Temperature Gradient Scale Research Articles

An edge pedestal model based on transport and atomic physics

A model is presented for the calculation of the characteristic scale lengths from transport considerations in the edge pedestal region of high confinement (H-mode) plasmas. The model is based on the requirements of heat and particle removal through the edge. Atomic physics effects on edge density and temperature gradient scale lengths are taken into account. An empirical fit for the width of the edge pedestal transport barrier is employed. Model problem calculations indicate that the model predicts the magnitudes and some trends of characteristic gradient scale lengths observed in current experiments.

Low frequency stability of geotail plasma

The local flux surface stability of magnetic dipole configurations is investigated in the magnetohydrodynamic (MHD) and drift frequency regimes. Solutions of the plasma equations in the very high beta limit are discussed. A novel procedure is developed for discussing stability in terms of the frequency ratio: the orbit averaged ion drift frequency divided by the ion diamagnetic frequency. This procedure is used to examine the stability of magnetospheric flux surfaces in the neighborhood of the equatorial plane at 6–10 Earth radii (where the plasma beta is ∼5 and where the onset of plasma instabilities may be responsible for triggering magnetic storms) with the following results: (1) MHD ballooning modes are predicted to be stable unless κvxp⩽2/5 where xp is the plasma pressure gradient scale length and κv the vacuum field line curvature at the equatorial plane; (2) drift modes may also be unstable unless η∼2/3, where η is the density gradient scale length divided by the temperature gradient scale length.

Multi-faceted asymmetric radiation from the edge formation in DIII-D high-confinement mode discharges with continuous gas puffing

A set of continuously gas fueled DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986) p. 159] high confinement mode (H-mode) shots at three neutral beam injection powers and two values of magnetic field (q95) have been analyzed to investigate the evolution of plasma edge conditions leading to the formation of X-point MARFEs (multifaceted asymmetric radiation from edge), which are followed by an H–L transition that constitutes a practical density limit for this class of shots in DIII-D. The MARFE initiation is found to be caused by a combination of a sharply increasing concentration of recycling neutrals in the plasma edge, decreasing edge inverse temperature and density gradient scale lengths, and increasing edge density. The line-average density at which MARFEs precipitates increases with increasing injection power and with decreasing q95. It is not clear whether the formation of the X-point MARFE causes or merely precedes the H–L transition.

Observations of the thermal structure of a lake using a submarine

This note describes how a submarine, the F.A. Forel, carrying a vertical array of high‐resolution temperature sensors, was used along with conventional measurements from a lowered conductivity‐temperature‐depth probe (CTD) to make novel measurements of the temperature field in Lake Geneva during summertime conditions of stable stratification and during winter convection. The submarine speed was about 0.5 m s−1. In addition to the temperatures, the pressure, orientation, and tilt were recorded at frequencies of at least 10 Hz. Observations were made on a vertical scale of 0.1 to 2.5 m and on a horizontal scale from 0.5 m to 1 km. Examples of the data are presented. During the summer, evidence was found of internal waves and of extensive layers of low vertical temperature gradient, with vertical and horizontal scales of 0.5 m and 0.5 km, respectively; within this gradient, the temperature changed monotonically in the horizontal. During periods favoring convection, in the winter, when air temperatures were about 7°C below the surface‐water temperature, convectively unstable regions, typically of 5‐m horizontal scale, were observed in the mixed layer. These appeared to be convective plumes. These winter measurements also included observations of a layer of cold water that was adjacent to the sloping boundary of the lake. This was identified as being a plume of dense cold water with thickness on the order of 10 m, which was driven by surface cooling, and consequent more rapid temperature decrease, in the shallow nearshore water. On meeting the thermocline at a depth of about 100 m, this plume spread horizontally and formed an intrusion some 30 m thick.

