| The interactions of relativistic electrons with relativistic plasma waves are studied by examining three novel applications: a high gradient particle accelerator, an electron beam diagnostic of relativistic plasma waves, and an undulator for producing short wavelength radiation. The focusing of a high energy particle beam in a ramped density, continuously focusing, plasma lens for use in future high energy {dollar}esp-esp+{dollar} colliders is also examined.; The trapping threshold, energy gain, phase evolution, beam focusing and energy spectrum are found for particles accelerated in the laser plasma beatwave accelerator, plasma wakefield accelerator, and laser wakefield accelerator schemes in which accelerating gradients on the order of 10's to 100's of GigaVolts per meter may exist. The limits due to beam emittance and plasma wave width are found for the measurement of relativistic plasma wave amplitude and wavelength using a relativistic electron beam as a diagnostic. The short wavelength ({dollar}approx{dollar}1 {dollar}mu{dollar}m) spontaneous radiation, particle bunching, stimulated radiation, and radiation gain are found for modest energy electrons ({dollar}approx{dollar}4 MeV) injected into a 1 cm long, 100 {dollar}mu{dollar}m period, plasma wave undulator which is shown to behave similarly to a free electron laser undulator. The compression of high energy beams to very small spot sizes in the ramped density plasma lens is found to be sensitive to beam and lens matching which is determined by adjusting the Courant-Snyder accelerator parameters. |
