Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (v), convectivity (V), and damping (s) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation.The main result is the approximation of v under the influence of V and s based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate v well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate v, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which v, V, and s can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and s in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and s based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possible to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain

Magnetic Barriers and their q95 dependence at DIII-D

It is well known that externally generated resonant magnetic perturbations (RMPs) can form islands in the plasma edge. In turn, large overlapping islands generate stochastic fields, which are believed to play a role in the avoidance and suppression of edge localized modes (ELMs) at DIII-D. However, large coalescing islands can also generate, in the middle of these stochastic regions, KAM surfaces effectively acting as "barriers" against field-line dispersion and, indirectly, particle diffusion. It was predicted in [H. Ali and A. Punjabi, Plasma Phys. Control. Fusion 49 (2007), 1565-1582] that such magnetic barriers can form in piecewise analytic DIII-D plasma equilibria. In the present work, the formation of magnetic barriers at DIII-D is corroborated by field-line tracing calculations using experimentally constrained EFIT [L. Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. According to these calculations, the occurrence and location of magnetic barriers depends on the edge safety factor q95. It was thus suggested that magnetic barriers might contribute to narrowing the edge stochastic layer and play an indirect role in the RMPs failing to control ELMs for certain values of q95. The analysis of DIII-D discharges where q95 was varied, however, does not show anti-correlation between barrier formation and ELM suppression

Non-local heat transport, rotation reversals and up/down impurity density asymmetries in Alcator C-Mod ohmic L-mode plasmas

Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν[subscript *] ≤ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with k[subscript θ] up to 15 cm[superscript −1] (k[subscript θ]ρ[subscript s] ~ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high k[subscript θ] turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.United States. Dept. of Energy (Contract DE-FC02-99ER54512)United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program

Role of turbulence and electric fields in the establishment of improved confinement in tokamak plasmas

An extensive (INTAS) research programme started in 2002 to investigate the correlations between on the one hand the occurrence of transport barriers and improved confinement in the medium-size tokamaks TEXTOR and T-10 and on the smaller tokamaks FT-2, TUMAN-3M and CASTOR, and on the other hand electric fields, modified magnetic shear and electrostatic and magnetic turbulence using advanced diagnostics with high spatial and temporal resolution and of various active means to externally control plasma transport . This has been done in a strongly coordinated way and exploiting the complementarity of TEXTOR and T-10 and the backup potential of the three other tokamaks, which together have all the relevant experimental tools and theoretical expertise

Role of turbulence and electric fields in the formation of transport barriers and the establishment of improved confinement in tokamak plasmas through inter-machine comparison

Over the past decade new regimes of tokamak operation have been identified, whereby electrostatic and magnetic turbulence responsible for anomalous transport, can be externally suppressed, leading to improved confinement. Although turbulence measurements have been performed on many confinement devices, the insight gained from these experiments is relatively limited. To make further progress in the understanding of plasma turbulence in relation to improved confinement and transport barriers, an extensive experimental and theoretical research programme should be undertaken. The present INTAS project investigates the correlations between on the one hand the occurrence of transport barriers and improved confinement in the tokamaks TEXTOR & T-10 and Tore Supra as well as on the smaller-scale tokamaks FT-2, TUMAN-3M and CASTOR, and on the other hand electric fields, modified magnetic shear and electrostatic and magnetic turbulence using advanced diagnostics with high spatial and temporal resolution. This is done in a strongly coordinated way and exploiting the complementarity of TEXTOR and T-10 and the backup potential of the other tokamaks, which together have all the relevant experimental tools and theoretical expertise. Advanced theoretical models and numerical simulations are used to check the experimental results.За останні десять років було отримано нові режими роботи токамаків, у яких електростатична і магнітна турбулентність, відповідальна за аномальний перенос, могла заглушатися шляхом зовнішнього впливу, і тим самим досягалося поліпшене утримання. Незважаючи на те, що дослідження турбулентності проводилися на багатьох установках, розуміння цих процесів залишається досить обмеженим. Для досягнення подальшого прогресу в розумінні плазмової турбулентності з погляду поліпшеного утримання і транспортних бар'єрів необхідні інтенсивні експериментальні і теоретичні дослідження. Проект INTAS спрямовано на з'ясування кореляції між виникненням транспортних бар'єрів і поліпшеного утримання в токамаках TEXTOR, Т-10 і Tore Supra, а також у токамаках малих розмірів ФТ-2, ТУМАН-3М и CASTOR, з одного боку, і електричними полями, модифікованим магнітним широм і електростатичною і магнітною турбулентністю, з іншого боку, з використанням передових діагностичних засобів з високим просторовим і тимчасовим розділенням. Дослідження проводяться з високим ступенем координації робіт і використанням взаємодоповнюваності установок TEXTOR і Т-10, і можливостей інших токамаків, що в сукупності забезпечить необхідну експериментальну і теоретичну перевірку. Для перевірки експериментальних результатів буде використано нові теоретичні моделі і чисельне моделювання.В последние десять лет были получены новые режимы работы токамаков, в которых электростатическая и магнитная турбулентность, ответственная за аномальный перенос, могла подавляться путём внешнего воздействия, и тем самым достигалось улучшенное удержание. Несмотря на то, что исследования турбулентности проводились на многих установках, понимание этих процессов остаётся весьма ограниченным. Для достижения дальнейшего прогресса в понимании плазменной турбулентности с точки зрения улучшенного удержания и транспортных барьеров необходимы интенсивные экспериментальные и теоретические исследования. Проект INTAS направлен на выяснение корреляции между возникновением транспортных барьеров и улучшенного удержания в токамаках TEXTOR, Т-10 и Tore Supra, а также в токамаках малых размеров ФТ-2, ТУМАН-3М и CASTOR, с одной стороны, и электрическими полями, модифицированным магнитным широм и электростатической и магнитной турбулентностью, с другой стороны, с использованием передовых диагностических средств с высоким пространственным и временным разрешением. Исследования проводятся с высокой степенью координации работ и использованием взаимодополняемости установок TEXTOR и Т-10, и возможностей других токамаков, что в совокупности обеспечит необходимую экспериментальную и теоретическую проверку. Для проверки экспериментальных результатов будут использованы новые теоретические модели и численное моделирование

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR