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Comment on dielectric losses in a polythylene insulated superconducting cable between 4 and 22K
An explanation is proposed for the surprisingly high field-dependent dielectric loss recently observed in a polyethylene-insulated ac superconducting cable at ~ 4 K and 50 Hz. The proposed explanation involves an extraneous loss contribution due to slight oscillation o f the cable conductors; similar effects have been observed in studies on polymer films, and give the correct field dependence. I f this proposal is correct, the actual loss o f the cable near its design stress could be reduced to an economically more attractive level. Means are suggested for reducing the present uncertainties in this measuremen t.
Comment on dielectric losses in a polythylene insulated superconducting cable between 4 and 22K P.S. Vincett
The dielectric losses in a polyethylene-insulated superconducting cable have recently been measured t between 4 and 22 K. This parameter is of considerable importance because the dielectric losses would constitute a substantial portion of the refrigeration heat-load in an ac superconducting cable, and because lapped polyethylene tape may 2 be a desirable dielectric for flexible superconducting cables. The principal conclusion of the recent study 1 was the value of the dielectric loss tangent, tan 5, in the polyethylene-insulated cable at ~ 4 K and 50 Hz; this was found to be ~ 13 x 10 -6 at a field strength of 7 x 10Sv m -1 , rising roughly linearly with field to 20 x 10 -6 at 7 x 1 0 6 V m -1, both values referred to the loss angle of the reference capacitor (~< 10-s). Even this highest field was rather lower than the design stress of the cable (107V m - l ) , so that at this design stress it appeared 1 likely that the cable loss might be beyond 3 x 10 -s. This is to be compared with estimates a stating that for an economically-attractive cable design, tan 6 should not exceed ~ 10-s for a dielectric with a permittivity o f about two. In contrast to the above values of tan 6 for the polyethylene insulated cable, it has been shown 4' s. 6 that polyethylene sheet which does not contain too high a concentration of certain impurities can have a tan 8 at ~ 4 K in the range of 2-6 × 10 -6 at 50 Hz and up to ~ 107 V m -1. Moreover, two of the above determinations 4, 6 used the calorimetric method; 4 in these cases, the values determined are absolute, and do not depend on the assumed value o f tan ~ for a P.s. Vincett is at the Xerox Research Centre of Canada, 2480 Dunwin Drive, Mississauga, Ontario, Canada L5L 1J9. Received 30 I~Oav 1978.
reference capacitor. Clearly, it is of considerable practical importance to ascertain the reason for the difference in tan 8 between the above film samples and the superconducting cable. It was suggested I that this difference is due to the incorporation o f bedding layers and screens in the cable. However, the loss calculated from the known bulk and surface resistance of these components is not sufficient to explain the difference, l Contact resistance between the various components was invoked I as a further possible cause o f the difference in the tan 8's, although it is not entirely clear how this would yield the observed linear dependence of tan 6 on field strength. While it is of course possible that some of the difference in the tan 8's could be due to impurities, 6 we wish to point out that there is another possible explanation for a substantial portion o f the excess loss, which would explain its field dependence. Moreover, if this explanation is correct, it implies an apparently simple means o f removing much of the observed loss. To discuss this possibility, we refer to the first-determination 4 o f the dielectric loss of high density polyethylene at ~ 4 K and audio frequencies. In this work, which used thin film samples in conjunction with the calorimetric method o f measurement at fields in the range o f 106-107 V m -1, substantial difficulties were initially found with extraneous losses which were attributed to electrode motion (relative to the sample) in the ac field;4 the loss was assumed to arise from the internal friction of the Pb electrodes, and it was finally made small by clamping the electrodes and the insulator in such a way as to make electrode motion almost impossible. The extraneous losses always gave an apparent tan 6 increasing with applied voltage V. (This is not surprising, since the power dissipated by this mechanism would be expected to
0 0 1 1 - 2 2 7 5 / 7 8 / 1 8 0 9 - 0 5 4 3 $ 0 2 . 0 0 © 1978 IPC Business Press CRYOGENICS. SEPTEMBER 1978
