  We derive a formula for the effective critical electric field for runaway
generation and decay that accounts for the presence of partially ionized
impurities in combination with synchrotron and bremsstrahlung radiation losses.
We show that the effective critical field is drastically larger than the
classical Connor-Hastie field, and even exceeds the value obtained by replacing
the free electron density by the total electron density (including both free
and bound electrons). Using a kinetic equation solver with an inductive
electric field, we show that the runaway current decay after an impurity
injection is expected to be linear in time and proportional to the effective
critical electric field in highly inductive tokamak devices. This is relevant
for the efficacy of mitigation strategies for runaway electrons since it
reduces the required amount of injected impurities to achieve a certain current
decay rate.
