Electron Heat Flux Research Articles

Electron critical gradient scale length measurements of ICRF heated L-mode plasmas at Alcator C-Mod tokamak

A profile for the critical gradient scale length (Lc) has been measured in L-mode discharges at the Alcator C-Mod tokamak, where electrons were heated by an ion cyclotron range of frequency through minority heating with the intention of simultaneously varying the heat flux and changing the local gradient. The electron temperature gradient scale length (LTe−1 = |∇Te|/Te) profile was measured via the BT-jog technique [Houshmandyar et al., Rev. Sci. Instrum. 87, 11E101 (2016)] and it was compared with electron heat flux from power balance (TRANSP) analysis. The Te profiles were found to be very stiff and already above the critical values, however, the stiffness was found to be reduced near the q = 3/2 surface. The measured Lc profile is in agreement with electron temperature gradient (ETG) models which predict the dependence of Lc−1 on local Zeff, Te/Ti, and the ratio of the magnetic shear to the safety factor. The results from linear Gene gyrokinetic simulations suggest ETG to be the dominant mode of turbulence in the electron scale (k⊥ρs > 1), and ion temperature gradient/trapped electron mode modes in the ion scale (k⊥ρs < 1). The measured Lc profile is in agreement with the profile of ETG critical gradients deduced from Gene simulations.

Simulations of particle and heat fluxes in an ELMy H-mode discharge on EAST using BOUT++ code

In order to study the distribution and evolution of the transient particle and heat fluxes during edge-localized mode (ELM) bursts on the Experimental Advanced Superconducting Tokamak (EAST), the BOUT++ six-field two-fluid model is used to simulate the pedestal collapse. The profiles from the EAST H-mode discharge #56129 are used as the initial conditions. Linear analysis shows that the resistive ballooning mode and drift-Alfven wave are two dominant instabilities for the equilibrium, and play important roles in driving ELMs. The evolution of the density profile and the growing process of the heat flux at divertor targets during the burst of ELMs are reproduced. The time evolution of the poloidal structures of T e is well simulated, and the dominant mode in each stage of the ELM crash process is found. The studies show that during the nonlinear phase, the dominant mode is 5, and it changes to 0 when the nonlinear phase goes to saturation after the ELM crash. The time evolution of the radial electron heat flux, ion heat flux, and particle density flux at the outer midplane (OMP) are obtained, and the corresponding transport coefficients D r, χ ir, and χ er reach maximum around 0.3 ∼ 0.5 m2 s−1 at ΨN = 0.9. The heat fluxes at outer target plates are several times larger than that at inner target plates, which is consistent with the experimental observations. The simulated profiles of ion saturation current density (j s) at the lower outboard (LO) divertor target are compared to those of experiments by Langmuir probes. The profiles near the strike point are similar, and the peak values of j s from simulation are very close to the measurements.

Validation of gyrokinetic simulations with measurements of electron temperature fluctuations and density-temperature phase angles on ASDEX Upgrade

Measurements of turbulent electron temperature fluctuation amplitudes, δTe⊥/Te, frequency spectra, and radial correlation lengths, Lr(Te⊥), have been performed at ASDEX Upgrade using a newly upgraded Correlation ECE diagnostic in the range of scales k⊥<1.4 cm−1, kr<3.5 cm−1 (k⊥ρs<0.28 and krρs<0.7). The phase angle between turbulent temperature and density fluctuations, αnT, has also been measured by using an ECE radiometer coupled to a reflectometer along the same line of sight. These quantities are used simultaneously to constrain a set of ion-scale non-linear gyrokinetic turbulence simulations of the outer core (ρtor = 0.75) of a low density, electron heated L-mode plasma, performed using the gyrokinetic simulation code, GENE. The ion and electron temperature gradients were scanned within uncertainties. It is found that gyrokinetic simulations are able to match simultaneously the electron and ion heat flux at this radius within the experimental uncertainties. The simulations were performed based on a reference discharge for which δTe⊥/Te measurements were available, and Lr(Te⊥) and αnT were then predicted using synthetic diagnostics prior to measurements in a repeat discharge. While temperature fluctuation amplitudes are overestimated by >50% for all simulations within the sensitivity scans performed, good quantitative agreement is found for Lr(Te⊥) and αnT. A validation metric is used to quantify the level of agreement of individual simulations with experimental measurements, and the best agreement is found close to the experimental gradient values.

