Achievement of atomic-resolution electron-beam tomography will allow determination of the three-dimensional structure of nanoparticles (and other suitable specimens) at atomic resolution. Three-dimensional reconstructions will yield "section" images that resolve atoms overlapped in normal electron microscope images (projections), resolving lighter atoms such as oxygen in the presence of heavier atoms, and atoms that lie on non-lattice sites such as those in non-periodic defect structures. Our first demonstrations of 3-D reconstruction to atomic resolution used five zone-axis images from test specimens of staurolite consisting of a mix of light and heavy atoms. We propose combining ultra-high (sub-Angstrom) resolution zone-axis images with off-zone images by first using linear reconstruction of the off-zone images while excluding images obtained within a small range of tilts (of the order of 60 milliradian) of any zone-axis orientation, since it has been shown that dynamical effects can be mitigated by slight off-axis tilt of the specimen. The (partial) reconstruction would then be used as a model for forward calculation by image simula-tion in zone-axis directions and the structure refined iteratively to achieve satisfactory fits with the experimental zone-axis data. Another path to atomic-resolution tomography would combine "zone-axis tomography" with high-resolution dark-field hollow-cone (DFHC) imaging. Electron diffraction theory indicates that dynamic (multiple) scattering is much reduced under highly-convergent illumination. DFHC TEM is the analog of HAADF STEM, and imaging theory shows that image resolution can be enhanced under these conditions. Images obtained in this mode could provide the initial reconstruction, with zone-axis images used for refinement.

Computer simulations using the 2D code "POSINST" were used to study the formation of the electron cloud in the wiggler section of the positron damping ring of the International Linear Collider. In order to simulate an x-y slice of the wiggler (i.e., a slice perpendicular to the beam velocity), each simulation assumed a constant vertical magnetic field. At values of the magnetic field where the cyclotron frequency was an integral multiple of the bunch frequency, and where the field strength was less than approximately 0.6 T, equilibrium average electron densities were up to three times the density found at other neighboring field values. Effects of this resonance between the bunch and cyclotron frequency are expected to be non-negligible when the beam bunch length is much less than the product of the electron cyclotron period and the beam velocity, for a beam moving at v~;;c. Details of the dynamics of the resonance are described.