Intense spreading of radar echoes from ionospheric plasmas

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (leaf 41).On December 25, 2004, a large-scale ionospheric plasma bubble was observed over Arecibo Observatory in Puerto Rico, inducing significant range spreading on ionograms. This phenomena may be explained by means of the E x B instability and gravitational Rayleigh-Taylor instability. A derivation of the dispersion relations for X and O mode waves transmitted from an ionosonde and an analysis of the collisional Rayleigh-Taylor instability leading to an expression for the growth rate are presented as background information. Ray tracing code developed by Nathan Dalrymple, a previous graduate student of Professor Min-Chang Lee, is extended, first to draw refractive index surfaces to illustrate a key principle in ray tracing and later to simulate range spreading due to depleted ionospheric ducts [1]. Data from Arecibo incoherent scatter radar and Arecibo's CADI digisonde is examined showing strong evidence for the development of a plasma bubble following a rise in the plasma layer and the appearance of a horizontal density gradient. In one portion of the ionosphere, this gradient is found to be at an angle of approximately 70 degrees to the Earth's magnetic field, a favorable condition for the excitation of the Rayleigh-Taylor instability over Arecibo.by Seth E. Dorfman.S.B

Improved Bounds for Multipass Pairing Heaps and Path-Balanced Binary Search Trees

We revisit multipass pairing heaps and path-balanced binary search trees (BSTs), two classical algorithms for data structure maintenance. The pairing heap is a simple and efficient "self-adjusting" heap, introduced in 1986 by Fredman, Sedgewick, Sleator, and Tarjan. In the multipass variant (one of the original pairing heap variants described by Fredman et al.) the minimum item is extracted via repeated pairing rounds in which neighboring siblings are linked. Path-balanced BSTs, proposed by Sleator (cf. Subramanian, 1996), are a natural alternative to Splay trees (Sleator and Tarjan, 1983). In a path-balanced BST, whenever an item is accessed, the search path leading to that item is re-arranged into a balanced tree. Despite their simplicity, both algorithms turned out to be difficult to analyse. Fredman et al. showed that operations in multipass pairing heaps take amortized O(log n * log log n / log log log n) time. For searching in path-balanced BSTs, Balasubramanian and Raman showed in 1995 the same amortized time bound of O(log n * log log n / log log log n), using a different argument. In this paper we show an explicit connection between the two algorithms and improve both bounds to O(log n * 2^{log^* n} * log^* n), respectively O(log n * 2^{log^* n} * (log^* n)^2), where log^* denotes the slowly growing iterated logarithm function. These are the first improvements in more than three, resp. two decades, approaching the information-theoretic lower bound of Omega(log n)

Nonlinear dynamics of small-scale Alfv\'en waves

We study the nonlinear evolution of very oblique small-scale Alfv\'en waves with $k_\perp d_i\gtrsim 1$. At these scales, the waves become significantly compressive, unlike in MHD, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when $k_\perp d_i \sim 1$. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfv\'en waves, an inherently 3D effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfv\'en wave also becomes dispersive once one or more of $k_\perp \rho_s$, $k_\perp d_e$, or $k_\parallel d_i$ becomes significant: for oblique waves at low $\beta$ as studied here, this can be at a much smaller scale than $d_i$. We show that the timescale for one-dimensional steepening of two-fluid Alfven waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfv\'en wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.Comment: 17 pages; submitted to Physics of Plasma