Kinetic electron model for plasma thruster plumes

A paraxial model of an unmagnetized, collisionless plasma plume expanding into vacuum is presented. Electrons are treated kinetically, relying on the adiabatic invariance of their radial action integral for the integration of Vlasov's equation, whereas ions are treated as a cold species. The quasi-2D plasma density, self-consistent electric potential, and electron pressure, temperature, and heat fluxes are analyzed. In particular, the model yields the collisionless cooling of electrons, which differs from the Boltzmann relation and the simple polytropic laws usually employed in fluid and hybrid PIC/fluid plume codes.

Heat transport modeling of the dot spectroscopy platform on NIF

Electron heat transport within an inertial-fusion hohlraum plasma is difficult to model due to the complex interaction of kinetic plasma effects, magnetic fields, laser-plasma interactions, and microturbulence. Here, simulations using the radiation-hydrodynamic code, HYDRA, are compared to hohlraum plasma experiments which contain a Manganese–Cobalt tracer dot (Barrios et al 2016 Phys. Plasmas 23 056307). The dot is placed either on the capsule or on a film midway between the capsule and the laser-entrance hole. From spectroscopic measurements, electron temperature and position of the dot are inferred. Simulations are performed with ad hoc flux limiters of f = 0.15 and f = 0.03 (with electron heat flux, q, limited to fnT3/2/m1/2), and two more physical means of flux limitation: the magnetohydrodynamics and nonlocal packages. The nonlocal model agrees best with the temperature of the dot-on-film and dot-on-capsule. The hohlraum produced x-ray flux is over-predicted by roughly ∼11% for the f = 0.03 model and the remaining models by ∼16%. The simulated trajectories of the dot-on-capsule are slightly ahead of the experimental trajectory for all but the f = 0.03 model. The simulated dot-on-film position disagrees with the experimental measurement for all transport models. In the MHD simulation of the dot-on-film, the dot is strongly perturbative, though the simulation predicts a peak dot-on-film temperature 2–3 keV higher than the measurement. This suggests a deficiency in the MHD modeling possibly due to the neglect of the Righi–Leduc term or interpenetrating flows of multiple ion species which would reduce the strength of the self-generated fields.

Numerical characterization of the edge transport conditions and limiter fluxes of the HIDRA stellarator

The Hybrid Illinois Device for Research and Applications (HIDRA) is a new device for education and Plasma-Material Interaction research at the University of Illinois at Urbana-Champaign. In advance of its first operational campaign, EMC3-EIRENE simulations have been run on the device. EMC3-EIRENE has been modified to calculate a per-plasma-cell relaxed Bohm-like diffusivity simultaneously with the electron temperature at each iteration. In our characterization, the electron temperature, diffusivity, heat fluxes, and particle fluxes have been obtained for varying power levels on a HIDRA magnetic grid, and scaling laws have been extracted, using constraints from previous experimental data taken when the device was operated in Germany (WEGA facility). Peak electron temperatures and heat fluxes were seen to follow a power-law dependence on the deposited radiofrequency (RF) power of type f(PRF)∝aPRFb, with typical exponents in the range of b ∼0.55 to 0.60. Higher magnetic fields have the tendency to linearize the heat flux dependence on the RF power, with exponents in the range of b ∼ 0.75. Particle fluxes are seen to saturate first, and then slightly decline for RF powers above 120 kW in the low-field case and 180 kW in the high-field case.

Characterization of an electrothermal plasma source for fusion transient simulations

The realization of fusion energy requires materials that can withstand high heat and particle fluxes at the plasma material interface. In this work, an electrothermal (ET) plasma source has been designed as a transient heat flux source for a linear plasma material interaction device. An ET plasma source operates in the ablative arc regime driven by a DC capacitive discharge. The current channel width is defined by the 4 mm bore of a boron nitride liner. At large plasma currents, the arc impacts the liner wall, leading to high particle and heat fluxes to the liner material, which subsequently ablates and ionizes. This results in a high density plasma with a large unidirectional bulk flow out of the source exit. The pulse length for the ET source has been optimized using a pulse forming network to have durations of 1 and 2 ms. The peak currents and maximum source energies seen in this system are 1.9 kA and 1.2 kJ for the 2 ms pulse and 3.2 kA and 2.1 kJ for the 1 ms pulse, respectively. This work is a proof of the principal project to show that an ET source produces electron densities and heat fluxes comparable to those anticipated in transient events in large future magnetic confinement fusion devices. Heat flux, plasma temperature, and plasma density were determined for each shot using infrared imaging and optical spectroscopy techniques. This paper will discuss the assumptions, methods, and results of the experiments.

