Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field

On the theory of large amplitude Alfven waves

Large amplitude Alfvenic disturbances of arbitrary spatial shape and polarization are described by MHD equations, without resort to the usual assumption of planarity. However, because of their nonplanar nature, the direction of propagation of these disturbances cannot, in general, be determined by looking for minima in a variance matrix constructed from observed field fluctuations. When such minima exist, one is observing that subset of interplanetary Alfven waves that is essentially planar

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed

Hysteresis-controlled instability waves in a scale-free driven current sheet model

Magnetospheric dynamics is a complex multiscale process whose statistical features can be successfully reproduced using high-dimensional numerical transport models exhibiting the phenomenon of self-organized criticality (SOC). Along this line of research, a 2-dimensional driven current sheet (DCS) model has recently been developed that incorporates an idealized current-driven instability with a resistive MHD plasma system (Klimas et al., 2004a, b). The dynamics of the DCS model is dominated by the scale-free diffusive energy transport characterized by a set of broadband power-law distribution functions similar to those governing the evolution of multiscale precipitation regions of energetic particles in the nighttime sector of aurora (Uritsky et al., 2002b). The scale-free DCS behavior is supported by localized current-driven instabilities that can communicate in an avalanche fashion over arbitrarily long distances thus producing current sheet waves (CSW). In this paper, we derive the analytical expression for CSW speed as a function of plasma parameters controlling local anomalous resistivity dynamics. The obtained relation indicates that the CSW propagation requires sufficiently high initial current densities, and predicts a deceleration of CSWs moving from inner plasma sheet regions toward its northern and southern boundaries. We also show that the shape of time-averaged current density profile in the DCS model is in agreement with steady-state spatial configuration of critical avalanching models as described by the singular diffusion theory of the SOC. Over shorter time scales, SOC dynamics is associated with rather complex spatial patterns and, in particular, can produce bifurcated current sheets often seen in multi-satellite observations

New Measure of the Dissipation Region in Collisionless Magnetic Reconnection

A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron's rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation

Distinct Scaling Regimes of Energy Release Dynamics in the Nighttime Magnetosphere

Based on a spatiotemporal analysis of POLAR UVI images, we show that the auroral emission events that initiate equatorward of the isotropic boundary (IB) obtained from a time-dependent empirical model, have systematically steeper power-law slopes of energy, power, area and lifetime probability distributions compared to the events that initiate poleward of the IB. The low-latitude group of events contains a distinct subpopulation of substorm-scale disturbances violating the power-law behavior, while the high latitude group is described by nearly perfect power-law statistics over the entire range of scales studied. The results obtained indicate that the inner and outer portions of the plasma sheet are characterized by substantially different scaling regimes of bursty energy dissipation suggestive of different physics in these regions.Comment: 11 pages, 2 figures, 2 table

Scaling, self-similar solutions and shock waves for V-shaped field potentials

We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(\phi)| = |\phi|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with infinite number of degrees of freedom. The model has an interesting scaling symmetry of the 'on shell' type. We find self-similar as well as shock wave solutions of the field equation in that model.Comment: Two comments and one reference adde

Fouling Enhancement under Flow Boiling at Elevated Steam Qualities

Under laboratory conditions of flow boiling in water at 272–285°C (5.7 to 7.0 MPa), it has been observed that fouling rates by colloidal iron oxides ( crud ) dramatically increase upon reaching a certain steam quality and mixture velocity. In loop tests, an increase in fouling rates by up to 3 orders of magnitude was repeatedly observed. This effect is called here “heavy fouling under elevated steam quality” (HFESQ). HFESQ is potentially very significant for once-through steam generators, and very large versions of recirculating nuclear steam generators, because it can lead to heavy fouling in the upper tube bundle. The mechanism of HFESQ is not certain, but its onset appears to be associated with significant droplet entrainment after the transition of flow to the annular pattern. The postulated connections between the flow pattern and the fouling mechanism will be discussed. This mechanism may also be the reason for an increased rate of flow-accelerated corrosion at high steam quality in piping and piping fittings. Experimental data will be shown suggesting that the onset of HFESQ is susceptible to the chemistry and size of the crud particles. This offers a route for possible mitigation of the fouling problem

Regeneration of Carapa guianensis (Aublet.) seedings in two forest types in Rio Branco, Acre, Brazil.

Extractive use of Carapa guianensis (andiroba), a multi-use species, provides an alternative for sustainable resource use. The objective of this study was to investigate the mortality of seedlings and saplings of Carapa guianensis, comparing two forest types (upland and occasionally inundated forest) at Embrapa’s experimental forest reserve in Acre, Brazil