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A summary is presented of the workshop "top physics at linear colliders" that was held at IFIC Valencia from the 30 th of June to the 3 nd July 2015. We present an up-to-date status report of studies into the potential for top quark physics of lepton colliders with an energy reach that exceeds the top quark pair production threshold, with a focus on the linear collider projects ILC and CLIC. This summary shows that such projects can offer very competitive determinations of top quark properties (mass, width) and its interactions with other Standard Model particles, in particular electroweak gauge bosons and the Higgs boson. In both areas the prospects exceed the LHC potential significantly -often by an order of magnitude.

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We discuss the nature of the electromagnetic fields excited by the beams in the beam pipe of an interaction region. In trying to find an optimum geometry for this region with a minimum of electromagnetic wave excitation, we have discovered one mode, which remains even in a very smooth geometry. This mode has a longitudinal electrical component and can be easily excited by the beam. By analyzing the structure of this mode we have found a way to absorb this mode. The work was done in connection with a proposal for a future electron-positron collider.

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