Fully Coherent X-ray Pulses from a Regenerative Amplifier Free Electron Laser Page: 4 of 11
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
the frequency yields
En+1(t) = dt'rummeC wr(t-t')_e6U(t-t/)2g(t')En(t'). (4)
Since there is no initial seed signal, E1(t) = 0, and
E2 (t) = dt,ru-m e (t-t/), a2(t-t/) oE1(t') (5)
is the spectrally filtered SASE from the first pass that seeds the second pass.
For n 1, we look for an exponentially growing solution
E,(t) = A-A(t)e- rt. (6)
Eq. (4) is then transformed to an integral equation:
AA(t) = dt'K(t, t')A(t'), (7)
with the kernel
K(t, t') = rume,_2t t_)g(t') .(8)
Since both r and g(t') may be complex, K(t, t') is in general not a hermitian kernel.
We expect that a Gaussian fundamental mode will have the largest gain A0l, i.e.,
Ao(t) = exp - . (9)
Here uo- is the rms pulse duration of the returning filtered radiation. Inserting Eq. (9) into
Eq. (7), we obtain
2 22ma (2nt2
Ao exp - 4u2 ) gor exp - ,t (10)
4uxo j1 + 42 22 1 + 4n ga
where Oxa = _o(ow/ 2uo + oT is the rms x-ray pulse duration at the undulator end (see
Eq. (14)). The self-consistent solution of Eq. (10) is
2 _1+ 4ao2(,a 1+ 8(2 UT+ 1
oz= 4uI2 8u1,
2 _ 1 +8O2 _
Oxa= 8u2 - (11)
A gm 4 a
Ao -gor1 + 4o2Oxa
Here’s what’s next.
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Huang, Zhirong & Ruth, Ronald D. Fully Coherent X-ray Pulses from a Regenerative Amplifier Free Electron Laser, report, February 17, 2006; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc876282/m1/4/: accessed February 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.