-density (κ, μ and ρ), Lamé-density (λ, μ' and ρ'''), impedance-density (IP, IS and ρ''), velocity-impedance-I (α', β' and I' P ), and velocity-impedance-II (α'', β'' and I'S). We begin analyzing the interparameter tradeoff by making use of scattering radiation patterns, which is a common strategy for qualitative parameter resolution analysis. In this paper, we discuss the advantages and limitations of the scattering radiation patterns and recommend that interparameter tradeoffs be evaluated using interparameter contamination kernels, which provide quantitative, second-order measurements of the interparameter contaminations and can be constructed efficiently with an adjoint-state approach. Synthetic W-VSP isotropic-elastic FWI experiments in the time domain verify our conclusions about interparameter tradeoffs for various model parameterizations. Density profiles are most strongly influenced by the interparameter contaminations; depending on model parameterization, the inverted density profile can be over-estimated, under-estimated or spatially distorted. Among the six cases, only the velocity-density parameterization provides stable and informative density features not included in the starting model. Field data applications of multicomponent W-VSP isotropic-elastic FWI in the time domain were also carried out. Finally, the heavy oil reservoir target zone, characterized by low α-to-β ratios and low Poisson’s ratios, can be identified clearly with the inverted isotropic-elastic parameters.

58 GEOSCIENCES↗

Galaxy properties as revealed by MaNGA – III. Kinematic profiles and stellar population gradients in S0s

ABSTRACT This is the third paper of a series where we study the stellar population gradients (SP; ages, metallicities, α-element abundance ratios, and stellar initial mass functions) of early-type galaxies (ETGs) at $z$ ≤ 0.08 from the Mapping Nearby Galaxies at APO Data Release 15 (MaNGA-DR15) survey. In this work, we focus on the S0 population and quantify how the SP varies across the population as well as with galactocentric distance. We do this by measuring Lick indices and comparing them to SP synthesis models. This requires spectra with high signal-to-noise ratio which we achieve by stacking in bins of luminosity (Lr) and central velocity dispersion (σ0). We find that: (1) there is a bimodality in the S0 population: S0s more massive than $3\times 10^{10}\, \mathrm{M}_\odot$ show stronger velocity dispersion and age gradients (age and σr decrease outwards) but little or no metallicity gradient, while the less massive ones present relatively flat age and velocity dispersion profiles, but a significant metallicity gradient (i.e. [M/H] decreases outwards). Above $2\times 10^{11}\, \mathrm{M}_\odot$, the number of S0s drops sharply. These two mass scales are also where global scaling relations of ETGs change slope. (2) S0s have steeper velocity dispersion profiles than fast-rotating elliptical galaxies (E-FRs) of the same luminosity and velocity dispersion. The kinematic profiles and SP gradients of E-FRs are both more similar to those of slow-rotating ellipticals (E-SRs) than to S0s, suggesting that E-FRs are not simply S0s viewed face-on. (3) At fixed σ0, more luminous S0s and E-FRs are younger, more metal rich and less α-enhanced. Evidently for these galaxies, the usual statement that ‘massive galaxies are older’ is not true if σ0 is held fixed.