Suppression of Electron Thermal Conduction by Whistler Turbulence in a Sustained Thermal Gradient.

The dynamics of weakly magnetized collisionless plasmas in the presence of an imposed temperature gradient along an ambient magnetic field is explored with particle-in-cell simulations and modeling. Two thermal reservoirs at different temperatures drive an electron heat flux that destabilizes off-angle whistler-type modes. The whistlers grow to large amplitude, δB/B_{0}≃1, and resonantly scatter the electrons, significantly reducing the heat flux. Surprisingly, the resulting steady-state heat flux is largely independent of the thermal gradient. The rate of thermal conduction is instead controlled by the finite propagation speed of the whistlers, which act as mobile scattering centers that convect the thermal energy of the hot reservoir. The results are relevant to thermal transport in high-β astrophysical plasmas such as hot accretion flows and the intracluster medium of galaxy clusters.

Simulation of density fluctuations before the L-H transition for Hydrogen and Deuterium plasmas in the DIII-D tokamak using the BOUT++ code

A six-field two-fluid model has been used to simulate density fluctuations. The equilibrium is generated by experimental measurements for both Deuterium (D) and Hydrogen (H) plasmas at the lowest densities of DIII-D low to high confinement (L-H) transition experiments. In linear simulations, the unstable modes are found to be resistive ballooning modes with the most unstable mode number n = 30 or .The ion diamagnetic drift and convection flow are balanced when the radial electric field (Er) is calculated from the pressure profile without net flow. The curvature drift plays an important role in this stage. Two poloidally counter propagating modes are found in the nonlinear simulation of the D plasma at electron density m−3 near the separatrix while a single ion mode is found in the H plasma at the similar lower density, which are consistent with the experimental results measured by the beam emission spectroscopy (BES) diagnostic on the DIII-D tokamak. The frequency of the electron modes and the ion modes are about 40 kHz and 10 kHz respectively. The poloidal wave number is about 0.2 cm−1 () for both ion and electron modes.The particle flux, ion and electron heat fluxes are ∼3.5–6 times larger for the H plasma than the D plasma, which makes it harder to achieve H-mode for the same heating power. The change of the atomic mass number A from 2 to 1 using D plasma equilibrium make little difference on the flux. Increase the electric field will suppress the density fluctuation. The electric field scan and ion mass scan results show that the dual-mode results primarily from differences in the profiles rather than the ion mass.

Progress in diagnostics of the COMPASS tokamak

The COMPASS tokamak at IPP Prague is a small-size device with an ITER-relevant plasma geometry and operating in both the Ohmic as well as neutral beam assisted H-modes since 2012. A basic set of diagnostics installed at the beginning of the COMPASS operation has been gradually broadened in type of diagnostics, extended in number of detectors and collected channels and improved by an increased data acquisition speed. In recent years, a significant progress in diagnostic development has been motivated by the improved COMPASS plasma performance and broadening of its scientific programme (L-H transition and pedestal scaling studies, magnetic perturbations, runaway electron control and mitigation, plasma-surface interaction and corresponding heat fluxes, Alfvenic and edge localized mode observations, disruptions, etc.). In this contribution, we describe major upgrades of a broad spectrum of the COMPASS diagnostics and discuss their potential for physical studies. In particular, scrape-off layer plasma diagnostics will be represented by a new concept for microsecond electron temperature and heat flux measurements - we introduce a new set of divertor Langmuir and ball-pen probe arrays, newly constructed probe heads for reciprocating manipulators as well as several types of standalone probes. Among optical tools, an upgraded high-resolution edge Thomson scattering diagnostic for pedestal studies and a set of new visible light and infrared (plasma-surface interaction investigations) cameras will be described. Particle and beam diagnostics will be covered by a neutral particle analyzer, diagnostics on a lithium beam, Cherenkov detectors (for a direct detection of runaway electrons) and neutron detectors. We also present new modifications of the microwave reflectometer for fast edge density profile measurements.

