The electron pulse broadening and energy spread, caused by space charge effects, in a photoelectron gun are studied analytically using a fluid model. The model is applicable in both the photocathode-to-mesh region and the postanode electron drift region. It is found that space charge effects in the photocathode-to-mesh region are generally unimportant even for subpicosecond pulses. However, because of the long drift distance, electron pulse broadening due to space charge effects in the drift region is usually significant and could be much larger than the initial electron pulse duration for a subpicosecond electron pulse. Space charge effects can also lead to a considerable electron energy spread in the drift region. Temporal broadening is calculated for an initial electron pulse as short as 50 fs with different electron densities, final electron energies, and drift distances. The results can be used to design electron guns producing subpicosecond pulses for streak cameras as well as for time resolved electron diffraction.

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An acceleration element is proposed for compressing the electron pulse duration in a femtosecond photoelectron gun. The element is a compact metal cavity with curved-shaped walls. An external voltage is applied to the cavity where a special electric field forms in such a way that the slow electrons in the electron pulse front are accelerated more than the fast electrons, and consequently the electron pulse duration will be compressed. The distribution of the electric field inside the acceleration cavity is analyzed for the geometry of the cavity. The electron dynamics in this acceleration cavity is also investigated numerically. Numerical results show that the electron pulse front and pulse duration can be improved by compensating for the effects of space charge and the initial energy spread of photoelectrons with a Lambertian angular distribution. Depending on the design parameters and the shape of the electron pulse, for a femtosecond electron gun with an electron energy of 30 keV, 10(3) electrons per pulse, and an electron drift length of 40 cm, the electron pulse duration can be reduced from 550 to 200 fs when using a compensating cavity with an average radius of 1.7 and 5.6 cm in length. Electron pulses shorter than 200 fs can be achieved if the length of the drift region is reduced.

The root-mean-squared (rms) envelope equations are derived and analyzed for an unbunched intense charged-particle beam in an alternating-gradient focusing field and a cylindrical conducting pipe. All higher-order image-charge effects from the cylindrical pipe are expressed in terms of so-called multiple moment factors in the rms beam envelope equations, and the multiple moment factors are evaluated. Numerical results show that for vacuum phase advance v < 90 , the image-charge effects on the matched and slightly mismatched beam envelopes are negligibly small, at all orders, for all beams with arbitrary beam density profiles (including hollow density profiles) as well as for arbitrary small apertures (including beams with large aspect ratios). However, the main unstable region for the envelope evolution with image-charge effects, which occurs for 90 < v < 270 , depending on the value of the normalized beam intensity SK=", is found to be narrower than its counterpart without image-charge effects.