It is widely accepted that the next lepton collider beyond a Higgs factory would require center-of-mass energy of the order of up to 15 TeV. Plasma based acceleration is considered a promising concept for the next generation of linear electron-positron colliders. Despite the great progress achieved over the last twenty years in laser technology, laser- and beam-driven particle acceleration, and special target availability, positron acceleration remains significantly underdeveloped if compared to electron acceleration. This is due to both the specifics of the plasma-based acceleration, and the lack of adequate positron sources tailored for the subsequent plasma based acceleration. Here several designs for laser plasma based positron sources are discussed. First, a set of compact, two-stage plasma-based positron sources is presented. In the first stage the positrons are created by a multi GeV electron beam produced by a laser-plasma accelerator interacting with a solid density foil. In the second stage the positrons are captured and accelerated in a plasma wave driven by either an electron beam or a laser pulse. Second, a positron source based on the collision of a high energy electron beam with a high intensity laser pulse is proposed. The source relies on the subsequent multi-photon Compton and Breit-Wheeleer processes to generate an electron-positron pair out of a high energy photon emitted by an electron. The remarkable property of this source is that low divergence positron beams can be generated by employing frequency doubled and quadrupled laser pulses. The resulting low emittance in the sub-micron range potentially makes such source interesting for collider applications.
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