Turbulent General Magnetic Reconnection

Plasma flows with an MHD-like turbulent inertial range, such as the solar wind, require a generalization of General Magnetic Reconnection (GMR) theory. We introduce the slip-velocity source vector, which gives the rate of development of slip velocity per unit arc length of field line. The slip source vector is the ratio of the curl of the non ideal electric field in the Generalized Ohm's Law and the magnetic field strength. It diverges at magnetic nulls, unifying GMR with magnetic null-point reconnection. Only under restrictive assumptions is the slip velocity related to the gradient of the quasi potential (integral of parallel electric field along field lines). In a turbulent inertial range the curl becomes extremely large while the parallel component is tiny, so that line slippage occurs even while ideal MHD becomes accurate. The resolution of this paradox is that ideal MHD is valid for a turbulent inertial-range only in a weak sense which does not imply magnetic line freezing. The notion of weak solution is explained in terms of spatial coarse-graining and renormalization group (RG) theory. We give an argument for the weak validity of the ideal Ohm's law in the inertial range, via rigorous estimates of the terms in the Generalized Ohm's Law for an electron-ion plasma. All of the nonideal terms (from collisional resistivity, Hall field, electron pressure anisotropy, and electron inertia) are shown to be irrelevant in the RG sense and large-scale reconnection is thus governed solely by ideal dynamics. We briefly discuss some implications for heliospheric reconnection, in particular for deviations from the Parker spiral model of interplanetary magnetic field. Solar wind observations show that reconnection in a turbulence broadened heliospheric current sheet, consistent with the Lazarian-Vishniac theory, leads to slip velocities that cause field lines to lag relative to the spiral model.Comment: 35 pages, 9 figure

Fluctuation Dynamo and Turbulent Induction at Small Prandtl Number

We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial-range, flux-freezing holds only in a stochastic sense. We show that field-lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anti-correlated and produce an "anti-dynamo" effect. We also study the problem of "magnetic induction" of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth-rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent inductionComment: 20 pages, 13 figue

A Guide to Critical Legal Studies

Review of: A Guide to Critical Legal Studies. By Mark Kelman. Harvard University Press, Cambridge, Massachusetts and London, England, 1987

ECONOMICS AND ECOSYSTEM MANAGEMENT: DISCUSSION

Environmental Economics and Policy,

VALUATION OF GROUNDWATER QUALITY CONTINGENT VALUES, PUBLIC POLICY NEEDS, AND DAMAGE FUNCTIONS

In a departure from past contingent valuation research of groundwater quality, this paper estimates a damage function for nitrate exposures based on actual water test results of individual wells. From the perspective of reliability, it is argued that such a full information approach more closely represents the goal of valuation research in this area -to estimate the economic values that people would place on improving water quality if they were actually experiencing contaminated water. The adoption of a damage function approach linking willingness to pay to actual exposures is also more useful to policy makers at the study site because it potentially provides benefit information to a broad range of policy options. Finally, because the damage function is based on objective data that could be obtained from other sources such as local well test programs, such an approach may be desirable from a benefits transfer perspective. Damages, as measured by willingness to pay for protecting individual well supplies within a 10 mg/L NO,-N health standards are estimated to be a concave function of nitrate exposure levels.Resource /Energy Economics and Policy,