Anomalous Heat Conduction Research Articles

Anomalous heat conduction and anomalous diffusion in one-dimensional systems.

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is <Deltax(2)>=2Dt(alpha)(0<alpha</=2), then the thermal conductivity can be expressed in terms of the system size L as kappa=cL(beta) with beta=2-2/alpha. This result predicts that normal diffusion (alpha=1) implies normal heat conduction obeying the Fourier law (beta=0) and that superdiffusion (alpha>1) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.

Anomalous heat conduction in a one-dimensional ideal gas.

We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e., the Fourier law does not hold. Our conclusions are confirmed by a theoretical and numerical analysis based on a Green-Kubo-type approach specialized to momentum-conserving lattices.

Anomalous heat conduction in one-dimensional momentum-conserving systems.

We show that for one-dimensional fluids the thermal conductivity generically diverges with system size L as L(1/3), as a result of momentum conservation. Our results are consistent with the largest-scale numerical studies of two-component hard-particle systems. We suggest explanations for the apparent disagreement with studies on Fermi-Pasta-Ulam chains.

Role of collisionless trapped electron mode in tokamak plasmas with electron internal transport barrier

A self-sustained turbulence model for collisionless trapped electron mode is presented to examine the role of dynamics of trapped electrons in forming electron internal transport barrier (ITB) in tokamak plasmas with negative magnetic shear. Results show that strong negative magnetic shear as well as large Shafranov shift can lead to the precession drift reversal of trapped electrons and large reduction of anomalous electron heat conductivity; it may further trigger the formation of electron ITB. The complete precession drift reversal seems to be in good agreement with the onset condition of electron ITB observed in JT-60U discharges.

How Many Convective Zones Are There in the Atmosphere of Venus

The qualitative characteristics of the vertical structure of the atmospheres of Venus and the Earth essentially differ. For instance, there are at least two, instead of one, zones with normal (thermal) convection on Venus. The first one is near the surface (a boundary layer); the second is at the altitudes of the lower part of the main cloud layer between 49 and 55 km. Contrary to the hypotheses proposed by Izakov (2001, 2002), the upper convective zone prevents energy transfer from the upper clouds to the subcloud atmosphere by “anomalous turbulent heat conductivity.” It is possible, however, that the anomalous turbulent heat conductivity takes part in the redistribution of the heat fluxes within the lower (subcloud) atmosphere.

Stationary Fluctuation Spectra and Anomalous Transport in a Three-Species Plasma

Low-frequency electromagnetic plasma excitations in the presence of an extra specie, are investigated. The stationary spectra of the low-frequency electromagnetic excitations and the relevant transport coefficients are found. It is conjectured that intrusion of an adiabatically distributed component decreases the level and additional nonlinear broadening of the convective spectrum. The anomalous electron heat conductivity associated with the short-wave motions, is reduced due to the presence of a third specie. The dope also affects anomalous diffusion relevant to the long-wave perturbations in the plasma periphery.

Metastability and Nucleation

fect crystals. This combination has allowed the construction of a unique IXS spectrometer, now in routine operation at the European Synchrotron Radiation Facility in Grenoble. Its main success lies in its capability to measure S(Q,E) at momentum transfers, Q= 0.5n30 nm-l, with basically unlimited energy transfer, and with an energy resolution of 1.5±0.2 meV. Thanks to the new instrument, it has been possible to begin to address issues on the high frequency dynamics of disordered materials as the following ones [3]: 1. Collective excitations have been discovered in all the investigated liquids and glasses at wavelengths approaching d. The Q-dependence of their energy values testify that they are the short wavelength evolution of the hydrodynamic sound mode. Important deviations are observed, however, from phonons in crystals. In particular, their Q-dependent broadening suggests that these modes deviate from the plane waves found in crystals. At present one is trying to relate these deviations to the behavior of the sound excitations observed in the long wavelength limit, and, in glasses, to the anomalous specific heat and thermal conductivity found at low temperatures. In this respect, one would like to understand, when compared to the Debye behavior of the corresponding crystal, the origin of the excess specific heat at low temperature and the excess density of vibrational states found in glasses. 2. The interference between density fluctuations and microscopic structural relaxation processes have been clearly identified in glass-forming liquids as glycerol, ortho-terphenyl and in hydrogen bonded liquids as water. These studies have allowed determining experimentally, as a function of temperature and Q-transfer, important parameters as the infinte-frequency sound velocities. These parameters enters in the modeling of the S(Q,E) of a liquid, and in the current efforts to relate the liquid-glass transition to a change in the ergodicity of the system [4]. The possibility to contribute with an FEATURES

