  We introduce a mechanism that can both hold and amplify electromagnetic waves
by rapidly changing the permittivity of the medium during the wave travel from
a positive to a dispersionless (i.e. non-Foster) negative value and then back
again. The underlying physics behind this phenomenon is theoretically explored
by considering a plane wave in an unbounded medium. Interestingly, we show that
a rapid positive-to-negative temporal change of {\epsilon}(t) causes the
propagation of the wave to stop (observed by a frozen phase in time) while the
amplitude of the frozen field exponentially grows. Stepping the permittivity
back to the original (or a new) positive value will cause the wave to thaw and
resume propagation with the original (or the new) frequency, respectively. We
numerically study the case of dipole radiation in such time-varying non-Foster
structures. As a possible implementation, we propose a parallel plate waveguide
platform loaded with time-dependent media emulating parallel lumped non-Foster
negative capacitors. Such non-Foster time-varying structures may open new
venues in controlling and manipulating wave-matter interaction.
