Electron Heat Diffusivity Research Articles

Tokamak-like confinement at high beta and low field in the reversed field pinch

For several reasons, improved-confinement achieved in the reversed field pinch (RFP) during the last few years can be characterized as ‘tokamak-like’. Historically, RFP plasmas have had relatively poor confinement due to tearing instability which causes magnetic stochasticity and enhanced transport. Tearing reduction is achieved through modification of the inductive current drive, which dramatically improves confinement. The electron temperature increases to >1 keV and the electron heat diffusivity decreases to ∼5 m2 s−1, comparable with the transport level expected in a tokamak plasma of the same size and current. This corresponds to a 10-fold increase in global energy confinement. Runaway electrons are confined, and Fokker–Planck modelling of the electron distribution reveals that the diffusion at high energy is independent of the parallel velocity, uncharacteristic of stochastic transport. Improved-confinement occurs simultaneously with increased beta ∼15%, while maintaining a magnetic field strength ten times weaker than a comparable tokamak. Measurements of the current, magnetic, and electric field profiles show that a simple Ohm's Law applies to this RFP sustained without dynamo relaxation.

Electron Heat Transport in an HL-1M Tokamak ECRH Plasma

Electron temperature profiles, the normalized temperature gradientlength and the electron heat diffusivity calculated by the heat pulsetransfer method in a plasma confinement region, are investigatedduring electron cyclotron resonance heating (ECRH) in an HL-1M tokamak.The electron temperature profiles remain almost constant. Thenormalized temperature gradient length is in the range of 7–13.Electron heat diffusivity in the ECRH plasmas is larger than that inthe ohmically heated plasmas. Electron heat diffusivity during off-axis(ρ<0.3) ECRH discharge is similar to that during on-axis ECRHdischarge.

Studies of electron heat pulse propagation at the T-10 tokamak with gyrotrons at two different frequencies**This paper is based on a report done at Strong Microwaves in Plasmas Int. Workshop (Nyznii Novgorod, Russia, August 2002) H-19.

The internal transport barrier (ITB) was found by means of heat pulse propagation (HPP) and cold pulse propagation (CPP) analysis in target sawteeth-free plasma. The target sawteeth-free plasma was created either by high-field-side off-axis ECRH (140 GHz) or by low-field-side off-axis ECRH (130 GHz) at normalized minor radius r/alimiter ≈ ± (0.45). Outward HPP with dynamic electron heat diffusivity (at 0.2 < r/a < 0.37 and R/LTe = R∇Te/Te up to 23, where Te is the electron temperature and R is the major radius) was created by switching on the on-axis ECRH (130 or 140 GHz) imposed on the background, which was created by off-axis ECRH. Inward CPP was created by turning off the off-axis ECRH. The central Te responds with significant ∼ 20 ms delay. Slow inward CPP with R/LTe rising up to 17 on the cold wave front, can be described well by at r/a < 0.3 in a time interval limited by the appearance of the first sawteeth oscillation. Off-axis ECRH forms the region of the improved transport in low-shear zone with q slightly above 1. Later, q reduces due to the current redistribution during CPP (HPP). The improved transport is able to survive under R/LTe up to 23 (10 is Ohmic value of R/LTe). In the context of a ‘critical gradient’ model, the Ohmic value of R/LTe lies above the ‘critical’ one because enhanced HPP (induced by sawteeth or on-axis ECRH) is observed at all tokamaks at Ohmic background. Somehow, off-axis ECRH and HPP (CPP) processes increase the ‘critical’ value of R/LTe over 2.3 times. The combination of large gradients with low transport means that ITB is present during ∼ 20 ms time interval of CPP (HPP). The analysis of HPP (CPP) at both sides of plasma column simultaneously confirms the validity of the results while also showing a light asymmetry of values.

Modulated ECRH power deposition in ASDEX Upgrade

In order to gain insight into the physics of modulated and localized electron heating, like the generation of heat waves by electron cyclotron heating, we solve the one-dimensional linearized electron heat diffusion equation in a homogeneous infinite plasma including a source term with a Gaussian profile. The amplitude and phase of the temperature oscillation in the centre of the deposition can then be analytically expressed as a product of two terms. Only one of them, a normalized complex function, describes the influence of heat diffusion. The analytical results are compared to experimental ones, and all characteristic dependences on modulation frequency, on heat diffusivity and on heating profile width are recovered.