Domínguez Sánchez, H.↗

Cuspy dark matter density profiles in massive dwarf galaxies

ABSTRACT Rotation curves of galaxies probe their total mass distributions, including dark matter. Dwarf galaxies are excellent systems to investigate the dark matter density distribution, as they tend to have larger fractions of dark matter compared to higher mass systems. The core-cusp problem describes the discrepancy found in the slope of the dark matter density profile in the centres of galaxies (β*) between observations of dwarf galaxies (shallower cores) and dark matter-only simulations (steeper cusps). We investigate β* in six nearby spiral dwarf galaxies for which high-resolution CO J = 1–0 data were obtained with ALMA (Atacama Large Millimeter/submillimeter Array). We derive rotation curves and decompose the mass profile of the dark matter using our CO rotation curves as a tracer of the total potential and 4.5 $\mu$m photometry to define the stellar mass distribution. We find 〈β*〉 = 0.6 with a standard deviation of ±0.1 among the galaxies in this sample, in agreement with previous measurements in this mass range. The galaxies studied are on the high stellar mass end of dwarf galaxies and have cuspier profiles than lower mass dwarfs, in agreement with other observations. When the same definition of the slope is used, we observe steeper slopes than predicted by the FIRE and NIHAO simulations. This may signal that these relatively massive dwarfs underwent stronger gas inflows towards their centres than predicted by these simulations, that these simulations overpredict the frequency of accretion or feedback events, or that a combination of these or other effects are at work.

Cooke, Lauren H. (ORCID:0000000284337553)↗

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗

Cation- and lattice-site-selective magnetic depth profiles of ultrathin Fe 3 O 4 (001) films

A detailed understanding of ultrathin film surface properties is crucial for the proper interpretation of spectroscopic, catalytic, and spin-transport data. We present x-ray magnetic circular dichroism (XMCD) and x-ray resonant magnetic reflectivity (XRMR) measurements on ultrathin Fe 3 O 4 films to obtain magnetic depth profiles for the three resonant energies corresponding to the different cation species F e o c t 2 + , F e t e t 3 + , and F e o c t 3 + located on octahedral and tetrahedral sites of the inverse spinel structure of Fe 3 O 4 . By analyzing the XMCD spectrum of Fe 3 O 4 using multiplet calculations, the resonance energy of each cation species can be isolated. Performing XRMR on these three resonant energies yields magnetic depth profiles that each correspond to one specific cation species. The depth profiles of both kinds of Fe 3+ cations reveal a (3.9 ± 1.0) -Å -thick surface layer of enhanced magnetization, which is likely due to an excess of these ions at the expense of the F e o c t 2 + species in the surface region. The magnetically enhanced F e t e t 3 + layer is additionally shifted about 2.9 ± 0.4 Å farther from the surface than the F e o c t 3 + layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Compton profile of VO 2 across the metal-insulator transition: Evidence of a non-Fermi liquid metal

Many-body diffusion Monte Carlo is used to obtain the first-principles momentum distribution and Compton profile of vanadium dioxide. Our results for the Compton profile are in good agreement with the experimental values, and we show that good qualitative agreement in the scaled Compton profile difference across the monoclinic to rutile phase transition depends on an accurate description of electron correlation. The electron momentum distribution enables new insights into the metal-insulator phase transition. For example, the probability for electron scattering in the proximity of the Fermi surface (forward scattering) is suppressed in the vanadium chain direction (rutile c axis) but enhanced in perpendicular directions. However, along the c axis we observe an increase at ~2k F in the momentum distribution, which is characteristic for Friedel oscillations (backscattering). Our analysis of the momentum distribution supports experimentally observed anisotropies and provides an explanation for the anomalously low electronic thermal conductivity observed recently in the metallic phase. Furthermore, our results indicate non-Fermi liquid behavior as well as quasi-one-dimensional Friedel oscillations in the metallic rutile phase, which is reminiscent of a Tomanaga-Luttinger liquid with impurities.

36 MATERIALS SCIENCE↗

Effects of matter density profiles on neutrino oscillations for T2HK and T2HKK

This paper explores the effects of changes in matter density profiles on neutrino oscillation probabilities, and whether these could potentially be seen by the future Hyper-Kamiokande long-baseline oscillation experiment (T2HK). The analysis is extended to include the possibility of having an additional detector in Korea (T2HKK). In both cases, we find that these effects will be immeasurable, as the magnitudes of the changes in the oscillation probabilities induced in all density profile scenarios considered here remain smaller than the estimated experimental sensitivity to the oscillation probabilities of each experiment, for both appearance and disappearance channels. Therefore, we conclude that using a constant density profile is sufficient for both the T2HK and T2HKK experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