The transverse emittance is one of the most important quantities which characterize the quality of an electron source. For high quality experiments low beam emittance is required. By means of theoretical considerations and simulation calculations we have studied how the emittance of the Rossendorf superconducting radio-frequency photoelectron source (SRF gun) can be minimized. It turned out that neither a solenoid magnet nor the effect of space charge forces is needed to create a pronounced emittance minimum. The minimum appears by just adjusting the starting phase of the electron bunch with respect to the RF phase of the gun in a suitable way. Investigation of various correlations between the properties of the beam particles led to an explanation on how the minimum comes about. It is shown that the basic mechanism of minimization is the fact that the longitudinal properties of the particles (energy) are strongly influenced by the starting phase. Due to the coupling of the longitudinal and transverse degrees of freedom by the relativistic equation of motion the transverse degrees of freedom and thereby the emittance can be strongly influenced by the starting phase as well. The results obtained in this study will be applied to minimize the emittance in the commissioning phase of the SRF gun.

High-mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors has been used experimentally and theoretically to study ballistic electron transport. The present project is motivated by recent experiments in magnetic electron focusing. The proposed device consists of two quantum point contacts (QPCs) serving as electron injector and detector which are placed in the same semiconductor GaAs/AlGaAs heterostructure. This thesis is focused on the theoretical study of electron flow coming from the injector QPC (a short quantum wire) and going into an open two-dimensional (2D) reservoir. The transport is considered for non-interacting electrons at different transmission regimes using the mode-matching technique. The proposed mode-matching technique has been implemented numerically using Matlab software. Electron flow through the quantum wire with rectangular, conical and rounded openings has been studied with and without an applied electric bias. We have found that the geometry of the opening does not play a crucial role for the electron flow propagation while the conical opening allows the electrons to travel longer distances into the 2D reservoir. When electric bias is applied, the electron flow also penetrates farther into the 2D region. The results of this study can be applied in designing magnetic focusing devices.

The transverse emittance is one of the most important quantities which characterize the quality of an electron source. For high quality experiments low beam emittance is required. By means of theoretical considerations and simulation calculations we have studied how the emittance of the Rossendorf superconducting radio-frequency photoelectron source (SRF gun) can be minimized. It turned out that neither a solenoid magnet nor the effect of space charge forces is needed to create a pronounced emittance minimum. The minimum appears by just adjusting the starting phase of the electron bunch with respect to the RF phase of the gun in a suitable way. Investigation of various correlations between the properties of the beam particles led to an explanation on how the minimum comes about. It is shown that the basic mechanism of minimization is the fact that the longitudinal properties of the particles (energy) are strongly influenced by the starting phase. Due to the coupling of the longitudinal and transverse degrees of freedom by the relativistic equation of motion the transverse degrees of freedom and thereby the emittance can be strongly influenced by the starting phase as well. The results obtained in this study will be applied to minimize the emittance in the commissioning phase of the SRF gun.