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This task originated in 1987 to explore the possibility of accelerating short bursts of electrons by pulsed power. The principal effort of our group was to demonstrate that electrons can be accelerated by picosecond-long electrical pulses which are compressed in a radial transmission line. This goal has now been achieved and our results are presented in this paper. We have achieved a gradient of 45 MV/m across a 250 (mu)m accelerating gap and have accelerated 10(sup 6) electrons in a 1 ps long pulse. The beam emerges from a 500 (mu)m hole and can be refocused to this transverse dimension. The efficiency of the system, is of order (eta) = 2 (times) 10(sup (minus)6) due to the small number of electrons accelerated. If we identify the gap spacing with one half wavelength of the ''accelerating r.f.,''our device is equivalent to a 600 GHz structure. The principal limitation in the accelerating gradient comes from the H.V. hold-off properties of the semiconductor disks that are used as photoconductive switches. We believe that with better materials a factor of 10 can be gained in the gradient. Similarly, the electron yield can be increased by at least three orders of magnitude if proper photocathodes are used in place of the metallic surface. The more difficult problem is the engineering of a multicell structure using our present design of the single cell. Our plans for the continuation of this work are given. One of the most promising applications of laser switched acceleration is in the operation of a very low emittance electron source. Thus we have turned our attention to this subject, and in particular to building a high brilliance electron source using a superconducting cavity. Also discussed is the possibility of picosecond x-ray sources.