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be proportional to the product of the average force on the electrode, and its average velocity; if the electrodes performed a reasonably free harmonic oscillation, the last two quantities should both be proportional to the square of the applied field. This would then give a power dissipation proportional to F 4, corresponding to an apparent extraneous tan ~ proportional to V~.) In fact, in situations where the electrodes possessed only a very limited freedom of movement, the extraneous tan 8 was found 4 to be proportional to V over a substantial range o f voltage. (We should point out that a loss proportional to V and apparently not due to electrode oscillation has also been observed at low temperatures in another dielectric, y) It should be emphasized that the electrode movement required for the above kind of behaviour can be very small; for example, overwhelming extraneous loss was observed 4 with evaporated Pb electrodes, even when they passed the adhesive tape test before and after cooling. (Slight loss of adhesion at low temperatures was demonstrated by capacitance measurements). In view of the above observations, it is clearly tempting to suggest that a substantial portion of the losses observed 1 in the superconducting cable, and particularly the increase of loss with field, may be due to an effect of this kind. For example, this could arise because of oscillation o f the outer foil (or even of the dielectric) in the regions beyond the clamp; ~ the foil is less firmly attached to the dielectric in these regions than elsewhere, a It is appropriate, however, to ask whether losses of the above type would show up in bridge-type measurements, l as well as in calorimetric experiments. While we have not demonstrated an exact correspondence between the two measurement techniques as far as effects of this kind are concerned, it is clear that a loose electrode with nonzero mechanical loss will move slightly out of phase with an applied ac field. This will give
544
rise to a capacitance which oscillates slightly out of phase with the applied field, and this 'imaginary capacitance' will presumably show up in bridge measurements as a resistive component, ie a loss. If we are correct that the voltage dependence of the apparent tan 6 of the superconducting cable 1 is due to electrode (or polymer) oscillation, then the estimated tan/5 of the polyethylene I at l0 ~ V m -1 should be reduced by more than 10 -s. Moreover, since the loss of the reference capacitor may 1 be less than 6 x 10 -6, the actual tan 5 of the polyethylene may be no more than ~ 1.5 x 10 -s, or little more than the desired value, a Moreover, different kinds of polyethylene could of course have lower values of 6. We note that our proposed mechanism could be checked by varying the clamping force on the suspected areas o f the cable, and that the uncertainty in the loss angle of the reference capacitor could be reduced by using one with a dielectric of either liquid helium s or liquid-helium-cooled PTFE (whose very low tan 5 has been determined absolutely by the calorimetric method4). Finally, it is clear that if we are correct, considerable care would need to be taken in any working superconducting cable to prevent oscillations of this kind.
References 1 2 3 4 5 6 7 8
Meats,RJ. Cryogenics 17 (1977) 229 Swift, D.A. RGE 84 (1975) 741 Swift, D.A. Proc IEE 118 (1971) 1237 Vincett, P.S. Brit JAppl Phys (J. Phys D) 2 (1969) 699 Nelson, R.L. Proc IEE 121 (1974) 764 Thomas, R.A., King, C.N. Appl Phys Lett 26 (1975) 406 Phillips,W.A. Proc Roy Soc A319 (1970) 565 Meats,R.J. private communication
CRYOGENICS. SEPTEMBER 1978
Comment on dielectric losses in a polythylene insulated superconducting cable between 4 and 22K P.S. Vincett
The dielectric losses in a polyethylene-insulated superconducting cable have recently been measured t between 4 and 22 K. This parameter is of considerable importance because the dielectric losses would constitute a substantial portion of the refrigeration heat-load in an ac superconducting cable, and because lapped polyethylene tape may 2 be a desirable dielectric for flexible superconducting cables. The principal conclusion of the recent study 1 was the value of the dielectric loss tangent, tan 5, in the polyethylene-insulated cable at ~ 4 K and 50 Hz; this was found to be ~ 13 x 10 -6 at a field strength of 7 x 10Sv m -1 , rising roughly linearly with field to 20 x 10 -6 at 7 x 1 0 6 V m -1, both values referred to the loss angle of the reference capacitor (~< 10-s). Even this highest field was rather lower than the design stress of the cable (107V m - l ) , so that at this design stress it appeared 1 likely that the cable loss might be beyond 3 x 10 -s. This is to be compared with estimates a stating that for an economically-attractive cable design, tan 6 should not exceed ~ 10-s for a dielectric with a permittivity o f about two. In contrast to the above values of tan 6 for the polyethylene insulated cable, it has been shown 4' s. 6 that polyethylene sheet which does not contain too high a concentration of certain impurities can have a tan 8 at ~ 4 K in the range of 2-6 × 10 -6 at 50 Hz and up to ~ 107 V m -1. Moreover, two of the above determinations 4, 6 used the calorimetric method; 4 in these cases, the values determined are absolute, and do not depend on the assumed value o f tan ~ for a P.s. Vincett is at the Xerox Research Centre of Canada, 2480 Dunwin Drive, Mississauga, Ontario, Canada L5L 1J9. Received 30 I~Oav 1978.
