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New technique for the measurement of the intrinsic drag torques of high temperature superconductor bearings
AppliedSuperconductivityVol. 3, No. 6, pp. 327-338, 1995
Pergamori
09644807(95)0007fL!3
Copyright0 1996ElscvicrScience Ltd Printedin Great Britain.All rights rcscrved 0964-1087/9539.50 + 0.00
NEW TECHNIQUE FOR THE MEASUREMENT OF THE INTRINSIC DRAG TORQUES OF HIGH TEMPERATURE SUPERCONDUCTOR BEARINGS A. D. CHEW’, A. CHAMBERS’ and A. P TROUP’ ’ Department of Physics, University of York, York YOl 5DD, U.K. 2 Edwards High Vacuum International, Manor Royal, Crawley, RHlO 2LW, U.K. (Received 7 June 1995)
Abstract-A new technique providing a non-intrusive means for the isolation and accurate measurement of the intrinsic drag torques of high temperature superconductor bearings is reported. It involves measuring the rotational acceleration and deceleration of a rotating symmetric object suspended in vacua on a bearing formed by the combination of a magnet and an I-ITS pellet. Accelerations are produced by exploiting molecular drag torque in medium vacuum while deceleration from low starting speeds in ultra high vacuum, in which gaseous drag and eddy current effects are minimized, enables intrinsic drag torques to be accurately determined. Experiments have been carried out on YBaaCusO, pellets and improvement in pellet grain structure is shown to decrease the&e of the intrinsic drag torque. Theoretical estimates are in reasonable agreement with measured values. The effect of the magnetic field intensity of the suspended magnet and the suspension height is also reported. A threshold type starting phenomenon was observed in which the torque required to accelerate the suspension was two to three orders of magnitude higher than the intrinsic drag torque obtained from deceleration measurements. Observations of spontaneous reacceleration and the potential for using the device to measure vacuum pressures is also discussed.
INTRODUCTION
There has been rapid progress made recently [l-4] in the development of passive, low friction, high critical temlperature superconductor (HTS) bearings for use, for example, in carrier and flywheel energy storage applications. This has created a need for accurate measurements of the intrinsic drag torques of these bearings. The methods currently employed include accelerating the levitated permanent magnet part of the bearings by inductive drive [5] or nitrogen gas jets [6]; deceleration measurements are then made to determine the intrinsic drag torque. These methods are somewhat intrusive and limit the achievable vacuum of the vessel in which the apparatus is located. In addition, results from these measurements show a pressure dependent component of the deceleration and demonstrate the need to operate in ultra high vacuum (UHV) to minimize gaseous drag effects. In this paper an instrument is described which affords a means for the accurate and systematic measurement of the intrinsic drag torques of HTS bearings. It uses molecular drag, due to residual gas at medium vacuum, to accelerate the suspended part of the bearing, followed by deceleration measurements in UHX
PRINCIPLE
AND
THEORY
The essential features of the instrument are shown schematically in Fig. 1. It is housed in a stainless steel vacuum vessel Vand consists of a drive unit D which drives a disc S, “the sender” of radius s, at high angular velocity R and a coaxial and parallel “receiver” disc R of radius r. The receiver disc is lolcated at a distance t from the sender and attached to the suspension system J which carries a mirror arrangement 0 for the measurement of rotational frequency. The attractive force allowing free suspension below the superconductor is provided between a permanent magnet M fixed to the top of the suspension and a cooled HTS pellet held outside the vacuum system. The residual gas in the vacuum chamber couples the motion of the sender to the receiver by either viscous or molecular drag forces, depending on the vacuum pressure. The motion of the 327
A, D. CHEW et al.
328
FLV
T
65 00
Fig. 1. Schematic diagram of the essential features of the apparatus.
suspended system about the vertical axis is described by G=Ih,
(1)
where G is the total torque, I is the total moment of inertia of the receiver suspension about the axis of rotation and 61 is the resultant angular acceleration, with w = 2rcf where f is the rotational frequency of the receiver. I is accurately calculable from dimension and mass measurements and h is measured directly. The high speed drive and dynamics of the sender-receiver interspace form the basis of a rotating disc vacuum gauge which has been fully investigated and described by the authors previously [7-131. The Knudsen number Kn relates mean free path I at a particular pressure to some important characteristic dimension, in this case t, by the formula Kn = n/t.
