There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

It has been suggested (Lindzen, 1967, 1968a, b; Lindzen and Blake, 1971; Hodges, 1969) that turbulence in the upper mesosphere arises from the unstable breakdown of tides and gravity waves. Crudely speaking, it was expected that sufficient turbulence would be generated to prevent the growth of wave amplitude with height (roughly as (basic pressure)−1/2). This work has been extended to allow for the generation of turbulence by smaller amplitude waves, the effects of mean winds on the waves, and the effects of the waves on the mean momentum budget. The effects of mean winds, while of relatively small importance for tides, are crucial for internal gravity waves originating in the troposphere. Winds in the troposphere and stratosphere sharply limit the phase speeds of waves capable of reaching the upper mesosphere. In addition, the existence of critical levels in the mesosphere significantly limits the ability of gravity waves to generate turbulence, while the breakdown of gravity waves contributes to the development of critical levels. The results of the present study suggest that at middle latitudes in winter, eddy coefficients may peak at relatively low altitudes (50 km) and at higher altitudes in summer and during sudden warmings (70–80 km), and decrease with height rather sharply above these levels. Rocket observations are used to estimate momentum deposition by gravity waves. Accelerations of about 100 m/s/day are suggested. Such accelerations are entirely capable of producing the warm winter and cold summer mesopauses.

http://climateknowledge.org/figures/Rood_Climate_Change_AOSS480_Documents/QC114_Lindzen_Gravity_Wave_Stress_JGR_1981.pdf

Turbulence and stress owing to gravity wave and tidal breakdown

Introduction: Early Ideas and Observations Tidal Patterns Meteorological and Other Non-tidal Disturbances Some Definitions of Common Terms Basic Statistics of Tides as Time Series Observations and Data Reduction Forces Analysis and Prediction Tidal Dynamics Biology: Some Tidal Influences Filters for Tidal Time Series Response Analysis Inputs and Theory Analysis of Currents Theoretical Tidal Dynamics Legal Definitions in the Coastal Zone

Tides, Surges and Mean Sea-Level

The subject of surface potentials on natural and artificial bodies in space is reviewed with particular emphasis on recent developments. Following a brief survey of work done up to the early 1970s on the charging of astrophysical objects in interstellar and interplanetary space and spacecraft charging, the various charging mechanisms in space are examined, including the collection of plasma particles, photoemission, and secondary electron emission by electron impact and ion impact, and the effects on charging of nonisotropic plasmas, wakes, and environmental magnetic and electric fields are considered. The concept of equilibrium potential is discussed, along with differential charging, potential barriers and discharge processes. The measurement of spacecraft potentials is then considered, and recent work on spacecraft potential modification and control by active and passive means is presented. Finally, astrophysical applications where charging effects may be important are discussed, and areas for further work are indicated.

http://iopscience.iop.org/article/10.1088/0034-4885/44/11/002/pdf

Potentials of surfaces in space

A description is given of the path leading to the first approximation expression for the solar wind-magnetosphere energy coupling function (epsilon), which correlates well with the total energy consumption rate (U sub T) of the magnetosphere. It is shown that epsilon is the primary factor controlling the time development of magnetospheric substorms and storms. The finding of this particular expression epsilon indicates how the solar wind couples its energy to the magnetosphere; the solar wind and the magnetosphere make up a dynamo. In fact, the power generated by the dynamo can be identified as epsilon through the use of a dimensional analysis. In addition, the finding of epsilon suggests that the magnetosphere is closer to a directly driven system than to an unloading system which stores the generated energy before converting it to substorm and storm energies. The finding of epsilon and its implications is considered to have significantly advanced and improved the understanding of magnetospheric processes.

Energy coupling between the solar wind and the magnetosphere

The buildup of static charge on satellite surfaces is an important issue in the utilization of satellite systems. The analysis of this phenomenon has required important advances in basic charging theory and the development of complex codes to evaluate the plasma sheaths that surround satellites. The results of these theories and calculations have wide application in space physics in the design of systems and in the interpretation of low-energy plasma measurements. In this review, those aspects of charge buildup on satellite surfaces relevant to the space physics community are summarized. The types of charging processes, models of charge buildup, satellite sheath theories, and charging observations are described with emphasis on basic concepts.

The charging of spacecraft surfaces

Energetic Ion and Electron Irradiation of the Icy Galilean Satellites

List of illustrations List of tables Preface Acknowledgement 1. Introduction 2. Fundamental length, time, and velocity 3. The ambient space environment 4. Neutral gas interactions 5. Plasma interactions 6. The space radiation environment 7. Particulate interactions 8. The state of the art References Index.

Spacecraft--environment interactions

In situ data from the Pioneer and Voyager spacecraft, supplemented by earth-based observations and theoretical considerations, are used as the basis for the present quantitative, compact model of the 1 eV-several MeV charged particle distribution in the Jovian magnetosphere. The thermal plasma parameters of convection speed, number density, and characteristic energy, are specified as functions of position for electrons and for the ion species H(+), O(+), O(2+), S(+), S(2+), S(3+), and Na(+). Major features of the magnetic field, thermal plasma, and trapped particle distributions, are modeled and results for each plasma region are compared with observed spectra. Comparisons show that the model represents the data to within a factor of 2 + or - 1, except where time variations are significant. Practical applications of the model to spacecraft near Jupiter are given.

Charged particle distributions in Jupiter's magnetosphere

The need for uniform criteria, or guidelines, to be used in all phases of spacecraft design is discussed. Guidelines were developed for the control of absolute and differential charging of spacecraft surfaces by the lower energy space charged particle environment. Interior charging due to higher energy particles is not considered. A guide to good design practices for assessing and controlling charging effects is presented. Uniform design practices for all space vehicles are outlined.

/pdf/design-guidelines-for-assessing-and-controlling-spacecraft-as1vumgku3.pdf

Henry B. Garrett

Papers

The charging of spacecraft surfaces

Energetic Ion and Electron Irradiation of the Icy Galilean Satellites

Spacecraft--environment interactions

Charged particle distributions in Jupiter's magnetosphere

Design guidelines for assessing and controlling spacecraft charging effects