It Hastened What We All Fought For, the End of the War: General Sherman\u27s Campaigns through Atlanta, Georgia, and the Carolinas and How They Impacted the Civil War

“It hastened what we all fought for, the end of the war: General Sherman’s campaigns through Atlanta, Georgia, and the Carolinas and how they impacted the Civil War” is my collection of research of the importance of Sherman’s campaigns through Atlanta, Georgia, and the Carolinas to bring the end of the war. My project is in fulfillment of the History 451: Proseminar within the requirements of a Bachelor’s Degree in history. My thesis paper covers those three campaigns and their importance in bringing the Civil War to an end. I have used primary and secondary evidence to provide facts and to support the importance of Sherman in the Civil War. Although Sherman’s role is a controversial topic of morality and necessity, I tried only to provide evidence and discussion for how it helped lead the Union to a victory on April 9, 1865. My goal was to offer analysis of 1864 and why Sherman’s marches were required.. Grant could not secure a victory around Richmond, Confederate forces attacked Washington DC and through all this a rising Pro-Peace Democratic Party led by former General, George McClellan threatened the re-election of Abraham Lincoln. It was not until General Sherman’s success at Atlanta that hope shone in the Union. From Atlanta and throughout Sherman’s remaining campaigns, he famously brought the war to Southern civilians making the war not only a physical war, but a psychological one as well. Sherman’s efforts against the Confederate forces and the Southern morale were imperative so the North could rise victorious in April, 1865

Charged particle motions in the distended magnetospheres of Jupiter and Saturn

Charged particle motion in the guiding center approximation is analyzed for models of the Jovian and Saturnian magnetospheric magnetic fields based on Voyager magnetometer observations. Field lines are traced and exhibit the distention which arises from azimuthally circulating magnetospheric currents. The spatial dependencies of the guiding center bounce period and azimuthal drift rate are investigated for the model fields. Non-dipolar effects in the gradient-curvature drift rate are most important at the equator and affect particles with all mirror latitudes. The effect is a factor of 10-15 for Jupiter with its strong magnetodisc current and 1-2 for Saturn with its more moderate ring current. Limits of adiabaticity, where particle gyroradii become comparable with magnetic scale lengths, are discussed and are shown to occur at quite modest kinetic energies for protons and heavier ions

The Jovian electron spectrum and synchrotron radiation at 375 cm

The synchrotron radiation expected at Earth from the region L=2.9-5 R sub J of Jupiter's magnetosphere is calculated using the Pioneer 10 electron model. The result is approximately 21 flux units (f.u.). This value is to be compared with 6.0 + or - 0.7 f.u., the flux density of synchrotron radiation measured from Jupiter's entire magnetosphere in ground-based radio observations. Most of the radiation at 375 cm is emitted by electrons in the 1 to 10 MeV range. If the electron model used for calculations is cut off below 10 MeV, the calculated flux is reduced to approximately 4 f.u., a level compatible with the radio observations

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.Comment: 18 page

Magnetospheric electrostatic emissions and cold plasma densities

A synoptic study of electric wave, magnetometer, and plasma data from IMP-6 was carried out for times when banded electrostatic waves are observed between harmonics of the electron gyrofrequency in the earth's outer magnetosphere. Four separate classes of such waves were previously identified. The spatial and temporal occurrences of waves in each class are summarized here, as are correlations of occurrence with geomagnetic activity. Most importantly, associations between the observations of waves of different classes and the relative portions of cold and hot electrons present at the position of the spacecraft are established. Finally, evidence for the signature of the loss cone is sought in the plasma data

Theory of flux anisotropies in a guiding center plasma

The one particle distribution function f on the scale of the bounce motion of particles in a magnetic field B is considered. The Vlasov equation is expanded through O(epsilon) in the adiabatic parameter which is the ratio of particle gyroradius to scale length of the magnetic field. Because f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the analysis is tailored to be explicitly applicable to space problems. To O(1), f is gyrotropic; its first velocity moment is (if non-vanishing) parallel to B, and hence macroscopic parallel flow is included in this term. The O(epsilon) contribution is non-gyrotropic and macroscopic flow parallel to B plus additional parallel flow results from these terms. The degree of non-gyrotropy and the amount of cross-field macroscopic flow depend on the perpendicular component of the electric field, on curvature and shear in the magnetic field, and on the spatial gradient, pitch angle derivative, and speed derivative of the lowest order distribution function

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory

A new approach to cosmic ray diffusion theory

An approach is presented for deriving a diffusion equation for charged particles in a static, random magnetic field. The approach differs from the usual, quasi-linear one, in that particle orbits in the average field are replaced by particle orbits in a partially averaged field. In this way the fluctuating component of the field significantly modifies the particle orbits in those cases where the orbits in the average field are unrealistic. The method permits the calculation of a finite value for the pitch angle diffusion coefficient for particles with a pitch angle of 90 rather than the divergent or ambiguous results obtained by quasi-linear theories. Results of the approach are compared with results of computer simulations using Monte Carlo techniques