CERN SL memorandum (23 October 1996)

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MEMORANDUM

23 October 1996

To:         O. Gröbner, P. Lebrun, A. Mathewson, A. Poncet, N. Siegel and L. Walckiers

cc:          J. Gareyte and L. Evans

From:     F. Caspers, M. Morvillo and F. Ruggiero

Subject: Preliminary Surface Resistance Measurements for the LHC Beam Screen.

We have obtained some preliminary results concerning surface resistance measurements of an LHC beam screen sample at different frequencies and temperatures, down to  K. Table 1 gives a summary of these measurements in chronologic order, from room temperature down to cryogenic temperatures and then up to about  K: the second column of the table gives the frequency in MHz, the third and fourth columns contain the average temperature and the temperature difference between top and bottom of the sample, about 1 m long, while the last two columns give the measured surface resistance in m for the inner conductors and for the outer tube, respectively. The two inner cylindrical conductors (of radius 8 mm) and the outer tube (of radius 18.6 mm) are all made out of stainless steel with a 50 m electrodeposited copper layer. However the inner conductors have been thermally treated at  C and their measured RRR is around 200, while the outer tube has not been thermally treated and its estimated RRR is between 30 and 100. We plan to use a thermally treated tube in future measurements. In Table 2, we show the conductivities extrapolated from the measured surface resistances in the relevant (classic or anomalous) regime. The ratios between these conductivities and those measured at room temperature at the same frequencies indicate a significant reduction w.r.t. the dc RRR values and may be attributed to surface roughness effects: the measured surface roughness is in the m range.

These preliminary results do not cover the full frequency range 150 MHz-3 GHz that we may be able to explore and still require close scrutiny and cross-check. For example, all the measurements at 947 MHz correspond to conductivities systematically lower for the outer tube and higher for the inner conductors: therefore they are not very reliable. Similarly, the single measurement at 2.8 GHz corresponds to a surface resistance for the inner conductors smaller then the minimum theoretical low temperature limit  m. These discrepancies should be clarified by future measurements with a modified geometry of the coupling ports. A detailed description of the measurement technique, including error estimates and an acknowledgement of the important contributions made by several people who helped us, will appear in a forthcoming LHC report.

Finally, in Fig. 1, we compare the measured surface resistances at  K with theoretical predictions based on the measured room temperature conductivities and dc RRR. In particular, the low temperature conductivity of the outer tube is comparable to that of the LHC beam screen in a magnetic field of 8.4 T, but the measured surface resistance is more then twice the classically predicted value. Since ohmic losses scale linearly with , if these preliminary results are confirmed at higher frequencies and also in future measurements with a strong magnetic field, we may anticipate an increase by a factor two of the LHC heating budget associated with resistive losses at 7 TeV, presently estimated at 75 mW/m for nominal beam parameters and at 188 mW/m for ultimate beam parameters.

 
Figure 1: Surface resistance measured at  K for the inner conductors (a) and for the outer tube (b), compared to the predictions in the classic (solid) and anomalous regime (dashed). We have assumed an electrical conductivity of  m (i.e., RRR  200) for the inner conductors and of  m (i.e., RRR 50) for the outer tube. Note that the measurements at 947 MHz are not very reliable.