Experimental Study of 3-D, Impulsive Reconnection Events in a Laboratory Plasma

Fast, impulsive reconnection is commonly observed in laboratory, space and astrophysical plasmas. Many existing models of reconnection attempt to explain this behavior without including variation in the third direction. However, the impulsive reconnection events observed on the Magnetic Reconnection Experiment (MRX) which are described in this dissertation cannot be explained by 2-D models and are therefore fundamentally three-dimensional. These events include both a slow buildup phase and a fast current layer disruption phase. The buildup phase is characterized by a slow transition from collisional to collisionless reconnection and the formation of “flux rope” structures; these “flux ropes” are defined as 3-D high current density regions associated with an O point at the measurement location. In the disruption phase, the “flux ropes” are ejected from the reconnection layer as the total current drops and the reconnection rate spikes. Strong out-of-plane gradients in both the density and reconnecting magnetic field are another key feature of disruptive discharges; after finite upstream density is depleted by reconnection during the buildup phase, the out of plane magnetic field gradient flattens and this disruption spreads in the electron flow direction. Electromagnetic fluctuations in the lower hybrid frequency range are observed to peak at the disruption time; however, they are not the key physics responsible for the impulsive phenomena observed. Important features of the disruption dynamics cannot be explained by an anomalous resistivity model. Furthermore, an important discrepancy in the layer width and force balance between the collisionless regime of MRX and kinetic simulations persists when the fluctuations are small or absent, implying that they are not the cause of the wider electron layers observed in the experiment. These wider layers may instead be due to the formation of flux ropes with a wide range of sizes; consistent with this hypothesis, flux rope signatures are observed down to the smallest scales resolved by the diagnostics. Finally, a 3-D two-fluid model is proposed to explain how the observed out-of-plane variation may lead to a localized region of enhanced reconnection that spreads in the direction of electron flow

Hybrid simulation of Alfv\'en wave parametric decay instability in a laboratory relevant plasma

Large-amplitude Alfv\'en waves are subject to parametric decays which can have important consequences in space, astrophysical, and fusion plasmas. Though the Alfv\'en wave parametric decay instability was predicted decades ago, observational evidence is limited, stimulating considerable interest in laboratory demonstration of the instability and associated numerical modeling. Here, we report novel hybrid simulation of the Alfv\'en wave parametric decay instability in a laboratory relevant plasma (based on the Large Plasma Device), using realistic wave injection and wave-plasma parameters. Considering only collisionless damping, we identify the threshold Alfv\'en wave amplitudes and frequencies required for triggering the instability in the bounded plasma. These threshold behaviors are corroborated by simple theoretical considerations. Other effects not included in the present model such as finite transverse scale and ion-neutral collision are briefly discussed. These hybrid simulations demonstrate a promising tool for investigating laboratory Alfv\'en wave dynamics that can provide guidance for future laboratory demonstration of the parametric decay instability.Comment: 8 pages, 3 figure

The Effects of Pharmaceutical Marketing and Promotion on Adverse Drug Events and Regulation

This paper analyzes the relationship between postmarketing promotional activity and reporting of adverse drug reactions (ADRs) by modeling the interaction between a regulator (the FDA) and a pharmaceutical firm. Promotion-driven market expansions enhance profitability yet may involve the risk of inappropriate drug prescriptions, leading to regulatory actions against the firm. We empirically test the relationship between drug promotion and reporting of ADRs using an innovative combination of commercial data on pharmaceutical promotion and FDA data on regulatory interventions and ADRs. We provide some evidence that increased levels of promotion and advertising lead to increased reporting of ADRs for certain conditions. (JEL L51, L65, M31, M37)

Experimental Study of the Hall Effect and Electron Diffusion Region During Magnetic Reconnection in a Laboratory Plasma

The Hall effect during magnetic reconnection without an external guide field has been extensively studied in the laboratory plasma of the Magnetic Reconnection Experiment (MRX) [Yamada et al., Phys. Plasmas 4, 1936 (1997)] by measuring its key signature, an out-of-plane quadrupole magnetic field, with magnetic probe arrays whose spatial resolution is on the order of the electron skin depth. The in-plane electron flow is deduced from out-of-plane magnetic field measurements. The measured in-plane electron flow and numerical results are in good agreement. The electron diffusion region is identified by measuring the electron outflow channel. The width of the electron diffusion region scales with the electron skin depth (~ 8c/ωpe) and the peak electron outflow velocity scales with the electron Alfven velocity (~ 0:11VeA), independent of ion mass. The measured width of the electron diffusion region is much wider and the observed electron outflow is much slower than those obtained in 2D numerical simulations. It is found that the classical and anomalous dissipation present in the experiment can broaden the electron diffusion region and slow the electron outflow. As a consequence, the electron outflow flux remain consistent with numerical simulations. The ions, as measured by a Mach probe, have a much wider outflow channel than the electrons, and their outflow is much slower than the electron outflow everywhere in the electron diffusion region