(2)
For Kn c 0.01, molecule-molecule interactions dominate gas behaviour and the transfer of torque is via viscous forces. At low pressures where Kn > 1 molecule-surface collisons dominate and the torque is transferred by molecular drag. The drive torque Gn developed [12] between the
Measurement of the intrinsic drag torques of high temperature superconductor bearings
sender and the stationary or quasi-stationary
329
receiver under viscous conditions is
Go =
;+r4,
(3)
where tl is the coefficient of viscosity, and the other quantities are already defined. Under molecular flow c:onditions, Kn > 1, the torque developed is 10
lW2p,
(4)
where r~is the coefficient of accommodation of tangential momentum of molecules on the receiver surface which may be taken as unity ( f 3%) for a smooth, flat and adsorbate covered surface [9,15,16]. R. is the gas constant, T the thermodynamic temperature, M the molar mass andp the pressure of the residual gas. E is the edge effect loss factor accounting for molecules which leave the discs’ interspace, and is discussed fully in Refs [ 11 and 131. For the conditions of this experiment t R a: c where c = (RoT/M)1’2 is a measure of molecular velocity, and 6 =
[$((3 + (s + r)y2-{t2 + (s - r)2}1/2)]4.
For the particular case T=S equation (5) reduces to
At a typical working separation of t = 12 mm and for I = s = 46 mm, E= 0.59. There are several sources of drag in superconductor magnetic bearings. Intrinsic drag in the bearing results from asymmetries in the magnet/superconductor arrangement which cause the hysteretic loss motion of flux vortices in the superconductors. This produces an intrinsic drag torque Gi which is frequency independent [1,5]. Davis et al. [14] derived an expression for Gi which in this application, of a disc magnet of diameter d or a ring magnet of mean diameter d, magnetized axially with their plane surface parallel to the superconductor’s surface is G, = AB is the twice maximum superconductor’s surface and J, due to eddy current interactions molecules on the various parts
5d2(AlQ3 48p;Jc
*
(7)
variation [1,5] of the magnet’s average field measured at the is the superconductor’s critical current. A drag torque GE may act and a molecular drag torque GM. By considering the impact of gas of the rotating suspension it may be shown that GM = AF’po,
(8)
where A is a constant dependent upon the shape and dimensions, V is the mean thermal velocity of molecules in the gas (464.4 m s-i for air at 295 K) and the pressure p is expressed in mbar. The values of A applicable here are given in Table 1. The angular acceleration of the receiver assembly h is therefore governed by the equation Zc;, = G = Go - G, - GM - GE.
(9)
Consequently Gi can be determined from acceleration measurements if Z, GM, GE and Gn are known. The undriven and decelerating system with Gn = 0 allows an alternative means for the determination of Gi by deceleration measurements. Equation (9) becomes Zc;, = -G, - GM - GE.
(10)
Gi is not frequency dependent but GM and GE depend linearly with frequency. Writing GM = uw and GE = /IO, equation (10) becomes ZcL=--Gi-aw-/3w.
(11)
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Table 1. Details of the three suspension apparatus used Suspension 2
Suspension 1
Property Receiver surface
Total suspension mass Total moment of inertia I Molecular drag constant A Permanent magnet
46.00 f 0.02 mm radius polished aluminium disc
46.00 f 0.02 mm radius machined silicon wafer; smooth surface face downwards 34.8 g 1.228f0.004 x IO-‘kg m2 1.001 f0.002 x 10e3 m4 Nd-Fe-B ring IRner radius: 13.75 mm Outer radius: 17.25 mm Depth: 4.00 mm Pole face field: 0.05 T
75.4 g 3.325 f0.002 x IO-’ kg m2 9.77 f 0.03 x 10e4 m4 Nd-Fe-B disc Radius: 12.5 mm Depth: 7.06 mm Pole face field: 0.11 T
Suspension 3 42.32 f 0.2 mm radius machined silicon wafer; smooth surface face downwards 33.6 g 9.91 f0.04 x 1O-6 kg m2 7.42 f0.02 x 10d4 m4 Nd-Fe-B ring Inner radius: 13.75 mm Outer radius: 17.25 mm Depth: 4.00 mm Pole face field: 0.05 T
When GE is negligible, as was arranged to be the case in the experiments equation (11) simplifies to Ib = -Gr - CIW,
reported here, (12)
which has the solution o(t) =
w,+z
exp(-:?