Magnetic Effects on Short-Wave Convective Cells in Finite-Pressure Plasma

Within the context of the general theory of low-frequency electromagnetic plasma fluctuations, the stationary spectra of short-wave convective and magnetostatic perturbations and the heat conductivity coefficient in finite-pressure plasma with βe ~ βi ~ 1, are obtained. It is shown that the nonlinear broadening of the potential spectrum can be determined by the magnetic field fluctuations when βe ~ 1. In this case, the renormalized damping coefficients display cubic k-dependence and do not keep logarithmic corrections, whereas the anomalous heat conductivity is essentially reduced.

Cross-Field Correlations in Plasma Fluctuation Spectra

The character and role of finite correlations between potential and magnetic low-frequency plasma excitations are investigated. Caused by the Lorentz force, they are significantly inherent to the nonlinear plasma behaviour. The cross-field correlations are found to narrow the renormalized width of the potential fluctuation spectrum and broaden that of the magnetic one. So the anomalous diffusion relevant to the long-wave perturbations, is increased. The anomalous heat conductivity associated with the short-wave motions, is not essentially influenced.

Transitions between metastable states in silica clusters

Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems responsible for the anomalous specific heat and thermal conductivity in disordered solids with respect to crystals. By using a recently developed numerical algorithm, we study the potential energy landscape of silica clusters, taking as a starting point the location of first order saddle points. This allows us to find a great number of adjacent minima. We analyze the degree of cooperativity of these transitions and the connection of physical properties with the topology of the configuration space. We also identify two-level systems (pairs of minima constituting a tunneling system) and calculate the quantum mechanical ground state splitting by means of the WKB approximation.

On ?A model of impulsive loop flares revisited? by Smith and Brecht

A criticism of my papers was recently presented by Smith and Brecht, that the electron distribution resulting from anomalous heat conduction is not unstable for electron plasma waves. The aim of the present letter is to show that their criticism is irrelevant.

A model of impulsive loop flares revisited

A critical examination of the components of the recent impulsive loop flare model of Takakura is made. It is found that his analysis of the stability of the electron distribution resulting from anomalous heat conduction is in error and electron plasma waves would not be excited. Rather, in the regions where the electron/proton temperature ratioT e/T i ≲ 10, electrostatic ion-cyclotron waves would be excited and in the regions whereT e ≳ 10, ion-acoustic waves would be excited. Ratios ofT e/T i ≳ 10 occur only in the late time development behind the conduction fronts. Since the anomalous resistivity due to electrostatic ion-cyclotron waves is fortuitously about 70% of the one used by Takakura, the general development will follow closely the one calculated by him. Because the anomalous resistivity due to ion-acoustic waves is about 95 times the one used by Takakura, the development in the parts of the loop whereT e/T i ≳ 10 for late times would be altered considerably.

Kolmogorov spectra of short-wave convective and magnetostatic fluctuations in a finite-pressure plasma

The Kolmogorov spectra of low-frequency short-wave potential and magnetic fluctuations are obtained in a plasma with finite ion and electron pressures, βi ∼ βe ∼ 1. Magnetic nonlinearities are found to make the dominant contribution to the renormalized width of the convective spectrum and result in its essential broadening, that gives rise to a reduced anomalous electron heat conductivity.

Low-frequency electromagnetic fluctuations and plasma heat conductivity

Stationary spectra of short-wave convective and magnetostatic fluctuations and the coefficient of anomalous heat conductivity are obtained in the ion-compressible plasma, βi ~ 1 and βe ≪ 1. The non-zero ion pressure results in a decrease of the potential spectrum intensity and width, whereas essential nonlinear broadening due to magnetic nonlinearities is expected in a plasma with βe ∼ 1. The electron heat conductivity is not strongly affected by non-zero ion beta.

