ALBERT

Description: Global, three-dimensional, ideal MHD simulations of Earth's bow shock are reported for low Alfven Mach numbers M(sub A) and quasi-perpendicular magnetic field orientations. The simulations use a hard, infinitely conducting magnetopauause obstacle, with axisymmetric three-dimensional location given by scaled standard model, to directly address previous gasdynamic (GD) and field-aligned MHD (FA-MHD) work. Tests of the simulated shocks' density jumps X for 1.4 approx. less than MA approx. less than 10 and the high M(sub A) shock location, and reproduction of the GD relation between magnetosheath thickness and X for quasi-gasdynamic MHD runs with M(sub A) much greater than M(sub s), confirm that the MHD code is working correctly. The MHD simulations show the standoff distance a(sub s), increasing monotonically with decreasing M(sub A). Significantly larger a(sub s), are found at low M(sub A) than predicted by GD and phenomenological MHD models and FA-MHD simulations, as required qualitatively by observations. The GD and FA-MHD predictions err qualitatively, predicting either constant or decreasing a(sub s), with decreasing M(sub A). This qualitative difference between quasi- perpendicular MHD and FA-MHD simulations is direct evidence for a(sub s), depending on the magnetic field orientation Theta. The enhancement factor over the phenomenological MHD predictions at MA approx. 2.4 agrees quantitatively with one observatiorial estimate. A linear relationship is found between the magnetosheath thickness and X, modified both quantitatively and intrinsically by MHD effects from the GD result. The MHD and GD results agree in the high M(sub A) limit. An MHD theory is developed for a(sub s), restricted to sufficiently perpendicular Theta and high sonic Mach numbers M(sub s). It explains the simulation results with excellent accuracy. Observational and further simulation testing of this MHD theory, and of its predicted M(sub A), Theta, and M(sub s) effects, is desirable.

Description: Maximum electric fields of Langmuir waves at planetary foreshocks are estimated from the threshold for electrostatic decay, assuming it saturates beam driven growth, and incorporating heliospheric variation of plasma density and temperature. Comparisons with spacecraft observations yields good quantitative agreement. Observations in type 3 radio sources are also in accord with this interpretation. A single mechanism can thus account for the highest fields of beam driven waves in both contexts.

Description: Excellent progress was made under this grant on the generation and scattering of the 2-3 kHz radio emissions observed by the Voyager spacecraft in the outer heliosphere. These are the most powerful radio emissions produced in our solar system, surpassing even those of Jupiter and the Sun. The widely-held hypothesis pursued is that the radiation is generated near the electron plasma frequency f(sub p) or near 2f(sub p) as a shock wave traverses the heliosheath regions and/or heliopause predicted in the interaction region between the solar wind and the local interstellar medium. (Note that f (sup 2) (sub p) is proportional to the plasma density.) The traveling shock wave is plausibly associated with a global merged interaction region (GMIR). Accordingly, this so-called GMIR model is strongly analogous to the common interpretation of type II solar radio bursts and to radio emissions associated with Earth's bow shock, with coronal mass ejections (CMEs) and Earth's magnetosphere playing the role of a GMIR, respectively. Accordingly, Dr Cairns work on type II bursts, Earth's foreshock, and stochastic growth theory (not described in detail) strongly aided and complemented the research progress on the 2-3 kHz emissions described.

Description: Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution is power-law P(bar)(log E) in the wave field E with the bar denoting this averaging over position, In this paper it is shown that stochastic growth theory (SGT) can explain a power-law spatially-averaged distributions P(bar)(log E), when the observed power-law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.

Description: Langmuir waves driven to high levels by beam instabilities are subject to nonlinear processes, including the closely related processes of scattering off thermal ions (STI) and a decay process in which the ion response is organized into a product ion acoustic wave. Calculations of the nonlinear growth rates predict that the decay process should always dominate STI, creating two paradoxes. The first is that three independent computer simulation studies show STI proceeding, with no evidence for the decay at all. The second is that observations in space of type 3 solar radio bursts and Earth's foreshock, which the simulations were intended to model, show evidence for the decay proceeding but no evidence for STI. Resolutions to these paradoxes follow from the realization that a nonlinear process cannot proceed when its growth rate exceeds the minimum frequency of the participating waves, since the required collective response cannot be maintained and the waves cannot respond appropriately, and that a significant number of e-foldings and wave periods must be contained in the time available. It is shown that application of these 'collective' and 'time scale' constraints to the simulations explains why the decay does not proceed in them, as well as why STI proceeds in specific simulations. This appears to be the first demonstration that collective constraints are important in understanding nonlinear phenomena. Furthermore, applying these constraints to space observations, it is predicted that the decay should proceed (and dominate STI) in type 3 sources and the high beam speed regions of Earth's foreshock for a specific range of wave levels, with a possible role for STI alone at slightly higher wave levels. Deeper in the foreshock, for slower beams and weaker wave levels, the decay and STI are predicted to become ineffective. Suggestions are given for future testing of the collective constraint and an explanation for why waves in space are usually much weaker than in the simulations.

Description: 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.