  Solutions to the backreaction equation in 1+1-dimensional semiclassical
electrodynamics are obtained and analyzed when considering a time-varying
homogeneous electric field initially generated by a classical electric current,
coupled to either a quantized scalar field or a quantized spin-$\frac{1}{2}$
field. Particle production by way of the Schwinger effect leads to backreaction
effects that modulate the electric field strength. Details of the particle
production process are investigated along with the transfer of energy between
the electric field and the particles. The validity of the semiclassical
approximation is also investigated using a criterion previously implemented for
chaotic inflation and, in an earlier form, semiclassical gravity. The criterion
states that the semiclassical approximation will break down if any linearized
gauge-invariant quantity constructed from solutions to the linear response
equation, with finite nonsingular data, grows rapidly for some period of time.
Approximations to homogeneous solutions of the linear response equation are
computed and it is found that the criterion is violated when the maximum value,
$E_{\rm max}$, obtained by the electric field is of the order of the critical
scale for the Schwinger effect, $E_{\rm max} \sim E_{\rm crit}\equiv m^2/q$,
where $m$ is the mass of the quantized field and $q$ is its electric charge.
For these approximate solutions the criterion appears to be satisfied in the
extreme limits $\frac{qE_{\rm max}}{m^2} \ll 1$ and $\frac{qE_{\rm max}}{m^2}
\gg 1$.
