The effect of ion density in a plasma channel on the profile of bubble rear is investigated theoretically. The wakefield contraction and the steepness of the bubble rear depend on the ratio of ions in a uniform plasma to those in a channel. With the decreasing of ion density in the channel, the bubble length becomes shorter and its bubble rear is steeper. The electron dynamics show that a typical electron can oscillate between the upper and lower boundaries of the channel, not like the betatron oscillation around the on-axis in homogeneous plasma. These results are verified by two-dimensional particle-in-cell simulations. By optimizing the radius of the hollow plasma channel, the front part of a self-injected electron bunch can be reflected back into the channel by the transverse focusing force, while its rear part will escape from the channel. The electric field is transversely uniform and has longitudinally plateau in the regime of self-injected electron bunch, which allows for monoenergetic acceleration.
The azimuthally polarized beam always keeps a zero intensity at the center of the doughnut shaped pulse. As a result, it
can be utilized to overcome the problem of not perfect zero in STED microscopy to exhibit a high resolution. This paper
examines the utilization of this beam as the stimulated emission depletion pulse in STED microscopy and the results are
compared with the effects of using a doughnut model generated by the linearly polarized lights with inserting the phase
plates in lights. The calculations show that the azimuthally polarized beam has a great potential in the STED microscopy.