The modeling of the interaction of charged particles with electromagnetic fields is important in a number of areas of electrophysics research including plasma based particle acceleration and beam driven generation of coherent radiation. It is frequently the case that the time duration of a simulation that is required to capture the important physical effects exceeds by a large factor the time during which an individual particle interacts with the fields. In this case direct simulation by PIC methods is inefficient and reduced models and algorithms are required. This talk will first attempt to present these reduced models in a unified way. Then examples of applications of these models will be given. Some of the problems associated with the use of these models and potential solutions to these problems will be discussed
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