Applied Physics B

, 125:80

# Correction to: Femtosecond X-ray induced electron kinetics in dielectrics: application for FEL-pulse-duration monitor

• Nikita Medvedev
Correction

## 1 Correction to: Appl. Phys. B (2015) 118:417–429  https://doi.org/10.1007/s00340-015-6005-4

In the original paper, there was a mistype in Eq. (1), which instead should read:
\begin{aligned} \frac{{{\text{d}}\sigma }}{{{\text{d}}w}} & = S\mathop \sum \limits_{n = 1}^{3} F_{n} \left( {\frac{1}{{(1 + w)^{n} }} + \frac{1}{{(K - w)^{n} }}} \right), \\ F_{1} & = - \frac{{F_{2} }}{K + 1},\;\;F_{2} = \frac{1}{K + u + 1},\;\;F_{3} = \frac{\ln \left( K \right)}{K + u + 1}, \\ S & = 4\pi a_{0}^{2} N\left( {\frac{Ry}{{I_{\text{p}} }}} \right)^{2} , \\ \end{aligned}
(1)
where all the notations are the same as in the original work; note the change in F1 term.
Equation (2) should be corrected as follows:
$$\sigma = \frac{S}{K + u + 1}\left[ {\frac{\ln \left( K \right)}{2}\left( {1 - K^{ - 2} } \right) + \left( {1 - K^{ - 1} } \right) - \frac{{{ \ln }(K)}}{K + 1}} \right].$$
(2)

Note the minus sign inside of the first bracket instead of a mistyped plus in the original article.

Additionally, there was an unfortunate hard-to-notice minor bug in the impact ionization subroutine of the code that resulted in cascade durations being erroneously stretched in time by a factor of ~ 1.5–2. It does not affect the qualitative results reported, neither does it invalidate the conclusions—all the drawn conclusions remain unaffected (the proposed scheme for selection of optimal materials tailored for a particular FEL photon energy has recently been confirmed experimentally [1]). However, quantitatively, electronic cascades are shortened after the fix. The corrected figures can be found below.

I am grateful to S. Ashok (TU Kaiserslautern) for pointing out the misprints in the paper and for the help in identifying the bug in the code.

The densities of holes shown in Fig. 2 are a result of interplay of two processes: impact ionization that increases their number, and Auger decay that decreases it. Only the former one was affect by the bug in the code, which results in it now being faster with respect to the erroneous one in the original work; whereas the latter one has the same (correct) characteristic time as before. Thus, the overall shape of the curves is now slightly different. The same effect is seen in derivatives of the electron densities, Fig. 6, where the curves shapes are slightly altered.

## Reference

1. 1.
K. Mecseki et al., Appl. Phys. Lett. 113, 114102 (2018)