Reflectivity Measurements for Copper and Aluminumin the Far Infrared and the Resistive Wall Impedance in the LCLSUndulator Page: 3 of 4
This article 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:
- ' 1-sqrt(1/Gti)
k= 1/et k= kp
. . . . .. . . . . . . . . . . . . . . . .. . . . . . . . k [ m - 1]
5 10 15 20
Figure 1: Reflectivity R vs. frequency k for an ideal con-
ductor, assuming the free-electron model (solid line). Ana-
lytic guideposts are also given (dashes).
Anomalous Skin Effect (ASE)
When the skin depth 6, becomes less than or compa-
rable to the mean free-path of electrons C the classical ac
model of conductivity no longer holds, and the (room tem-
perature) anomalous skin effect (ASE) applies [6,7]. [For
Cu, 6, ~ t when k (20 pm)-1.] Different expression
are known for the cases of specular and diffuse reflection of
electrons at the surface. Fitting these formulas to infrared
measurements for Cu, Ag, Au, Lenham and Treherne con-
cluded that the diffuse model is normally applicable, even
for well-prepared samples . This is the model we use.
For diffuse reflection, the surface impedance is 
47rikr A ikcrA (4)
ZS= 1 + ikcr 3 'T, 0 t(1 + ikcr)3 10 n 1 + m d ( )
Ar 1 ThnA
t(t) = [(1 + t2) tan -- t] (6)
with ASE parameter A 37rCf2/c2T. Then = 47r/Z7c.
For given a, r, ASE's effect on R(k) will be small in
the lowest energy region (region 1); in region 2 (the flat
region), R(k) will be lower than for the classical, ac model.
Three samples were measured: an Al film, solid Al,
and solid Cu. The samples (thickness ~ few mm) were
mounted on an optically-black cone, and the room temper-
ature reflectivity was measured in a near-normal-incidence
arrangement from k ~ 0.02-10 pm-- on a Bruker IFS
66v/S and a Bruker IFS 113v Fourier transform infrared
(FTIR) spectrometer. By evaporating a thick gold film in
situ in ultra-high vacuum (< 1 x 10-8 Torr) over the sam-
ple, the precise ratio of sample reflectivity to the reflectiv-
ity of Au was measured. Knowing the reflectivity of Au,
the absolute reflectivity of the sample was thus determined.
The details of this technique have been described previ-
ously [8-10]. Using this in situ evaporation technique, the
errors associated with misalignments, window interference
and surface inhomogeneity can be eliminated. As a result,
absolute reflectivity of the sample R(k) can be measured
to a precision of 0.1% or better.
Fig. 2 shows R(k) for Cu and evaporated Al over the
entire measured range. [The solid Al sample is consid-
ered a bad sample: it had poor reflectivity (R 0.95 at
k= 0.5 pm-1) and noticeable granularity. This sample's
data is considered no further.] Comparing the general fea-
tures of the data with the literature, we see for Cu the onset
to interband absorption at 10 pm-1 as in Ref.  (p. 297),
for Al a weakly suggested absorption spike at 7.5 pm-1
that is very pronounced in Ref. . For Cu, the dip begin-
ning at 1.5 pm--1 is not seen in Ref. . We assume the
differences are due to sample variability (finish, etc).
2.5 5 7.5 10
Figure 2: Measurement results: Reflectivity R vs. fre-
quency k for copper and evaporated aluminum.
Focusing on frequencies below 1 pm-1: we see in R a
possibly correct dependence at the very low end [(1- R) ~
Ik]. But this is followed, unexpectedly, by a linear de-
crease (not a constant). When comparing the Al curve with
reflectivity measurements performed in 1980 by Shiles, et
al , we can see that the earlier measurements also have a
slope, but that is a factor of 2 less steep. The non-zero slope
is not understood. The data is, nevertheless, smooth and
well-behaved at low k, to 0.5 pm for Al, to 0.3 pm-- for
Cu (representing, respectively, 85% and 50% of our range
of interest). We assume our models are valid in these re-
gions, and in these regions we will perform our fits.
Fitting to the Data
The aluminum comparison, over nearly twice the region
of interest, is given in Fig. 3. Blue repeats the measured
results. The result of the nominal free-electron model, with
a 3.35 x 1017/s and r 0.75 x 10-14 s (at 295 K)
, is given in green. The fit to the ac model (the red
curve) gives parameters, relative to their nominal values:
or =0.63, r= 0.78. The fit to the ASE model (t
0.016 pm; the dashed curve) gives: a 0.61, T-T 1.28.
We note that the fitted curves fit the data very well up to
0.5 pn 1, that a is less than ideal by a factor of 2/3 (which
is plausible), and that r is near nominal. Note that the ASE
model, which differs from the ac model only when k is not
too small, gives a fit that is unique only in r.
The copper comparison is shown in Fig. 4. Given are the
measured data (blue) and the nominal calculation, with a
Here’s what’s next.
This article 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 Article.
Bane, K.L.F.; Stupakov, G.; /SLAC; Tu, J.J. & /City Coll., N.Y. Reflectivity Measurements for Copper and Aluminumin the Far Infrared and the Resistive Wall Impedance in the LCLSUndulator, article, June 27, 2006; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc876471/m1/3/: accessed June 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.