The Effect of Heat Flux Limiting on Divertor Fluid Models

AbstractThe classical plasma electron heat flux can greatly overestimate the physical heat flux when the electron mean‐free‐path becomes long compared to the electron temperature gradient scale length. For fluid modelling of plasmas, a common remedy is to apply an artificial „flux limiter”︁ that keeps the heat flux at a physically reasonable value in this long mean‐free‐path regime. The ad‐hoc limiter is not derived from first principles and it introduces a poorly understood free parameter into the model. We study the effect of this parameter in our divertor plasma models to understand how it influences the computed solution. We investigate regimes of both short and long mean‐free‐path and consistently find large parameter sensitivity. Thus, without additional experimental or theoretical guidance in the choice of flux‐limit parameter, flux limiting does not appear to provide an acceptable basis for predictive plasma fluid modelling.

Dynamics of Core Electron Temperature Fluctuations during Sawtooth Oscillations on TEXT-U.

Core electron temperature fluctuations are measured in a tokamak plasma where some degree of time resolution is achieved. There is a strong correlation between the turbulence level and the phase of the sawtooth oscillations. The enhancement in fluctuations at the sawtooth crash is correlated to a steepening of the electron temperature gradient created as the sawtooth heat pulse propagates outward. A global linear relationship between the temperature fluctuation amplitude and the electron temperature gradient scale length is found.

A phenomenological model for cross-field plasma transport in non-ambipolar scrape-off layers

A simplified two-fluid transport model which includes phenomenological coefficients of particle diffusion, mobility, and thermal diffusivity is used to investigate the effects of nonambipolar particle transport on scrape-off layer (SOL) plasma profiles. A computer code (BSOLRAD3) has been written to iteratively solve for 2-D cross-field plasma density, potential, and electron temperature profiles for arbitrary boundary conditions, including segments of “limiters” that are electrically conducting or non-conducting. Numerical results are presented for two test cases: (1) a 1-D slab geometry showing the interdependency of the density, potential, and temperature gradient scale lengths on particle diffusion, mobility, and thermal diffusivity coefficients and limiter bias conditions, and (2) a 2-D geometry illustrating E × B plasma flow effects. It is shown that the SOL profiles can be quite sensitive to non-ambipolarity conditions imposed by the limiter and, in particular, whether the limiter surfaces are biased. Such effects, if overlooked in SOL transport analysis, can lead to erroneous conclusions about the magnitude of the local ambipolar diffusion coefficient.

Theory of ion temperature gradient instabilities: Thresholds and transport

An investigation of the ion temperature gradient instability that focuses on the behavior of the mode when it is weakly unstable is presented. It is shown that ηi= (2)/(3) is the threshold for long wavelength instability, ηi being the ratio of the density gradient scale length to the ion temperature gradient scale length. For ηi>0.902, a short wavelength mode is concomitantly unstable. The transport resulting from both the short and the long wavelengths is shown to constitute a ‘‘soft’’ turn on of anomalous transport for ηi<2, with long (short) wavelengths dominating for high (weak) enough collisionality. The point ηi=2 represents a ‘‘hard’’ threshold for transport: Beyond this point, large, collisionless transport over all wavelengths is precipitated. A nonlocal collisional theory as well as a kinetic theory with a Krook collision operator are presented to describe the progression from weak to strong instability. Transport estimates, based on mixing length arguments, are given for the various regimes incorporated by the critical points ηi= (2)/(3) , 0.902, and 2.

Electron temperature gradient modes in tokamaks

Effects of kinetic damping, resulting from electron magnetic and Landau resonances, have been investigated for the electron temperature gradient mode in tokamaks. Damping is strong, and the instability can occur only when the temperature gradient is very steep, LT/R<0.1, where LT is the temperature gradient scale length and R is the magnetic curvature radius.

Ion temperature gradient mode and H-mode confinement

The stability properties of the toroidal ion temperature gradient (ITG) mode change dramatically for plasmas with flat density profiles, as found in H-mode plasmas. Even though ηi ≫ 1, the relevant stability parameter is is the ion temperature gradient scale length and R is the major radius). It is proposed that a significant element in the improved confinement observed in the L- to H-mode transient is the diminution of ITG mode turbulence, mediated by broader H-mode ion temperature profiles. Confinement results of L- and H-mode simulations of DIII-D, based on a simplified energy transport equation, are presented to support this hypothesis.

