On Closed Sets with Convex Projections

A shadow of a subset A of Rⁿ is the image of A under a projectiononto a hyperplane. Let C be a closed nonconvex set in Rⁿ suchthat the closures of all its shadows are convex. If, moreover,there are n independent directions such that the closures ofthe shadows of C in those directions are proper subsets of therespective hyperplanes then it is shown that C contains a copyof R^n–2. Also for every closed convex set B ‘minimalimitations’ C of B are constructed, that is, closed subsetsC of B that have the same shadows as B and that are minimalwith respect to dimension.     

Plasma electron trapping and acceleration in a plasma wake field using a density transition

A new scheme for plasma electron injection into an acceleration phase of a plasma wake field is presented. In this scheme, a single, short electron pulse travels through an underdense plasma with a sharp, localized, downward density transition. Near this transition, a number of background plasma electrons are trapped in the plasma wake field, due to the rapid wavelength increase of the induced wake wave in this region. The viability of this scheme is verified using two-dimensional particle-in-cell simulations. To investigate the trapping and acceleration mechanisms further, a 1D Hamiltonian analysis, as well as 1D simulations, has been performed, with the results presented and compared.     

Pulse compression in radio frequency photoinjectors-applications toadvanced accelerators

While RF photoinjectors are an excellent source of high brightness electron beams, there are constraints to tying together the expected emittance and peak current performance of a given photoinjector system. These constraints, which arise from the complicated dynamics of the electrons due to the interplay of RF and space-charge forces within the photoinjector, tend to favor lower peak current operation. For some ultimate uses of photoinjector beams, such as linear collider test beams, wakefield accelerators, and free-electron lasers (FEL's), one may desire much higher peak currents. In this case, an inexpensive and reliable method for producing extremely short high-current electron bunches is to use magnetic compression. We examine this scheme analytically and by computer simulation. Many applications are illustrated, including the TESLA Test Facility/FEL injector, ultra-high current beams for plasma wakefields and generation of femtosecond electron pulses for injection into short wavelength laser-based accelerators. It is shown that the injection timing jitter associated with the laser can be nearly eliminated using this scheme, making it an indispensable component in many of the advanced accelerator injectors we consider