uniformly accelerated mirror is well localized around the past horizon $V_0 = 0$. Since the mirror starts to accelerate in the distant past, that means the mirror only radiates particles when it starts accelerating. It radiates no particles when it is uniformly accelerating. Although in Eq. (\[ParticleNumber\]) the integrand explicitly depends on the central frequency $k_0$ of the Gaussian wave packet, in the large $k_0$ limit the integration turns out to be almost independent of $k_0$. That means the particle number $N(f) \sim \frac{1}{k_0}$ in the large central frequency limit (see Appendix \[appendixC\]), yielding the relationship $E(f) \approx k_0 N(f) \sim \mathcal{O}(1)$, for the energy of the wave packet, as shown in Fig. \[Fig:energy\]. Adding up the energy of all wave packets yields a divergent result. This ultraviolet divergence arises as a consequence of the physically unrealistic assumption that the mirror is accelerated eternally, so that it appears to any inertial observers when they cross the past horizon. This ultraviolet divergence can be removed by smoothly switching on the mirror [@Obadia01], or by considering an accelerated mirror whose acceleration was slowly increased from zero. For a switch-on timescale of $\Delta T$, the particle number is suppressed for wave packets with 