Some useful calculations on the use of a Kapton or Be window in a white beam.

        The transmission and phase shift are calculated for a 1/2 mil Kapton window using data from the  CXRO . The phase shift is the product of the X-ray wavevector k, the index of refraction decrement and the foil thickness t.  The chemical formula of Kapton is C₂₂H₁₀N₂0₅,  its density is 1.43, and its  thickness is 12.7 microns.
 

        In the range of energies we most likely would operate, 7-12 keV, the absorption of 1/2 mil window is negligible. In a given experiment, we could have up say 6 windows in the beam (2 for the multilayers, 2 for an Ion chamber, 2 for a sample chamber), so these six windows would absorb less than 10 % of the beam in the 7-12 keV range. If we replace these 1/2 mil windows by 1mils one, they would absorb twice as much.
        The phase shift acquired in a single window thickness ranges from 226 to 93 degrees between 5 and 12 keV. If the thickness of the foil is uniform, then this uniform phase shift will not modify the beam profile. A random 5% variation of the foil thickness would cause a random 5 to 11 degree phase shift which could cause spatial variation in the beam profile. It is hard to predict how uniform the thickness of a Kapton foil is. 5% of 12.7 microns is 650 nm, about one wavelength of an He-Ne laser.  It would be interesting just for fun to measure the thickness and density variations in a Kapton window using an interferometric method, perhaps ellipsometry would be adequate.
 
        To estimate the thermal rise of the window illuminated by a canonical 0.1mm by 0.1mm white beam, with a fundamental set at about 8.3 keV (k=1.19),  I used a similar treatment derived in our filter report.  The white beam was generated by the program URGENT with the current  APS source parameters (4% vertical coupling) and the absorbed power was calculated by the filter module of  XOP .  The window is assumed to be 27 m from the source.  In an experiment, the window would most likely be beyond the 33 m mark so this calculation will overestimate the thermal rise by a factor (33/27)² = 1.49.   Using the room temperature thermal conductivity of Kapton (0.16W/mK) from Goodfellow, a cooling radius of 6.25 mm, and a foil thickness of 13 microns, I find that the foil absorbs 4.43 mW of the total 0.85 W emitted by the source in the small aperture, which gives rise to a maximum temperature of 1765 C!  Correcting for the distance scaling, one finds a temperature increase of about 1182 C.
 
        If you try to cool this window by radiative cooling, assuming the two surfaces of the foil  are emitting,  you still find a temperature rise of  T -T₀=[4.43mW/(2*5.67x10^-8Wm^-2K^-4*(0.1mm)²)]^0.25 = 1405 K = 1133 C.  I also considered whether free convection would cool the window to a reasonable temperature, but my initial calculation are not cooling it more than conduction or radiation.  Scaling the beam area by a factor 100 would reduce the absorbed power by a factor 100, and would thus reduce the maximum temperature of the foil to about 20 C.
 
        In conclusion, although a thin 1/2 mil Kapton  window absorbs the beam by only a few percents, a  rather small 0.1mm by 0.1 mm white beam would melt it.  A monochromatic beam would  reduce this heating effect by a factor of order 200 due to the reduced total flux.  One can always let the beam burn a hole in the Kapton window, resulting in a most favorable windowless operation!  The IMM recently used flight path sealed with Kapton.  They made a small needle hole to let the beam through, causing a  negligible  He leak.

        One should use Be windows as a permanent window material for a  small white beam. Be has a thermal conductivity of 0.201 W/mmK at room temperature, a factor 1260 larger than Kapton.  A Be window could  most likely accept a white beam cross-section on the order of  1 mm by 1 mm without melting.  Detailed calculations are performed next for the Be window to calculate the maximum beam cross-section that can be accepted before melting.   Using previous derived  peak heat density in our recent filter report, we estimate the aborbed power density in a 5 mils Be window to be about 3.6 W/mm²  at 33 m from the source and a completely closed undulator gap.  This represents the worst case scenario.   The next table shows the thermal rise of a 5 mils window cooled on its outer radius of 12.5 mm for different square beam of cross-section a²,  using the melting point  thermal conductivity of Be of 0.0751 W/mm/K (T=1278C).
 

P.S. FYI, You'll find below some anecdotal evidence of the effect of a Kapton, Be or Commissioning window on the beam profile.
 
 

Reports on speckle pattern at last TWG meeting:

3.1 Speckles - Alec Sandy (MIT) Experiments at the ESRF showed a significant contrast improvement using polished Be-windows: unpolished contrast ~ 0.3 polished contrast ~ 0.5 Similar experiments at 8-ID were not conclusive because of unexpected overall low contrast in the measurements, but left many open questions:
- Does a Si mirror effect the contrast, and how important is the distance between mirror and detector ?
- How does the mirror surface effect the contrast ?

3.2 Speckle pattern (?) from commissioning windows (?)
- Gerd Rosenbaum (SBC-CAT) The intensity profile of a pinhole (15microns) located at z=52.9m was measured by scanning a 15 micron slit at z=62.25m and 63.87m vertically through the scattering pattern. The data shows large intensity fluctuations and a much to large FWHM, i.e. 60 microns. When the Be exit window (z=60.25) was moved no change was detected. The experiment was repeated with a 50micron pinhole, resulting in a FWHM of 335micron for the vertical scan. Raytracing to the origin indicates as source an area of 8micron height at the position of the commissioning window (a virtual light source ?).

3.3 Beam structure from monochromator surface roughness
- Wenbing Yun (SRI-CAT) These experiments were performed at 3-ID, a beamline without commissioning windows. Two separate Be windows (250microns, unpolished) are located at z=63m and z=68m. Since the beginning of operations multiple causes for beam structures were found:
- Kapton foil causes large intensity variations as the foil ages.
- Highly polished crystals show no distortion of the beam pattern while crystals which are only etched cause significant coherence distortion. The observed effects can be explained by interference effects at macroscopic (~100 A) surface defects.

3.4 Early results from experiments at ID-13
- Mark Rivers (GeoCARS) First experiments at the beamline showed 'speckles' within the beam profile. A closer look revealed small dust and phosphor particles on the first monochromator crystal as the cause for this effect. The experiments further confirmed Wenbing's report on the distortion introduced by Kapton windows.

Summary of changes done to this document:

On 8/13/02, I fixed the typo on the chemical composition of Kapton.  N_{205}
was replaced by N_2 O_5. This typo was first pointed out by Nino Pereira, then
recently by Peter Stefan.  I also modified the data in the table (transmission
only which changed slightly in 4 years (less than 0.1%). Thanks to Nino and
Peter for pointing out the typo. I also corrected my address and corrected
the stale WWW links. Please note that this link is very old, written before 
we even did experiment at the APS so take it with a grain of salt.

5/10/2007 Minor address change.