can someone please show me the derivation to the width of the potential barrier w=Ip/(e*E), where Ip is the ionization enery, for electron tunneling in the presence of strong electronmagnetic wave, which Keldish wrote in his paper:"Ionization in the field of a strong electromagnetic wave"
I guess the derivation might be carried out in the following way:
From Coulomb's law, the force on electron e is F=e*E; (e is the charge of the electron and E is the electric field.
Now work done is force * displacement.
Therefore, let the work done in displacing electron e by small length dw be dp
So, dp = F.dw
Therefore, the work done to cross the barrier is :
Integral of dp = integral of F.dw
or, p = integral of e*E.dw, where integration is over the width of the barrier. The dot product can be replaced by multiplication as the direction of E vector is along the barrier width.
Assuming barrier is small enough for E to be invariant across it, E can be taken out of the integral,
Therefore, p = e*E* integral of dw
or, p = e*E*w.
Hence w = p/(e*w)
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetics
- Electromagnetic Fields