  In strong electromagnetic fields, unique plasma phenomena and applications
emerge, whose description requires recently developed theories and simulations
[Y. Shi, Ph.D. thesis, Princeton University (2018)]. In the classical regime,
to quantify effects of strong magnetic fields on three-wave interactions, a
convenient formula is derived by solving the fluid model to the second order in
general geometry. As an application, magnetic resonances are exploited to
mediate laser pulse compression, using which higher intensity pulses can be
produced in wider frequency ranges, as confirmed by particle-in-cell
simulations. In even stronger fields, relativistic-quantum effects become
important, and a plasma model based on scalar quantum electrodynamics (QED) is
developed, which unveils observable corrections to Faraday rotation and
cyclotron absorption in strongly magnetized plasmas. Beyond the perturbative
regime, lattice QED is extended as a numerical tool for plasma physics, using
which the transition from wakefield acceleration to electron-positron pair
production is captured when laser intensity exceeds the Schwinger threshold.