(
-4,
>
(13)
where t is the time and o. is the starting frequency. In the case of Gr,,,= 0 the solution to the above differential equation is o(t) =
00
-
GI
yt,
(14)
i.e. there is a linear decay of the rotational speed with time. APPARATUS
AND EXPERIMENTAL
PROCEDURE
The instrument is shown schematically in Fig. 1 and in a photograph in Fig. 2. The vacuum is maintained by a turbomolecular pump and pressure is controlled from lo- lo up to 10-i mbar by using a fine-leak valve FLV to admit gas; laboratory air was used exclusively in the experiments reported here. The drive unit D is a modified Edwards High Vacuum International EXT250M turbomolecular pump in which the blades have been replaced by an aluminium alloy disc of radius s = 46 mm. It operates in the frequency range 0 < R < 1000 Hz. The plate H is a pneumatically operated, and rapidly removable, aluminium shield located between the sender and the receiver, which enables the receiver to be exposed to a near step-function of molecular torque from the high speed sender or shielded from its influence. A Leybold VM2 12 second generation spinning rotor gauge (SRG) was used for accurate measurement of vacuum pressures in the range 2 x 10B2 to 4 x 10m6 mbar. Hot and cold cathode ionization gauges were used to measure lower pressures and a residual gas analyser was used to monitor the vacuum composition. Three different receiver suspensions were used in order to facilitate various comparisons and their dimensions and details of the associated disc and ring permanent magnets are given in Table 1. The highly polished side of a silicon wafer was used as the receiver surface in suspensions 1 and 3 and a highly polished aluminium disc was used in suspension 2. The value of 0 on similar receiver surfaces has been measured [9,15,16] to be unity. The receiver disc was attached to the magnet in each suspension via an ahnninium spindle J. Three YBazCuaOr HTS pellets, made and investigated in the chronological order A, B, C, whose details are given in Table 2 were supplied by the Forschungszentrum, Karlsruhe [ 171. They were produced by the melt texturation process and the sequence A-B-C had an improved grain structure with the aim to reduce the internal losses giving rise to the intrinsic drag torque. The HTS pellets were seated in a flat-bottomed re-entrant Kodial glass tube which also served as a dewar vessel enabling the pellet to be immersed in liquid nitrogen LN outside the vacuum chamber with the magnet and shaft arrangement suspended
Measurement of the intrinsic drag torques of high temperature superconductor bearings
Fig. 2. Photograph of the apparatus showing suspension 1 suspended below HTS pellet A.
Table 2. Details of the thnx superconductors
Diameter (mm) Depth (nW Density (kg me3)
Pellet A
Pellet B
Pellet C
42.30 10.40 6.2 x 10’
42.72 13.10 6.2 x lo3
42.10 12.54 6.7 x lo3
331
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A. D. CHEW et al.