The Study of Heat Pulse Propagation on HT-7 Tokamak

The propagation of heat pulses originating from sawtooth activity has been studied on the HT-7 tokamak. Two theoretical models are used for determining electron heat diffusivity from the experimental data measured by a diagnostic system of soft x-ray diode-array. The results show that one model called `dipole model' is more suitable for HT-7 tokamak. In order to improve the signal-to-noise (S/N) ratio of the original signals, over a few tens of sawteeth are averaged to generate nice waveforms. The space-time evolution is found to be diffusive in character, which is consistent with the theoretical model. The electron heat diffusivity determined from heat pulse propagation is larger than that determined from background plasma power balance. The variation of χe in different discharge phases has been also discussed.

Enhanced Plasma Performance by ICRF Boronization

Boronization with carborane (C2B10H12) by ICRF has been applied routinely to the walls of HT-7 super-conducting tokamak for the reduction of impurity influx, especially carbon and oxygen. Significant suppression of metallic impurities and radiating power fraction are achieved. The improved confinement for both particle and energy is observed in full range of operation parameters. Energy balance analysis shows that electron heat diffusion coefficient is strongly reduced. Measurements by Langmuir probes at the edge plasma show that the poloidal velocity shear after boronization is changed to a profile favoring to good confinement. The main emphasis of this paper is to describe effects of boronization on aspects of the enhanced plasma performance.

Dynamics and interplay of L-H-L transitions and ITB events in reversed shear plasmas withinternal barriers in JT-60U

Abrupt in time (correlated within a few ms with L-H and H-L transitions) and wide in space (from the edge up to ~0.3 of minor radius in the extreme case) variations of electron heat diffusivity δχe were found in reversed shear (RS) JT-60U tokamak plasmas with internal transport barrier (ITB) at various profiles of safety factor q. The δχe profile follows the position of q minimum (qmin ) and penetrates into the RS region deeper for the weak ITB than for the strong one, suggesting the presence of `global' edge-core connection throughout qmin in a ms timescale at L-H and H-L confinement bifurcations. The δχe value at the position of qmin is small for the strong ITB (~0.05 m2 s-1) and increases by an order of magnitude for the weak ITB. The ITB event is another non-local transport bifurcation (improvement or degradation) inside and around ITB. The case of strong ITB formation in H-mode via a series of ITB events in ELM-induced L-mode is described. ITB event degradation in the positive shear zone causes L-H transition.

RF discharge in CO2 laser mixtures at moderate pressures

The voltage-power characteristics and spatial structure of an RF discharge in the mixtures of CO2 and N2 molecular gases with He at total pressures of tens of torr are studied. One-dimensional numerical simulations of an RF discharge are carried out within two approaches: (i) the distribution function and the related kinetic coefficients are assumed to be functions of the local reduced field, and (ii) the kinetic coefficients are functions of the electron mean energy, which is calculated with allowance for both electron heat conduction and diffusion. The latter approach is shown to better describe the existing experimental dependence of the discharge voltage and the phase shift between the discharge current and voltage on the driving power.

Electron Heat Diffusivity in the HT-7 Tokamak with Si-Coating Wall

Electron heat diffusivity inferred from the electron power balance wasstudied in the ohmically heated plasma on an HT-7 tokamak. The resultsobtained before and after siliconization were compared and it is found thatthe diffusivity is reduced obviously in the half of the outer region(r/a>0.5) after siliconization, which was the reason why energy confinementwas improved after siliconization.

ECRH experiments in ASDEX upgrade

Modulated Electron Cyclotron Resonance Heating was applied in ASDEX Upgrade to study the electron heat diffusivity χ e. Its dependence on the isotope mass was found to be opposite to that one known from the power balance analysis. Off-axis ECRH deposition leads to a reduced electron heat transport in the centre which cannot be explained by an inward heat pinch. Electron Cyclotron Current Drive was applied to completely stabilise a (3/2)-neoclassical tearing mode with a consequent recovery of the plasma energy. High electron and ion temperatures have been simultaneously achieved by application of central counter ECCD in a discharge with an internal ion transport barrier.

