Relaxation Time

The relaxation time, $\tau _r$, is the amount of time it would take for an electric field to decay by $1/e$ in the absence of additional forcing. The relaxation time is related to the conductivity, $\sigma$, by the well known result: $\tau_r\!=\!\epsilon_o/\sigma$, where $\epsilon_o$ is the permittivity of free space.

Figure 2.6: The blue and red lines plotted above are the relaxation time profiles corresponding to the total conductivities in Figure 2.5 with ``quiescent'' $T_e\!=\!T_{air}$ and $T_e\!=\!T_e(E_k)\!\gg\!T_{air}$ conditions respectively. The thick solid line is a best estimate of the relaxation time profile which would exist just prior to sprite initiation by a conventional breakdown mechanism at $E\!\ge\!E_k$.

The total conductivity profiles in Figure 2.5 were used to determine the corresponding relaxation times in Figure 2.6. Note that the effect of the change in the electron conductivity component due to electron heating just below the base of the conductitivy ledge increases the sharpness of the ionosphere conductivity ``ledge''. The relaxation time rapidly drops to less than 1 ms above $\simeq\,81$ km altitude. This height will be used in Section 2.5 as the base of the ionosphere.