below it inside the chamber, as shown in Fig. 2. An automatic filler was used to keep the liquid nitrogen level constant. The experimental procedure was as follows. The fork F, machined from a non-conducting vacuum-compatible ceramic, was used to align the receiver and the sender discs and then to place the magnet within the vicinty of the HTS pellet under investigation prior to field cooling. The fork also served as a safety device. Following the cooling of the pellet by LN the HTS pelletmagnet distance y and the disc-separation t were measured with a travelling microscope. The sender was run up to speed, the pressure raised and the shield H then withdrawn. Small increments in pressure were made to determine the threshold pressure, and hence the molecular drive starting torque GDs at which the suspension could be continuously accelerated; below this threshold the suspension would oscillate but not rotate continuously. The pressure required to achieve acceleration was about 10B3 mbar which is in the molecular flow regime where equation (4) applies. The suspension was accelerated to a low frequency, typically 90 rpm, to keep the effects of molecular and eddy current drag small and the shield was then replaced. The frequency of the receiver rotation ( f 0.001 rpm) was measured using a commercially available tachometer whose internal laser was reflected from a polished and machined flat 0 on the shaft of the suspension apparatus. Early trials indicated that there was an accelerating interaction between the rotating magnetic field of the sender and the magnetic field of the receiver suspension 2. To avoid this problem, when the shutter had been replaced, the rotor was turned off and measurements were taken only after the drive unit had come to rest and power to its drive magnets turned off. The simple geometry of the apparatus and experimental procedure and the application of equations (9) and (10) to interpret acceleration and deceleration allowed an efficient method for the investigation of the effects of residual gas pressure and the properties of individual HTS-magnet combinations. RESULTS
AND ANALYSIS
Figure 3 shows the deceleration of suspension 3, using HTS pellet A with frequency measured as a function of time for vacuum pressures in the range 2 x IO-* to 1.7 x lo-* mbar and a constant value of the HTS pellet-magnet distance y of 2.9 mm. The slowing rate is strongly pressure dependent. At higher pressures the decay curve has a general exponential-like form; at the lower pressures it approaches a simple linear form. It is evident that at the lowest pressure (1.7 x IO-* mbar) the deceleration rate becomes almost independent of pressure. The pressure dependence evident in Fig. 3 is also shown in Fig. 4 as a plot of the time to slow to half the initial speed or,/2 vs pressure. At the lowest pressure the almost perfect linearity of the curve in Fig. 3 indicates, in the light of equation (14), that eddy current and molecular contributions to the drag are negligible. Using a least squares fit to the data at this pressure and then equation (14) gives a value of Gi of 8.82 f 0.04 x lo-’ Nm. (The value of GM at this pressure and 80 rpm is 2.3 x lo-l3 Nm and therefore negligible in comparison.) A theoretical estimate of Gi using equation (7) and values [l] of Jc = lo7 A m-* and AB = 0.001 T (which are subject to an unknown uncertainty) is 9.6 x lo-’ Nm, in reasonable agreement with the measured value. In Fig. 5 the deceleration of suspension 1 using HTS pellet A at a pressure of 1.5 x lo-* mbar is shown for a range of HTS pellet-magnet distances y. The minimum value ofy was limited by the thickness (2.5 mm) of the Kodial tube. At the larger values of y the suspension was (unavoidably) slightly tilted. As above, using a least squares fit to the linear data of the curves at y = 5.2-5.5 mm and 2.8 mm gives the lowest and highest values of Gi of 2.65 f 0.03 x lo-’ Nm and 9.13 f 0.07 x lo-’ Nm, respectively. This is as expected since the highest magnetic field intensity at the pellet, and hence larger value of AB, occurs at the smallest value of y. The theoretical estimates of Gi are 4.8 x lo-’ Nm, and 1.O x lo-* Nm, respectively. A comparison of the deceleration using two different magnets at the same pellet-magnet distance (3.0 mm) and the same HTS pellet A is shown in Fig. 6 for suspensions 1 and 2 and a pressure of 1.2 x lo-* mbar. Using a least squares fit to the linear part of the curves gives Gi values of 8.67 f 0.04 x lo-’ Nm and 4.20 f0.02 x lo-* Nm for suspension 1 and 2, respectively, and the respective theoretical estimates are 9.3 x lo-’ Nm and 6.4 x lo-* Nm. Another effect to be noted is the increased curvature of the data of suspension 2 which has a much
Measurement
of the intrinsic drag torques of high temperature
superconductor
bearings
333
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[3
20
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40
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120
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Time (minutes) Fig. 3. Deceleration of receiver suspension 3, using HTS pellet A, for a range of vacuum pressures and a constant HTS pellet-magnet distance y of 2.9 mm.
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A. D. CHEW et al.
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20
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Time (minutes) Fig. 5. Deceleration of receiver suspension 1, using HTS pellet A, for a range of HTS pellet-magnet distances y and a pressure of 1.5 x 10e8 mbar. The full lines are a least squares fit to the data.