Short wavelength fluctuations and electron transport in TFTR

Correlation between electron heat diffusivity and short wavelength ( kρ i ∼5) fluctuation amplitude was observed in the TFTR tokamak in the core of ERS plasmas (Phys. Lett. A 236 (1997) 339). These fluctuations propagate in the ion diamagnetic drift direction with wave number comparable to ω pe / c. Further analysis of these data yields the ratios χ e / χ i and χ e / D e , and their values are consistent with the picture that the electron transport is mainly induced by the short wavelength fluctuations in the plasma core where the long wavelength ( kρ i ∼1) fluctuations are absent. Although there is not enough information to identify these short wavelength modes, the values of χ e is found to be comparable to theoretical predictions based on the current diffusive ballooning mode theory (Plasma Phys. Control. Fusion 36 (1994) 279).

Electron current to a probe in a magnetized, collisional plasma

A collisional analysis of electron collection by a probe in a strongly magnetized, fully ionized plasma is carried out. A solution to the complete set of macroscopic equations with classical transport coefficients that is wholly consistent in the domain 1≪R2/le∞2≪(mi/me)3/2 is determined; R and le∞ are probe radius and electron gyroradius, respectively. If R2/le∞2 is large compared with mi/3me (probe large compared with ion gyroradius), ion–electron energy exchange—rather than electron heat diffusion—keeps electrons isothermal. For smaller probes at negative bias, however, electron cooling occurs in the plasma beyond the sheath, with a potential overshoot lying well away from it. The probe characteristic in the electron-retarding range may then mimic the characteristic for a two electron-temperature plasma and lead to an overestimate of electron temperature; the validity of these results for other transport models is discussed.

Density control problems in large stellarators with neoclassical transport

With respect to the particle flux, the off-diagonal term in the neoclassical transport matrix becomes crucial in the stellarator long-mean-free-path regime. Central heating with peaked temperature profiles can make an active density profile control by central particle refuelling mandatory. The neoclassical particle confinement can significantly exceed the energy confinement at the outer radii. As a consequence, the required central refuelling may be larger than the neoclassical particle fluxes at outer radii leading to the loss of the global density control. Radiative losses as well as additional `anomalous' electron heat diffusivities further exacerbate this problem. In addition to the analytical formulation of the neoclassical link of particle and energy fluxes, simplified model simulations as well as time-dependent ASTRA code simulations are described. In particular, the `low-' and `high-mirror' W7-X configurations are compared. For the W7-X `high-mirror' configuration especially, the appearance of the neoclassical particle transport barrier is predicted at higher densities.

High Core Electron Confinement Regimes in FTU Plasmas with Low- or Reversed-Magnetic Shear and High Power Density Electron-Cyclotron-Resonance Heating

Electron temperatures in excess of 8 keV have been obtained by electron-cyclotron-resonance heating on FTU plasmas at peak densities up to 8×1019m−3. The magnetic shear in the plasma core is low or negative, and the electron heat diffusivity remains at, or below, the Ohmic level (0.2m2/s), in spite of the very large heating power density (10–20MW/m3) which produces extremely high temperature gradients (up to 120 keV/m). The ion heat transport remains at the neoclassical level.Received 4 June 1998DOI:https://doi.org/10.1103/PhysRevLett.82.560©1999 American Physical Society

Strong impact of neutrals on anomalous inward drift and width of steep gradient zone

The fundamental properties of the anomalous inward drift and the width of the steep gradient zone in H mode plasmas are explored. A special version of the 1.5-D BALDUR transport code is used to determine the profiles of the electron heat diffusivity and vin/D by transport analysis. The strong rise with radius of vin/D in the edge region is explained by a linear dependence on the neutral deuterium density n0, resulting in a new scaling expression vin(x)/D(x) = F0Zeff(x)n0(x)2x/(ρwxs2). Applying this in simulations reproduces the empirical fit of the vin/D profile not only in the edge plasma but also in the bulk plasma. Modellings with this scaling yield the observed flattening of density profiles with rising line averaged density. The decreasing penetration of deuterium atoms to the core causes a decline of the inward drift. The new scaling is shown to be compatible with gas oscillation experiments, while n0-independent scalings are not. This further explains the strong density profile peaking and rise of vin/D during and after pellet injection by the increase in neutral density. The width of the steep gradient zone is found to be connected with the penetration of neutrals at the edge and the presence of high inward drift velocities. The anomalous inward drift is attributed to ion dynamics, i.e. to the friction between fluctuating deuterons and deuterium atoms diffusing inward. A more general vin/D scaling including impurity effects is presented.