Entropy gradient-driven electron inertial instabilities

In the vicinity of a density transition region or surface, electron temperature fluctuations are known to drive low frequency electromagnetic surface waves which may be connected with the self-generation of magnetic fields in the laser–plasma interaction. Two methods of destabilization are considered. In the first approach an accelerating plasma surface is considered and this leads to instability only when an accompanying temperature gradient scale length is at most as large as the density gradient scale length. In the second approach the introduction of current is also found to cause instability near the plasma surface provided an identical temperature gradient threshold is exceeded. In both cases the growth rates for each instability are enhanced by the square root of the ion to electron mass ratio over the associated growth rates for ion-inertial-type instability.

Ion temperature gradient mode in the weak density gradient limit

The toroidal ion temperature gradient mode (ITG mode) is analyzed in the fluid limit for flat density profiles, typical of many H-mode plasmas. It is shown that the stability boundary is not Ln/LTi=const ≊O(1 ■2) (Ln and LTi are the density and ion temperature gradient scale lengths, respectively), as typically quoted. Rather, for large Ln/R the stability threshold is characterized by LTi/R =const≊O(0.1) with R the major radius. This result could substantially reduce the impact of ITG-mode turbulence, allowing a reconciliation of present drift wave transport models with improved H-mode energy confinement.

Collisionless internal kinks

The paper presents an investigation of internal kink modes in high temperature plasmas. The relevant dynamics within the mode resonant layer is described by the collisionless kinetic equations. The approach covers a wide range of plasma parameters and, in particular, applies to situations in which the ion gyroradius is comparable to the resonant layer width and the temperature gradient scales are comparable to the density gradient scale. Several dispersion relations applicable to different plasma parameter regimes are derived.

Temporal development of spatial oscillations in a confined rotating fluid—a numerical study

Abstract This paper studies numerically the temporal development of spatial oscillations in a confined rotating fluid differentially heated from below. It is found that spatial oscillations occur when the internal Rayleigh number is larger than the critical Rayleigh number obtained from linear analysis. Because the internal Rayleigh number depends on the vertical temperature gradient and length scale which are time dependent, the stability of the transient flows cannot be predicted from an external Rayleigh number. The numerical resolutions of boundary layers are discussed.

Electron heat transport of non-Maxwellian distributions

Electron heat transport is studied for a variety of presumed non-Maxwellian distribution functions in the presence of steep temperature gradients. For a representative group of distribution functions the heat flow in the region lambda T/LT approximately=0.1 relevant for laser-plasma interaction ( lambda T is the thermal mean free path, LT is the temperature gradient scale length) is much smaller than the free streaming value.

Linear theory of tearing in a high‐β plasma

We calculate the linear dispersion relation for a collisionless plasma in a sheared one‐dimensional current sheet and extend the existing calculations to include β ∼1 plasmas, where β is the ratio of the thermal pressure to the magnetic pressure. Defining Bz as the component of the magnetic field which reverses sign as a function of x and By as that component which is nonzero but does not reverse sign (the guide‐field), we find that the tearing mode eigenstructure and temporal growth rate are a sensitive function of the ratios ls/lG, ls/ln, and ls/lT, where ls is the shearing length of the magnetic field, lG is the gradient scale length of the guide field By, ln is the number density gradient scale length, and lT is the temperature gradient scale length. In particular, if β ≳1, and ls <lG, ln, and lT, then the thickness of the layer over which particles are resonantly accelerated by the induction electric field is ∼ρ, a thermal gyroradius. In this limit the growth rate reduces to that derived by Laval et al. (1966). If the above conditions are not satisfied, plasma gradients may electrostatically stabilize the mode.

Kinetic Theory of Inhomogeneous Plasmas Situated in RE Fields

The stability effect that an RF electric field imposes on drift instabilities in a magnetized plasma, inhomogeneous in density and temperature, is investigated in the kinetic approximation, taking account of the finite ion Larmor radii. Stabilization of drift instabilities is examined in three frequency ranges:?/k? ?th,e, where k? is the component of the wave vector parallel to the applied dc magnetic field, and ?th, e and ?th, i are the electron and ion thermal speeds, respectively. It is found that stabilization is most effective for the medium phase-velocity range, where the drift instability, driven by streaming electrons, is strongest and sensitive to the ratio Ln/LT, where Ln and LT are the density and temperature gradient scale lengths, respectively.