Theory of the pulse response from a small antenna in a magnetized plasma

The electrostatic plasma response to a small pulsed antenna in a magnetic field is analyzed. The ringing of the plasma at three discrete frequencies--the upper-hybrid frequency and two resonance cone branch frequencies--is evidenced, and the amplitudes of these frequency responses is determined as a function of the characteristic plasma frequencies, the angle of observation with respect to the magnetic field, and the pulse length. Applications to plasma diagnostics are discussed. It is shown that the upper hybrid response and the response at either of the resonance cone branch frequencies is adequate information to determine the plasma density, and the magnetic field magnitude and angle

Wave emissions from planetary magnetospheres

An important development in the Earth magnetosphere was the discovery of the boundary of the plasma sheet and its apparent role in the dynamics of the magnetotails. Three instabilities (negative energy mode, counterstreaming, and the Buneman instability) were investigated through analytical and numerical studies of their frequency and growth rate as a function of the angle of propagation

Towards an MHD Theory for the Standoff Distance of Earth's Bow Shock

A magnetohydrodynamic (MHD) theory is developed for the standoff distance a(s) of the bow shock and the thickness Delta(ms) of the magnetosheath, using the empirical Spreiter et al. relation Delta(ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for Delta(ms) and As. In general, however, MHD effects produce major differences from previous models, especially at low Alfev (Ma) and Sonic (Ms) Mach numbers. The magnetic field orientation Ma, Ms and the ratio of specific heats gamma are all important variables of the theory. In contrast, the fast mode Mach number need play no direct role. Three principle conclusions are reached. First the gasdynamic and phenomenological models miss important dependences of field orientation and Ms generally provide poor approximations to the MHD results. Second, changes in field orientation and Ms are predicted to cause factor of approximately 4 changes in Delta(ms) at low Ma. These effects should be important when predicting the shock's location or calculating gramma from observations. Third, using Spreiter et al.'s value for k in the MHD theory leads to maxima a(s) values at low Ma and nominal Ms that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or a breakdown in the Spreiter-like relation at very low Ma

Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers

A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a modified phenomenological model proposed recently. The similarities and differences between these results are illustrated using plots of X and a(s) predicted for the Earth's bow shock. The plots show that the new analytic solutions agree very well with the exact numerical MHD solutions and that these MHD solutions should replace the corresponding phenomenological relations in comparisons with data. Furthermore, significant differences exist between the standoff distances predicted at low M(A) using the MHD models versus those predicted by the new modified phenomenological model. These differences should be amenable to observational testing

International money markets: eurocurrencies

Eurocurrencies are international markets for short-term wholesale bank deposits and loans. They emerged in Western Europe in the late 1950s and rapidly reached a global scale. A Eurocurrency is a form of bank money: an unsecured short-term bank debt denominated in a currency (for instance, US dollars) but issued by banks operating offshore, in a geographical location or a legal space situated outside of the jurisdiction of the national authorities presiding over that currency (for instance, the Federal Reserve). In Eurocurrency markets, banks intermediate mainly between foreign residents. They borrow funds by "accepting" foreign currency deposits and lend foreign currency-denominated funds by "placing" deposits with other banks, by granting short-term loans or investing in other liquid assets. Historically, Eurodollars accounted for the largest share of Eurocurrencies, although other international currencies (Deutsche Marks, Japanese yens, and especially Euros since 1999) played an important role. Eurocurrency markets were a manifestation of financial integration and interdependence in a globalizing economy and performed critical functions in the distribution and creation of international liquidity. At the same time, their fast growth was a recurrent source of concerns for central bankers and policymakers due to their implications for macroeconomic policies and financial stability. This chapter analyzes different aspects of the historical development of Eurocurrency markets and their role in the international monetary and financial system. The first part discusses theoretical interpretations, presents estimates of markets' size, describes their structure, and explains the determinants of their growth. The second part analyzes the spread between Eurodollar rates and other US money market rates, the role of arbitrage, the evolution of risk factors, and the causes of historical episodes of stress and contagion in the interbank market. The last part discusses political economy issues, such as the role of governments and market forces in the emergence of Eurodollars in the 1950s and the failed attempts to impose multilateral controls on Eurocurrency markets in the 1970s

Resonance Cones and Mode Conversion in a Warm Magnetized Bounded Plasma

The warm plasma resonance cone structure of the quasistatic field produced by a gap source in a bounded magnetized slab plasma is determined theoretically. This is initially determined for a homogeneous or mildly inhomogeneous plasma with source frequency lying between the lower hybrid frequency and the plasma frequency. It is then extended to the complicated case of an inhomogeneous plasma with two internal lower hybrid layers present, which is of interest to radio frequency heating of plasmas. In the first case, the potential is obtained as a sum of multiply reflected warm plasma resonance cones, each of which has a similar structure, but a different size, amplitude, and position. An important interference between nearby multiply-reflected resonance cones is found. The cones are seen to spread out as they move away from the source, so that this interference increases and the individual resonance cones become obscured far away from the source. In the second case, the potential is found to be expressible as a sum of multiply-reflected, multiply-tunnelled, and mode converted resonance cones, each of which has a unique but similar structure. The effects of both collisional and collisionless damping are included and their effects on the decay of the cone structure studied. Various properties of the cones such as how they move into and out of the hybrid layers, through the evanescent region, and transform at the hybrid layers are determined. It is found that cones can tunnel through the evanescent layer if the layer is thin, and the effect of the thin evanescent layer is to subdue the secondary maxima of cone relative to the main peak, while slightly broadening the main peak and shifting it closer to the cold plasma cone line. Energy theorems for quasistatic fields are developed and applied to determine the power flow and absorption along the individual cones. This reveals the points of concentration of the flow and the various absorption mechanisms.</p