Multi-scale gyrokinetic simulations of an Alcator C-Mod, ELM-y H-mode plasma

High fidelity, multi-scale gyrokinetic simulations capable of capturing both ion () and electron-scale () turbulence were performed in the core of an Alcator C-Mod ELM-y H-mode discharge which exhibits reactor-relevant characteristics. These simulations, performed with all experimental inputs and realistic ion to electron mass ratio () provide insight into the physics fidelity that may be needed for accurate simulation of the core of fusion reactor discharges. Three multi-scale simulations and series of separate ion and electron-scale simulations performed using the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) are presented. As with earlier multi-scale results in L-mode conditions (Howard et al 2016 Nucl. Fusion 56 014004), both ion and multi-scale simulations results are compared with experimentally inferred ion and electron heat fluxes, as well as the measured values of electron incremental thermal diffusivities—indicative of the experimental electron temperature profile stiffness. Consistent with the L-mode results, cross-scale coupling is found to play an important role in the simulation of these H-mode conditions. Extremely stiff ion-scale transport is observed in these high-performance conditions which is shown to likely play and important role in the reproduction of measurements of perturbative transport. These results provide important insight into the role of multi-scale plasma turbulence in the core of reactor-relevant plasmas and establish important constraints on the the fidelity of models needed for predictive simulations.

Return current instability driven by a temperature gradient in ICF plasmas

Hot plasmas with strong temperature gradients in inertial confinement fusion experiments are examined for ion acoustic instabilities produced by electron heat flow. The return current instability (RCI) due to a neutralizing current of cold electrons arising in response to a large electron heat flux has been considered. First, the linear threshold and growth rates are derived in the non-local regime of thermal transport. They are compared with the results of Vlasov–Fokker–Planck (VFP) simulations in one spatial dimension. Very good agreement has been found between kinetic VFP simulations and the linear theory of the RCI. A quasi-stationary state of ion acoustic turbulence (IAT) produced by the RCI is achieved in the VFP simulations. Saturation of the RCI involves heating of ions in the tail of the ion distribution function and convection of the enhanced ion acoustic fluctuations from the unstable region of the plasma. Further evolution of the IAT and its effects on absorption and transport are also discussed.

Peculiar properties of internal transport barrier formation near the q = 1 and q = 2 surfaces in tokamaks

A new type of internal transport barrier (ITB) was found in the T-10 tokamak plasma for the first time. It is created by sawtooth oscillations which are almost damped by off-axis electron cyclotron resonance heating and electron cyclotron current drive (ECRH and ECCD). During the ITB formation, the electron temperature, Te, at a relative radius r/a ≤ 0.45 rapidly rises to a new quasi-steady state, while the turbulence level, which is measured at the ITB, falls below its pre-crash value, and the turbulence spectrum shrinks in a wide range of frequencies. The ITB appears near the q = 1 magnetic surface and exists for approximately 50–70% of the plasma energy confinement time. During this process, accumulation of impurities was not observed. An abrupt and non-local reduction of the electron heat flux (ITB-event) around the q = 1 surface (within 1 ms in the spatial zone with a relative radius 0.2 < r/a < 0.5) was observed for the first time for the case with a gas puffing cut-off in OH T-10 discharges with an increasing high density. In contrast to the ITB that forms during the ECR heating, in this case, impurities begin to accumulate simultaneously with the ITB event. Analysis of the D-III-D experiments with a weak reverse magnetic shear shows that the appearance of a qmin = 2 surface leads to this ITB event in a very wide spatial region (the relative radius of the plasma column is 0 < r/a < 0.7).

