International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 6.1, pp. 159-160   | 1 | 2 |

Section 6.1.2.2. Rotating-anode X-ray tubes

U. W. Arndta

aLaboratory of Molecular Biology, Medical Research Council, Hills Road, Cambridge CB2 2QH, England

6.1.2.2. Rotating-anode X-ray tubes

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The sealed tubes described above are convenient and require little maintenance, but their power dissipation, and thus their X-ray output, is limited. For macromolecular crystallography, the most commonly used tubes are continuously pumped, demount­able tubes with water-cooled rotating targets [see the reviews by Yoshimatsu & Kozaki (1977[link]) and Phillips (1985[link])]. At present, these tubes mostly employ ferro-fluidic vacuum shaft seals (Bailey, 1978[link]), which have an operational life of several thousand hours before they need replacement. The need for a beam with a small cross fire calls for a focal spot preferably not larger than 0.15 × 0.15 mm. This is usually achieved by focusing the electrons on the target to a line 0.15 mm wide and 1.5 mm long (in the direction parallel to the rotation axis of the target). The line is then viewed at an angle of 5.7° to give a 10:1 foreshortening. Foci down to this size can be produced on a target mounted close to an electron gun. For smaller focal spots, such as those of the microfocus tube described below, it is necessary to employ an electron lens (which may be magnetic or electrostatic) to produce on the target a demagnified image of the electron cross-over, which is close to the grid of the tube cathode.

The maximum power that can be dissipated in the target without damaging the surface has been discussed by Müller (1929,[link] 1931[link]), Oosterkamp (1948a[link],b[link],c[link]), and Ishimura et al. (1957[link]). The later calculations are in adequate agreement with Müller's results, from which the power W for a copper target is given by [W = 26.4\; f_{1} (f_{2}\nu)^{1/2}.]Here, W is in watts, f1 and f2 are the length and the width of the focal line in mm, and ν is the linear speed of the target surface in mm s−1; it is assumed that the surface temperature of the target reaches 600 °C, well below the melting point of copper (1083 °C). Thus, for a focal spot 1.5 × 0.15 mm and for an 89 mm-diameter target rotating at 6000 revolutions min−1 (ν = 28 000 mm s−1), Müller's formula gives a maximum permissible power loading of 2.5 kW or 57 mA at 45 kV. This agrees well with the experimentally determined loading limit.

Green & Cosslett (1968[link]) have made extensive measurements of the efficiency of the production of characteristic radiation for a number of targets and for a range of electron accelerating voltages. Their results have been verified by many subsequent investigators. For a copper target, they found that the number of Kα photons emitted per unit solid angle per incident electron is given by [N/4\pi = 6.4 \times 10^{-5} [E/E_{k} - 1]^{1.63},]where E is the tube voltage in kV and Ek = 8.9 keV is the K excitation voltage.

Accordingly, the number of Kα photons generated per second per steradian per mA of tube current is 1.05 × 1012 at 25 kV and 4.84 × 1012 at 50 kV.

Of the generated photons, only a fraction, usually denoted by f(χ) (Green, 1963[link]), emerges from the target as a result of X-ray absorption in the target. f (χ) decreases with increasing tube voltage and with decreasing take-off angle. It has a value of about 0.5 for E = 50 kV and for a take-off angle of 5°.

The X-ray beam is further attenuated by absorption in the tube window (∼80% transmission), by the air path between the tube and the sample, and by any β-filters which may be used.

In a typical diffractometer or image-plate arrangement where no beam conditioning other than a β-filter is employed, the sample may be 300 mm from the tube focus and the limiting aperture at that point might have a diameter of 0.3 mm, so that the full-angle cross fire at the sample is 1.0 × 10−3 rad. The solid angle subtended by the limiting aperture at the source is 7.9 × 10−7 steradians. At 50 kV and 60 mA, the X-ray flux through the sample will be approximately 4.5 × 107 photons s−1. These figures are approximately confirmed by unpublished experimental measurements by Arndt & Mancia and by Faruqi & Leslie. It is interesting to note that the power in this photon flux is 5.8 × 10−8 W, which is a fraction of 2 × 10−11 of the power loading of the X-ray tube target.

Instead of simple aperture collimation, one of the types of focusing collimators described in Section 6.1.4.1[link] below may be used. They collect a somewhat larger solid angle of radiation from the target of a conventional X-ray source than does a simple collimator and some produce a higher intensity at the sample.

References

Bailey, R. L. (1978). The design and operation of magnetic liquid shaft seals. In Thermomechanics of Magnetic Fluids, edited by B. Berkovsky. London: Hemisphere.
Green, M. (1963). The target absorption correction in X-ray microanalysis. In X-ray Optics and X-ray Microanalysis, edited by H. H. Pattee, V. E. Cosslett & A. Engström, pp. 361–377. New York and London: Academic Press.
Green, M. & Cosslett, V. E. (1968). Measurements of K, L and M shell X-ray production efficiencies. Br. J. Appl. Phys. Ser. 2, 1, 425–436.
Ishimura, T., Shiraiwa, Y. & Sawada, M. (1957). The input power limit of the cylindrical rotating anode of an X-ray tube. J. Phys. Soc. Jpn, 12, 1064–1070.
Müller, A. (1929). A spinning target X-ray generator and its input limit. Proc. R. Soc. London Ser. A, 125, 507–516.
Müller, A. (1931). Further estimates of the input limits of X-ray generators. Proc. R. Soc. London Ser. A, 132, 646–649.
Oosterkamp, W. J. (1948a). The heat dissipation in the anode of an X-ray tube. Philips Res. Rep. 3, 49–59.
Oosterkamp, W. J. (1948b). The heat dissipation in the anode of an X-ray tube. Philips Res. Rep. 3, 161–173.
Oosterkamp, W. J. (1948c). The heat dissipation in the anode of an X-ray tube. Philips Res. Rep. 3, 303–317.
Phillips, W. C. (1985). X-ray sources. Methods Enzymol. 114, 300–316.
Yoshimatsu, M. & Kozaki, S. (1977). High brilliance X-ray source. In X-ray Optics, edited by H.-J. Queisser, ch. 2. Berlin: Springer.








































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