A model of impulsive loop flares caused by anomalous heat conduction

Numerical simulation is made of the impulsive loop flare caused by transient heat conduction along the loop with an applied axial electric current.

Transport analysis of lower hybrid current drive plasmas in ASDEX

A transport code has been developed which comprises lower hybrid (LH) wave propagation, absorption, plasma heating, current drive, MHD induced transport and anomalous electron heat conductivity. This code was applied to a set of ASDEX discharges covering a wide range of LH experiments. Suppression of sawteeth and m=1 oscillations with subsequent strong peaking of the electron temperature profile and the dependence of the confinement time on power and density are described self-consistently in the simulation. In MHD stable LHCD plasmas with high central electron temperatures and peaked Te(r) profiles, the electrons heat conductivity in the central plasma region approaches the magnitude of neoclassical values

Temperature distribution of a tokamak with a constant heat conductivity

An analytical expression of the detached plasma radius in an Ohmically heated tokamak plasma was obtained. The assumption was made that the (anomalous) heat conductivity is constant and independent of minor radius r. The resultant nonlinear differential equation has a universal solution for the plasma temperature as a function of r. The shape is very similar to the so-called profile consistency model. As the average plasma density increases, the tokamak plasma, which is first attached to either the limiter or divertor, detaches itself from the limiter and forms a toroidal plasma whose boundary is clearly marked by a radiative boundary layer where the power input to the plasma is radiated away. As the plasma density increases, the radius of the plasma shrinks until the surface safety factor becomes less than ∼2, whereupon the plasma disruption starts. The density limit calculated by this model agrees with the experimental observation.

Evolution of pellet clouds and cloud structures in magnetically confined plasmas

The subject of this study is the space and time evolution of initially low temperature high density particle clouds in magnetically confined hot plasmas, such as those produced by ablating cryogenic hydrogen pellets in fusion machines. Particular attention is given to such physical processes as heating of the cloud by the energy fluxes carried by incident plasma particles (classical flux limited energy transport by thermal electrons along the magnetic field lines and anomalous heat conduction across them), gas dynamic expansion with j⃗ × B⃗ produced deceleration in the transverse direction, finite rate ionization and recombination (collisional and radiative) processes, and magnetic field convection and diffusion. The results show the existence of a distinct structure in the ablatant cloud surrounding and ablating pellet: a hollow temperature profile coupled to a peaked density profile in the plane normal to the magnetic field direction. The separation distance between the high and low temperature and density layers is typically the ionization or confinement radius. Also the flutes developing preferentially at the cloud surface have, at a certain phase of their development, the same wavelength. The temperature and density variations from the cloud interior to the cloud periphery may exceed two orders of magnitude. The lifetime of this structure is measured on hydrodynamic time-scales.

Ion temperature gradient driven turbulence in the weak density gradient limit

The anomalous heat transport arising from the ion temperature gradient driven mode or ηi-mode turbulence is extended to the range of the weak density gradient limit (ηi=Ln/LT→∞), which is appropriate for H-mode dishcarges. It is shown that the anomalous ion heat conductivity χi with Ln→∞ scales as χi=g(ρs/LT) (cTi/eB) exp(−βσ) with σ=(Te/Ti) (LT/Ls), β≂4, and g≂1. This χi scaling is the natural extension for high ηi of the scaling of χi for K=(Ti/Te) (1+ηi)≲4 obtained [Phys. Fluids B 2, 1833 (1990)] from analytical and numerical studies.

Fluctuation spectrum and transport from ion temperature gradient driven modes in sheared magnetic fields

The ion temperature gradient driven mode or ηi-mode turbulence is reinvestigated based on two-component compressible fluid equations with the polarization drift velocity and adiabatic electrons. The scaling of the anomalous ion heat conductivity with magnetic shear s=Ln/Ls and the excess of ηi over the critical value ηi,c for marginal stability is found to vary as χi=g(ρs/Ln)(cTi/eB) (ηi−ηi,c)exp(−αs), where g≂1 and α≂5.