Boundary‐Value Problems of Linear‐Transport Theory—Green's Function Approach

Case's technique utilizing Green's functions for dealing with boundary‐value problems of the neutron linear‐transport theory is exploited. We show that the Fourier coefficients of the Green's function over the Case spectrum are precisely the normal modes. In particular, if we assume that the scattering kernel is rotationally invariant (which indeed we do assume) and approximate it by a degenerate kernel consisting of spherical harmonics, the set of modes is deficient for problems lacking azimuthal symmetry. We also show that the expansion of the scattering kernel, in terms of spherical harmonics (or any set of orthogonal functions for that matter), permits the linear factorization of the Fourier coefficients of the Green's function in terms of the lowest element, with the proportionality functions consisting of complete orthogonal polynomials. As a consequence of this attribute of Fourier coefficients, the eigenfunctions (continuum and discrete) also factorize, which then permits decoupling of the appropriate singular integral equations. To illustrate our idea, we solve half‐space and slab problems. However, the basic procedure is kept sufficiently general so that the extension to problems involving other geometrics remains straightforward.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71085/2/JMAPAQ-11-10-3042-1.pd

Green's Function Technique For Dealing With Boundary Value Problems Of The Linear Transport Theory.

PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/188357/2/7014560.pd

Theory of current collection of moving cylindrical probes

http://deepblue.lib.umich.edu/bitstream/2027.42/5855/5/bac5480.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/5855/4/bac5480.0001.001.tx

Theory of Current Collection of Moving Cylindrical Probes

The theory of current collection of a moving cylindrical probe is investigated. Volt‐ampere relations are derived for two distinct cases: (i) The general‐ion current for accelerating collector potential and its special cases, including general‐ion current to the stationary probe, orbital‐motion‐limited current to the moving and the stationary probes, and sheath‐area‐limited current to the moving and the stationary probes; (ii) the general‐electron current for the retarding collector potential and its special cases, including general‐electron current to the stationary probe and random‐electron current to the moving and the stationary probes. Orientation of the cylinder with respect to the drift velocity vector is taken into account. Volt‐ampere characteristics are included for illustrating the functional behavior of the current relations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70301/2/JAPIAU-35-6-1697-1.pd

Spherically Symmetric Boundary‐Value Problems in One‐Speed Transport Theory

A Green's function technique is applied to one‐velocity neutron problems with spherical symmetry. The main advantage of the approach is that it bypasses the need to construct explicitly the appropriate spherical eigenfunctions. Indeed, these can be directly deduced from this new formulation, if one so desires.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69386/2/JMAPAQ-11-1-223-1.pd

Theoretical and experimental investigation of plasma waves, space vehicle plasma sheaths, and ionospheric electron temperatures : semi-annual report

http://deepblue.lib.umich.edu/bitstream/2027.42/4935/5/bac2828.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/4935/4/bac2828.0001.001.tx

A theoretical study of the effect of collective interaction on the electron temperature in the ionosphere and of the Langmuir probe characteristics in the presence of a magnetic field: semiannual report no. 1

http://deepblue.lib.umich.edu/bitstream/2027.42/4937/5/bac2278.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/4937/4/bac2278.0001.001.tx

Volt-ampere characteristics of cylindrical and spherical langmuir probes for various potential models

http://deepblue.lib.umich.edu/bitstream/2027.42/5856/5/bac5461.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/5856/4/bac5461.0001.001.tx

An ejectable ion trap--Langmuir probe experiment for ionosphere direct measurements

http://deepblue.lib.umich.edu/bitstream/2027.42/3788/5/bab3454.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3788/4/bab3454.0001.001.tx