Mahleret al.Respond

Abstract

ERRATAWe regret that an incorrect version of the Response of Mahler etal. to the Comment by Combescot was published [Phys. Rev. Lett. ^9, 1744]. The correct version follows. Mahler et al. Respond: (1) The nonuniform state of a binary (or multicomponent) system is governed to zero order by the Euler hydrodynamic equations supplemented by the thermodynamic equation of state. The first -order approximation (Enskog) 1 then leads to the irreversible processes of diffusion, heat conduction, and thermal diffusion (neglecting here internal friction) as phenomenologically treated by the Onsager linear transport equations. 2 ' 3 When applied to electronic transport phenomena in solids the binary system is built up by the electrons (and/or holes) and the lattice atoms (where any macroscopic drift of the latter is usually excluded). This is the basis for a large variety of transport effects ranging from Ohm's law to complicated cross effects with or without external fields, including our thermodiffusion model. 4 Alternatively one may try to model the electronhole transport process by a one-component Euler equation to which a phenomenological damping term has been added to simulate the coupling to the lattice. 5 In a way, the resulting equation resembles the Navier-Stokes equation, in which the internal damping term is replaced by an external one, though of different functional dependence.Obviously, these two approaches are by no means equivalent: Combescot 6 just succeeded in proving this for a special case. However, starting from the Euler equation it is certainly not possible to say anything about thermal diffusion, in general, or the sign of the resulting gradients, in particular. This renders Combescot's whole section (1) invalid.(2) First, the condition of vanishing heat current j Q =0 is not essential for obtaining our interesting confinement behavior. The dominant sources for j Q are Auger heating and lattice cooling (through which the bath temperature comes in), with the boundary condition j Q (?c -°°) =0. Only in extreme cases will this lead to a destruction of the confinement, as will be shown in a forthcoming paper.Second, it is textbook knowledge that there exist linear transformations for the currents and forces in the Onsager equations which leave the Onsager reciprocity relations unchanged. 3 The force V(~ MA 1 ), where M is the chemical potential and T the temperature, is the correct force when 3 q is taken to be the heat current while V(-\i) T enters with the so-called reduced heat current (for details see Ref.3).Third, for the {n, T) region we discuss, N =L qq L mm -L qm 2 is certainly positive. N becomes negative in the extreme quantum limit, where not only the present transport theory but any hydrodynamic approach breaks down.(3) Under actual experimental conditions the particle current j m (0) and the initial density n(0) are related to each other. In our approach, however, j m together with the isothermal diffusion constant D only defines the length scale of our profiles, as is easily seen from Eq. (3)...

Plasma Physics and Controlled Nuclear Fusion Research (Summaries of the 10th IAEA International Conference, London, 12–19 September 1984)

“…This paper extended the authors' previous work [6] to include more constraints by restricting attention to the reduced MHD equations, considering only local resistive fluid turbulence, and taking into account transport along stochastic magnetic field lines. These were the same ingredients as in the Carreras-Diamond renormalized turbulence model [7] of anomalous electron heat transport due to resistive ballooning modes at high j3 p that correlated well with ISX-B experimental results; the authors were able to reproduce the Carreras-Diamond scaling law using their scale invariance method. They also applied their method to estimating the anomalous transport in reverse-field-pinch plasmas (see also Section 4 below).…”

“…The mechanisms by which this process can redistribute the magnetic energy and current density to produce the dynamo effect were also discussed. In the edge region resistive-g (gravity) mode turbulence is invoked and its non-linear state found to be describable by a mixing-length-type approach, as was possible for resistive ballooning mode turbulence [7]. The magnetic stochasticity, anomalous transport and confinement scaling produced by these modes in an RFP were also estimated in this paper by Diamond (E-III-10); similar final scaling results were obtained by Taylor (E-I-2) from scale invariance properties of the underlying equations (see Section 1C above).…”

Features of edge magnetic turbulence in DIII-D expanded boundary divertor discharges

“…Magnetic turbulence has been considered to cause anomalous transport in tokamaks. Early experimental studies [1][2][3][4][5] in small tokamaks demonstrated the existence of magnetic turbulence. Previously, we reported [6] that magnetic turbulence also existed in larger, high power discharges in the Doublet III device; we established a clear correlation between magnetic turbulence and edge plasma transport by observing that the magnetic fluctuation amplitude abruptly changes when transitions from a poor confinement regime (L-mode) to a good confinement regime (H-mode) [7], or vice versa, take place.…”

Search for exotic decay modes at the proton drip line

“…The decay of 22 Al was studied about 15 years ago in several experiments using a helium-jet technique [9,10]. β-delayed proton emission from the isobaric analogue state (IAS) of the intermediate nucleus 22 Mg to the ground state and to the first excited state in 21 Na was observed [9] and a half-life of T 1/2 = (70 +50 −35 ) ms was deduced.…”

“…β-delayed proton emission from the isobaric analogue state (IAS) of the intermediate nucleus 22 Mg to the ground state and to the first excited state in 21 Na was observed [9] and a half-life of T 1/2 = (70 +50 −35 ) ms was deduced. The second experiment reported on the first observation of a β-delayed two-proton decay [10] with sequential emission of the two protons.…”