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Time (minutes) Fig. 6. Deceleration of receiver suspensions 1 and 2, using HT.9 pellet A, at a HTS pellet-magnet distance y of 3.0 mm and a pressure of 1.2 x lo-* mbar.
Measurement
of the intrinsic drag torques of high temperature
superconductor
bearings
335
stronger magnet of 0.11 T compared to 0.05 T for suspension 1. Since the vacua are the same, this implies that eddy current interactions with surroundings are not negligible for suspension 2. The effect of the improvement in the grain structure in the HTS pellets is shown in Fig. 7 where the deceleration of suspension 3 is measured at a pressure of 1.3 x 10d8 mbar for the three HTS pellets at the same value of y = 2.7 mm. The data are linear and again using a least squares fit the values of Gi for the pellets A, B and C are measured as 8.70 f0.03 x 10m9 Nm, 2.65 fO.O1 x 10M9 Nm and 1.191 ho.005 x 10M9 Nm, respectively. It can be seen that an improvement in lthe fabrication process has decreased the intrinsic drag torque by a factor of seven. The measured and predicted values of Gi for the above experiments are summarised in Table 3 which also gives the measured starting torque Gus calculated from equations (4) and (5) using the threshold pressure needed to continuously accelerate the suspension. The uncertainty in Gus includes a f 4% uncertainty [9] in the threshold pressure measured using the SRG. In all cases, there is a marked difference between the Gi and GDs values such that Gns is between 100 and 1600Gi. This is possibly due to a “potential well” type of phenomenon in which a threshold kinetic energy is needed to overcome a starting potential barrier in the magnet-pellet bearing; below the threshold the suspension would only oscillate. In all experiments a sharp fall of frequency at the end of each deceleration curves was observed as is shown in Figs 3 and 6. On each occasion the last recorded frequency was about 3 rpm, after which continuous rotation ceased and oscillation occurred as though a potential barrier could no longer be surmounted. The fact that Gi does not equal Gns is an important observation and shows that Gr can only be evaluated above 10 rpm and beyond an effective potential barrier. These phenomena remain to be investigated further. Spontaneous reacceleration was observed on one occasion when the deceleration of suspension 1, using HTS pellet A, was measured as a function of time at a pressure of 1.5 x 10m3 mbar and y = 4-5 mm. The deceleration was in accord with that of other experiments until a frequency of approximately 7 r]pm at which point deceleration ceased and spontaneous reacceleration occurred, 90. LL
65. 0
5
10
15
20
25
30
35
Time (minutes) Fig. 7. Decelemtion of receiver suspension 3 using HTS pellets A, B and C at a HTS pellet-magnet distancey of 2.7 mm and a pressure of 1.3 x 10m8 mbar. The full lines are a least squares fit to tbe data.
40
A. D. CHEW et al.
336
Table 3. Summary of measured drag torques y (f0.1
Graph 3 5 5 6 6 7 7 7
mm)
2.9 2.8 5.2-5.5 3.0 3.0 2.7 2.7 2.7
Suspension
Pellet
G, measured x 10’ Nm
G, predicted x 10’ Nm
3 1 1 2 1 3 3 3
A A A A A A B
8.82 f 0.04 [9.13 rto.071 2.65 f 0.03 42.0 f 0.2 8.67 f0.04 8.70f0.03 2.65 f 0.01 1.191 f0.005
9.6 10.0 4.8 64.4 9.3 10.3
C
Gas measured x lo6 Nm 1.52f0.08
1.47f 0.07 4.47 f 0.22 1.05f0.05 1.92f0.10
as is shown in Fig. 8. At points A on the graph the pressure was rapidly reduced to 1.4 x 10B7 mbar and deceleration recommenced, but acceleration could then be induced by raising the pressure to 1.5 x low3 mbar. A similar observation has been reported by other workers who attributed the phenomenon to a temperature gradient in the magnet [ 181 giving rise to a change in magnetization, but this explanation does not easily accord with observations made here, which remain puzzling. This phenomenon was not reproducible. The dependence of deceleration on vacuum pressure is clearly shown in Fig. 4 and demonstrates a way of using the instrument to measure pressure by utilising equation (12). If, as is shown in Fig. 9, the system is driven up to a certain frequency and the drive disconnected (at point X) the acceleration is controlled by Zci,= Go - GA and the deceleration by I&’ = - GA, where GA represents the sum of the retarding torques which operate over a small frequency range. Thus GD = Z(b - ~7) and pressure may be deduced by equation (4). The example of Fig. 9 is for suspension 3 using pellet A. Substituting the values $2= 4 18.8 Hz, c = 1.00, E =0.58, r=42.32 x 10T3 m and M=28.96 x 10V3 kg in equation (4) and combining with the measured torque values, from a least squares fit to the data, gives a measured
a3
b
300
350
400
O” 0
500 450 Time (minutes)
0
550
600
Fig. 8. Frequency of receiver suspension 1, using HTS pellet A, at a HTS pellet-magnet distance y of 4-5 mm, showing spontaneous reacceleration. The pressure was reduced from 1.5 x 10e3 mbar to 1.4 x lo-’ mbar at point A.
