The propagation of short-pulse lasers through underdense plasmas at ultra-high intensities (I≥1019 W/cm) is examined. The pulse evolution is found to be significantly different than it is for moderate intensities. The pulse breakup is dominated by leading edge erosion and plasma wave wake formation rather than from Raman forward scattering type instabilities. A differential equation which describes local pump depletion is derived and used to analyze the formation and evolution of the erosion. Pulse erosion is demonstrated with one dimensional particle in cell (PIC) simulations. In addition, two dimensional simulations are presented which show pulse erosion along with other effects such as channeling and diffraction. Possible applications for plasma based accelerators and light sources are discussed.
The validity and usefulness of linear wakefield theory for electron and positron bunches is investigated. Starting from the well-known Green's function for a cold-fluid plasma, engineering formulas for the maximum accelerating field for azimuthally symmetric bi-Gaussian beams of the form n b = n b e −r 2 /2 r 2 e −z 2 /2 z 2 are derived. It is also found that for fixed beam parameters the optimum wake is obtained for k p z =2 1/2 , for k p r ഛ 1. The validity and usefulness of linear-fluid theory is studied using fully nonlinear particle-in-cell simulations. It is found that linear theory can be useful beyond the nominal range of validity for narrow bunches. The limits of usefulness differ significantly between electron and positron bunches. For electron bunches, scaling laws are found for three limits for optimal plasma density ͑k p z =2 1/2 ͒, characterized by the normalized spot size k p r and the normalized charge per unit length of the beam, ⌳ ϵ͑n b / n p ͒k p 2 r 2. These are ϵ eE / mc p = 1.3͑n b / n p ͒ for k p r Ͼ 1 and n b / n p Ͻ 1, = 1.3 ⌳ ln͑1/k p r ͒, for ͑⌳ /10͒ 1/2 Ͻ k p r Ͻ 1 and ⌳Ͻ1, and = 1.3 ⌳ ln͓͑10/ ⌳͔ 1/2 ͒, for k p r Ͻ ͑⌳ /10͒ 1/2 and ⌳Ͻ1. Linear theory breaks down for n b / n p Х 10. On the other hand, for positron drivers linear-fluid theory breaks down for n b / n p ജ 1 independent of spot size.
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