The physical principles are considered on intense wakefields excitation in plasma and dielectric by high-powerudshort laser pulse or by a train of electron bunches for high-gradient acceleration of charged particles with purpose toudelaborate the concept of future compact accelerators for high-energy physics and high technology applications, andudalso for creation of contemporary short pulsed radiation sources. The results of investigations on laser’s accelerationudin vacuum, electrons acceleration in plasma by high power laser pulse with obtaining beams of small angle and energyuddispersion, concepts of plasma and dielectric wakefield accelerators are presented. The perspective researchudprogram of the schemes of laser/beam acceleration in plasma and dielectric is considered.
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