650
Measurement of the intrinsic drag torques of high temperature superconductor bearings
T
A
A
A
A
A
AA
337
AAA
A A A \
X
LfhA A A A AA A
I
0
50
I
loo
I
150
I
200
I
260
I
I
I
300
350
400
I
450
500
Time (secondsl Fig. 9. Accele:ration and deceleration of receiver suspension 3, using HT.5 pellet A, for the case of nonzero (before point X) and zero drive torque Go, respectively. The HTS pellet-magnet distance y was 2.9 mm and the spinning rotor gauge reading was 3.97 x 10m4 mbar. pressure
3.97 f0.16
of 3.60 SO.18 x 10m4 mbar in reasonable x 10e4 mbar.
agreement
with the SRG reading
of
CONCLUSIONS
A new technique for the systematic measurement of the intrinsic drag torques Gt of HTS bearings with high accuracy has been developed. The results show that an ultra high vacuum environment is required to make residual gas effects negligible. Careful construction of the apparatus made eddy current drag effects negligible in most cases. The lowest value of Gr measured using a YBCO pellet of high quality with large grain structure was 1.2 x 10d9 Nm at a HTS pellet-magnet distance of 2.7 mm. Theoretical estimates of Gr are in reasonable accord with the measured values. The threshold torque needed to continuously accelerate the suspension was 100-l 600Gt. A non-reproducible phenomenon of spontaneous reacceleration was observed at a pressure of 1.5 x 10m3 mbar. Using the accelerating mode of the instrument enabled measurement of vacuum pressure in reasonable agreement with a spinning rotor gauge value; further pressure measurements will be reported in a separate article. Acknowledgements-The authors would like to record thanks to Thomas Burghardt, Wolfgang Hennig and Hans Bornemann of the Forschungszentrum, Karlsruhe for the provision of HTS pellets and useful discussion on this work. Technical assistance at the University of York was provided by Ian Wright. This work was jointly funded by the EPSRC (award GR/J07105) and Edwards High Vacuum International. REFERENCES 1. H. J. Bomemann, T. Ritter, C. Urban, 0. Zaitsev, K. Weber and H. Rietschel, Appl. Supercond. 2, 439 (1994). 2. F. C. Moon, C. Golkowski and D. Kuppennann, Appl. Supercond. 1, 1175(1993). 3. H. Ogiwara, T. Azukizawa and M. Morishita, Appl. Supercond. 1, 1185 (1993).