An improved and fully implicit multi-group non-local electron transport model and its validations

The combined effect of thermal flux inhibition and non-local electron heat flux in the radiation hydrodynamics (RHD) simulation of laser-driven systems can be accurately predicted by using non-local electron transport (NLET) models. These models can avoid commonly used space and time-independent ad-hoc flux-limiting procedures. However, the use of classical electron collision frequency in these models is rigorously valid for high temperature non-degenerate plasmas. In laser-driven systems, the electron thermal energy transport is important in regions between the critical density and ablation surface where the plasma is partially degenerate. Therefore, an improved model for electron collision frequency in this regime is required to accurately predict the thermal energy transport. Previously, we have reported an improved single group non-local electron transport model by using a wide-range electron collision frequency model valid from warm-dense matter (WDM) to fully ionized plasmas. In this work, we have extended this idea into a two-dimensional multi-group non-local electron transport (MG-NLET) model. Moreover, we have used a fully implicit numerical integration scheme in which the models for multi-group thermal radiation transport, laser absorption, electron-ion thermal energy relaxation and ion heat conduction are included in a single step. The performance of this improved MG-NLET model has been assessed by comparing the simulated foil trajectories with the reported experimental data for laser-driven plastic foils. The results indicate that the improved model yields results that are in better agreement with the experimental data.

Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER

The XGC1 edge gyrokinetic code is used to study the width of the heat-flux to divertor plates in attached plasma condition. The flux-driven simulation is performed until an approximate power balance is achieved between the heat-flux across the steep pedestal pressure gradient and the heat-flux on the divertor plates. The simulation results compare well against the empirical scaling λ q 1/ obtained from present tokamak devices, where λ q is the divertor heat-flux width mapped to the outboard midplane, γ = 1.19 as found by Eich et al (2013 Nucl. Fusion 53 093031), and B P is the magnitude of the poloidal magnetic field at the outboard midplane separatrix surface. This empirical scaling predicts λ q ≲ 1 mm when extrapolated to ITER, which would require operation with very high separatrix densities (n sep/n Greenwald > 0.6) (Kukushkin et al 2013 J. Nucl. Mater. 438 S203) in the Q = 10 scenario to achieve semi-detached plasma operation and high radiative fractions for acceptable divertor power fluxes. Using the same simulation code and technique, however, the projected λ q for ITER’s model plasma is 5.9 mm, which could be suggesting that operation in the ITER Q = 10 scenario with acceptable divertor power loads may be obtained over a wider range of plasma separatrix densities and radiative fractions. The physics reason behind this difference is, according to the XGC1 results, that while the ion magnetic drift contribution to the divertor heat-flux width is wider in the present tokamaks, the turbulent electron contribution is wider in ITER. Study will continue to verify further this important projection. A high current C-Mod discharge is found to be in a mixed regime: While the heat-flux width by the ion neoclassical magnetic drift is still wider than the turbulent electron heat-flux width, the heat-flux magnitude is dominated by the narrower electron heat-flux.

Changes in divertor conditions in response to changing core density with RMPs

The effects of changes in core density on divertor electron temperature, density and heat flux when resonant magnetic perturbations (RMPs) are applied are presented, notably a reduction in RMP induced secondary radial peaks in the electron temperature profile at the target plate is observed when the core density is increased, which is consistent with modeling. RMPs is used here to indicate non-axisymmetric magnetic field perturbations, created using in-vessel control coils, which have at least one but typically many resonances with the rotational transform of the plasma (Evans et al 2006 Phys. Plasmas 13 056121). RMPs are found to alter inter-ELM heat flux to the divertor by modifying the core plasma density. It is shown that applying RMPs reduces the core density and increases the inter-ELM heat flux to both the inner and outer targets. Using gas puffing to return the core density to the pre-RMP levels more than eliminates the increase in inter-ELM heat flux, but a broadening of the heat flux to the outer target remains. These measurements were made at a single toroidal location, but the peak in the heat flux profile was found near the outer strike point where simulations indicate little toroidal variation should exist and tangentially viewing diagnostics showed no evidence of strong asymmetries. In experiments where divertor Thomson scattering measurements were available it is shown that local secondary peaks in the divertor electron temperature profile near the target plate are reduced as the core density is increased, while peaks in the divertor electron density profile near the target are increased. These trends observed in the divertor electron temperature and density are qualitatively reproduced by scanning the upstream density in EMC3-Eirene modeling. Measurements are presented showing that higher densities are needed to induce detachment of the outer strike point in a case where an increase in electron temperature, likely due to a change in MHD activity, is seen after RMPs are applied.

Effect of nonlinear energy transport on neoclassical tearing mode stability in tokamak plasmas

An investigation is made into the effect of the reduction in anomalous perpendicular electron heat transport inside the separatrix of a magnetic island chain associated with a neoclassical tearing mode in a tokamak plasma, due to the flattening of the electron temperature profile in this region, on the overall stability of the mode. The onset of the neoclassical tearing mode is governed by the ratio of the divergences of the parallel and perpendicular electron heat fluxes in the vicinity of the island chain. By increasing the degree of transport reduction, the onset of the mode, as the divergence ratio is gradually increased, can be made more and more abrupt. Eventually, when the degree of transport reduction passes a certain critical value, the onset of the neoclassical tearing mode becomes discontinuous. In other words, when some critical value of the divergence ratio is reached, there is a sudden bifurcation to a branch of neoclassical tearing mode solutions. Moreover, once this bifurcation has been triggered, the divergence ratio must be reduced by a substantial factor to trigger the inverse bifurcation.

Kinetic simulations of electron heat flux in the scrape-off layer

Parallel electron heat flux qe|| on open field lines is studied with the 1D2V kinetic Vlasov-Fokker-Planck (VFP) code KIPP [15–17]. In order to assess the importance of kinetic effects on the scrape-off layer heat transport in a systematic way, a series of self-similar KIPP cases with the stagnation point and one target, logical sheath condition, parabolic ion velocity profiles reaching ion sound speed at the target were run. The variable parameter was upstream electron collisionality v* (collisionality scan cases) and for each collisionality two different numerical schemes of particle source were implemented for comparison. It shows no significant difference between the results with two different schemes of particle source for any scanned collisionality. In high collisionality cases, heat flux converges to Braginskii formula as expected, while in comparatively low collisionality cases transport coefficients deviate far away from classical value due to target cut-off effect implicating that fluid model is not applicable near the target.Enhanced radiation near the target, forcing Te drop by factor 10 for low upstream v* comparable to that expected at the separatrix in the ITER baseline H-mode scenario, was required in KIPP runs. Pairs of such cases with two different ways of radiation power sink, by modeling sink (a) evenly from all velocity space, and (b) only from high energy electrons, were compared. The simulation results show almost no difference between the two cases in the steady-state, despite the presence of a strong heat flux limiting upstream and enhancement downstream.

Collisionality scaling of the electron heat flux in ETG turbulence

In electrostatic simulations of MAST plasma at electron-gyroradius scales, using the local flux-tube gyrokinetic code GS2 with adiabatic ions, we find that the long-time saturated electron heat flux (the level most relevant to energy transport) decreases as the electron collisionality decreases. At early simulation times, the heat flux ‘quasi-saturates’ without any strong dependence on collisionality, and with the turbulence dominated by streamer-like radially elongated structures. However, the zonal fluctuation component continues to grow slowly until much later times, eventually leading to a new saturated state dominated by zonal modes and with the heat flux proportional to the collision rate, in approximate agreement with the experimentally observed collisionality scaling of the energy confinement in MAST. We outline an explanation of this effect based on a model of ETG turbulence dominated by zonal–nonzonal interactions and on an analytically derived scaling of the zonal-mode damping rate with the electron–ion collisionality. Improved energy confinement with decreasing collisionality is favourable towards the performance of future, hotter devices.

Validation of nonlinear gyrokinetic simulations of L- and I-mode plasmas on Alcator C-Mod

New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale (cross-scale coupling) effects [Howard PoP 2016] may be less important in I-mode than in L-mode. New results presented here, however, show that global, nonlinear, ion-scale GYRO simulations are able to match the experimental ion heat flux, but underpredict electron heat flux (at most radii), electron temperature fluctuations, and perturbative thermal diffusivity in both L- and I-mode. Linear addition of electron heat flux from electron scale runs does not resolve this discrepancy. These results indicate that single-scale simulations do not sufficiently describe the I-mode core transport, and that multi-scale (coupled electron- and ion-scale) transport models are needed. A preliminary investigation with multi-scale TGLF, however, was unable to resolve the discrepancy between ion-scale GYRO and experimental electron heat fluxes and perturbative diffusivity, motivating further work with multi-scale GYRO simulations and a more comprehensive study with multi-scale TGLF.