reference capacitor. Clearly, it is of considerable practical importance to ascertain the reason for the difference in tan 8 between the above film samples and the superconducting cable. It was suggested I that this difference is due to the incorporation o f bedding layers and screens in the cable. However, the loss calculated from the known bulk and surface resistance of these components is not sufficient to explain the difference, l Contact resistance between the various components was invoked I as a further possible cause o f the difference in the tan 8's, although it is not entirely clear how this would yield the observed linear dependence of tan 6 on field strength. While it is of course possible that some of the difference in the tan 8's could be due to impurities, 6 we wish to point out that there is another possible explanation for a substantial portion o f the excess loss, which would explain its field dependence. Moreover, if this explanation is correct, it implies an apparently simple means o f removing much of the observed loss. To discuss this possibility, we refer to the first-determination 4 o f the dielectric loss of high density polyethylene at ~ 4 K and audio frequencies. In this work, which used thin film samples in conjunction with the calorimetric method o f measurement at fields in the range o f 106-107 V m -1, substantial difficulties were initially found with extraneous losses which were attributed to electrode motion (relative to the sample) in the ac field;4 the loss was assumed to arise from the internal friction of the Pb electrodes, and it was finally made small by clamping the electrodes and the insulator in such a way as to make electrode motion almost impossible. The extraneous losses always gave an apparent tan 6 increasing with applied voltage V. (This is not surprising, since the power dissipated by this mechanism would be expected to
0 0 1 1 - 2 2 7 5 / 7 8 / 1 8 0 9 - 0 5 4 3 $ 0 2 . 0 0 © 1978 IPC Business Press CRYOGENICS. SEPTEMBER 1978
543
be proportional to the product of the average force on the electrode, and its average velocity; if the electrodes performed a reasonably free harmonic oscillation, the last two quantities should both be proportional to the square of the applied field. This would then give a power dissipation proportional to F 4, corresponding to an apparent extraneous tan ~ proportional to V~.) In fact, in situations where the electrodes possessed only a very limited freedom of movement, the extraneous tan 8 was found 4 to be proportional to V over a substantial range o f voltage. (We should point out that a loss proportional to V and apparently not due to electrode oscillation has also been observed at low temperatures in another dielectric, y) It should be emphasized that the electrode movement required for the above kind of behaviour can be very small; for example, overwhelming extraneous loss was observed 4 with evaporated Pb electrodes, even when they passed the adhesive tape test before and after cooling. (Slight loss of adhesion at low temperatures was demonstrated by capacitance measurements). In view of the above observations, it is clearly tempting to suggest that a substantial portion of the losses observed 1 in the superconducting cable, and particularly the increase of loss with field, may be due to an effect of this kind. For example, this could arise because of oscillation o f the outer foil (or even of the dielectric) in the regions beyond the clamp; ~ the foil is less firmly attached to the dielectric in these regions than elsewhere, a It is appropriate, however, to ask whether losses of the above type would show up in bridge-type measurements, l as well as in calorimetric experiments. While we have not demonstrated an exact correspondence between the two measurement techniques as far as effects of this kind are concerned, it is clear that a loose electrode with nonzero mechanical loss will move slightly out of phase with an applied ac field. This will give
544
rise to a capacitance which oscillates slightly out of phase with the applied field, and this 'imaginary capacitance' will presumably show up in bridge measurements as a resistive component, ie a loss. If we are correct that the voltage dependence of the apparent tan 6 of the superconducting cable 1 is due to electrode (or polymer) oscillation, then the estimated tan/5 of the polyethylene I at l0 ~ V m -1 should be reduced by more than 10 -s. Moreover, since the loss of the reference capacitor may 1 be less than 6 x 10 -6, the actual tan 5 of the polyethylene may be no more than ~ 1.5 x 10 -s, or little more than the desired value, a Moreover, different kinds of polyethylene could of course have lower values of 6. We note that our proposed mechanism could be checked by varying the clamping force on the suspected areas o f the cable, and that the uncertainty in the loss angle of the reference capacitor could be reduced by using one with a dielectric of either liquid helium s or liquid-helium-cooled PTFE (whose very low tan 5 has been determined absolutely by the calorimetric method4). Finally, it is clear that if we are correct, considerable care would need to be taken in any working superconducting cable to prevent oscillations of this kind.
References 1 2 3 4 5 6 7 8
Meats,RJ. Cryogenics 17 (1977) 229 Swift, D.A. RGE 84 (1975) 741 Swift, D.A. Proc IEE 118 (1971) 1237 Vincett, P.S. Brit JAppl Phys (J. Phys D) 2 (1969) 699 Nelson, R.L. Proc IEE 121 (1974) 764 Thomas, R.A., King, C.N. Appl Phys Lett 26 (1975) 406 Phillips,W.A. Proc Roy Soc A319 (1970) 565 Meats,R.J. private communication
CRYOGENICS. SEPTEMBER 1978