Transient heat transport studies using laser ablated impurity injection in JET

Following impurity injection by laser ablation (LA) in JET plasmas, the electron temperature, Te, is observed to drop at a rate that cannot be accounted for by changes in radiated power, ΔPrad. Te starts to drop promptly over a large fraction of the plasma volume, which can be explained by a non-local change in electron heat diffusivity. The change in diffusivity, Δχe, is generally short lived, lasting a few milliseconds, even if ΔPrad can persist for longer times. No clear relation between ΔPrad and the strength of the prompt plasma response to LA can be observed, but only those events with ΔPrad/Prad > 0.5 give rise to detectable Te perturbations. In hot ion H mode plasmas, Δχe is found to be spatially non-uniform and increasing exponentially with the time delay of the LA relative to the onset of the H mode. Examples of non-monotonic Δχe profiles are found in plasmas of lower heating power. Energy transport models combining local and non-local (or strongly non-linear) features are possible candidates for an explanation of these observations.

Transient transport phenomena induced by cold pulses in W7-AS

Cold-pulse experiments were carried out in the W7-AS stellarator for the first time. Carbon was injected by a laser blow-off system into the plasma edge. The electron density increase due to the injected carbon is found to be responsible for the edge electron temperature drop. In all cases, the propagation of the edge temperature perturbation to the plasma centre could be modelled with a local parameter-dependent electron heat diffusivity. Unlike in tokamaks, non-local transport effects were not observed in these experiments.

Validation of a new mixed Bohm/gyro-Bohm model for electron and ion heat transport against the ITER, Tore Supra and START database discharges

A new model based on a combination of a Bohm-like term plus a gyro-Bohm-like term is proposed for the electron and ion heat diffusivity in the L mode regime, which is the commonest regime of operation of tokamaks. This model is derived using the dimensionless analysis technique taking into account the indications of scaling laws for the global confinement time and other experimental constraints on the diffusivity. The model has been successfully tested against data from several different experiments from the ITER database and the local Tore Supra database. Statistical analysis has shown it to perform better than purely Bohm or gyro-Bohm models and global scaling laws in the chosen dataset.

Internal magnetic fluctuations and electron heat transport in the Tore Supra tokamak: Observation by cross-polarization scattering

Magnetic fluctuations (radial size ≈ 5 mm) are measured by a cross polarization scattering (CPS) diagnostic in Tore Supra. In the scenario O + B̃ → X, only the poloidal component of the magnetic fluctuations is measured, while both the radial and the poloidal component are measured in the scenario X + B̃ → O. These fluctuations are investigated quantitatively in the ohmic and low confinement regimes over a wide range of plasma currents, densities and additional heating powers. At the same time, the electron heat diffusivities expected from these fluctuations are compared with those obtained by profile analysis. Three main results are obtained: (a) The radial profile of the poloidal magnetic fluctuations in the gradient region (0.3 < r/a < 0.7) is established from these measurements. The magnetic fluctuation levels are found to increase towards the plasma edge, and this feature is compatible with that of electron heat diffusivity. (b) A strong correlation between the measured magnetic turbulence and the local temperature gradient is observed during the additional heating. (c) The local electron heat diffusivity induced by magnetic fluctuations is estimated using the non-collisional quasi-linear formula χmage = πqRvth(δBr/B)2, where the radial component of the magnetic turbulence is assumed to be of the same order as the poloidal component. Both the order of magnitude and the parametric dependence of χmage show similarities with electron diffusivities determined by transport analysis. In particular, a threshold is observed for the dependence of fluctuation induced heat fluxes on the local temperature gradient, which is close to the critical gradient observed for the measured heat fluxes.

Electron heat diffusivity in the sawtoothing tokamak core

The electron heat diffusivity has been measured in the sawtoothing core of the TEXT-U tokamak plasma during electron cyclotron heating (ECH). ECH creates a non-steady-state electron temperature gradient on a time scale faster than a single sawtooth ramp, whose relaxation is measured with two ECE systems. The measured diffusivity is considerably smaller than that measured in the steady state during the ohmic phase of the discharge outside the sawtooth inversion radius. In these conditions, high-resolution ECE has also shown the presence of small scale, non-symmetric structures characterized by very large temperature gradients. These spatially localized, temporally cyclical structures, previously described as plasma filamentation, have been identified as plasma magnetic islands. If these small-scale gradients are taken into account then the reported measurements imply an electron heat diffusivity which approaches the neoclassical prediction.