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4. B. R. Weinberger, L. Lynds, J. Van Valzah, H. E. Eaton, J. R. Hull, T. M. Mulcahy ++ndS. A. Basinger, IEEE Trans. Magn. 27, 2415 (1991). 5. D. E. Weeks, 1 Appl. Phys. 70, 1820 (1991). 6. B. R. Weinberger, L. Lynds, J. R. Hull and U. Balachandran, Appl. Phys. Lett. 59, 1132 (1991). 7. A. Chambers, A. D. Chew and A. P. Troup, Vacuum 43, 9 (1992). 8. A. Chambers. A. D. Chew and A. P Trouu, 1 Vat. Sci. Technol. A 10, 2655 (1992). 9. A. D. Chew, A. Chambers and A. P Troup, Vacuum44, 583 (1993). ’ ’ 10. A. D. Chew, Doctor of Philosophy thesis, University of York, U.K. February (1993). 11. G. J. Pert, A. Chambers and A. D. Chew, Vacuum45, 937 (1994). 12. A. D. Chew, A. Chambers, G. J. Pert, S. L. Bastow and A. P. Troup, kuum 46, 773 (1995). 13. A. D. Chew, A. Chambers, G. J. Pert and A. P Troup, J kc. Sci. Technol. A 13, 2271 (1995). 14. L. C. Davis, E. M. Logothetis and R. E. Soltis, J Appl. Phys. 64, 4212 (1988). 15. G. Comsa, J. K. Fremerey and B. Lindenau, in Proceedings ofthe Eighth International kcuum Congress, Vol. II (Edited by J. P Langeron and L. Maurice), p. 218. Societe Fratqaise du Vide, Paris (1981). 16. L. B. Thomas, in Rarefield Gas Dynamics-Proceedings of the lbelfrh International Symposium, Part 1 (Edited by S. S. Fisher), p. 83. American Institue of Aeronautics and Astronautics, New York (1981). 17. Pellets manufactured and supplied by Forschungszentrum Karlsruhe GmbH, Institut filr Nukleare Festkiirperphysik, PO. Box 3640, 76021 Karlsruhe, Germany. 18. K. B. Ma, J. R. Liu, C. McMichael, R. Bruce, D. Mims and W. K. Chu, 1 Appl. Phys. 70, 3961 (1991).
Pergamori
09644807(95)0007fL!3
Copyright0 1996ElscvicrScience Ltd Printedin Great Britain.All rights rcscrved 0964-1087/9539.50 + 0.00
NEW TECHNIQUE FOR THE MEASUREMENT OF THE INTRINSIC DRAG TORQUES OF HIGH TEMPERATURE SUPERCONDUCTOR BEARINGS A. D. CHEW’, A. CHAMBERS’ and A. P TROUP’ ’ Department of Physics, University of York, York YOl 5DD, U.K. 2 Edwards High Vacuum International, Manor Royal, Crawley, RHlO 2LW, U.K. (Received 7 June 1995)
Abstract-A new technique providing a non-intrusive means for the isolation and accurate measurement of the intrinsic drag torques of high temperature superconductor bearings is reported. It involves measuring the rotational acceleration and deceleration of a rotating symmetric object suspended in vacua on a bearing formed by the combination of a magnet and an I-ITS pellet. Accelerations are produced by exploiting molecular drag torque in medium vacuum while deceleration from low starting speeds in ultra high vacuum, in which gaseous drag and eddy current effects are minimized, enables intrinsic drag torques to be accurately determined. Experiments have been carried out on YBaaCusO, pellets and improvement in pellet grain structure is shown to decrease the&e of the intrinsic drag torque. Theoretical estimates are in reasonable agreement with measured values. The effect of the magnetic field intensity of the suspended magnet and the suspension height is also reported. A threshold type starting phenomenon was observed in which the torque required to accelerate the suspension was two to three orders of magnitude higher than the intrinsic drag torque obtained from deceleration measurements. Observations of spontaneous reacceleration and the potential for using the device to measure vacuum pressures is also discussed.
INTRODUCTION
There has been rapid progress made recently [l-4] in the development of passive, low friction, high critical temlperature superconductor (HTS) bearings for use, for example, in carrier and flywheel energy storage applications. This has created a need for accurate measurements of the intrinsic drag torques of these bearings. The methods currently employed include accelerating the levitated permanent magnet part of the bearings by inductive drive [5] or nitrogen gas jets [6]; deceleration measurements are then made to determine the intrinsic drag torque. These methods are somewhat intrusive and limit the achievable vacuum of the vessel in which the apparatus is located. In addition, results from these measurements show a pressure dependent component of the deceleration and demonstrate the need to operate in ultra high vacuum (UHV) to minimize gaseous drag effects. In this paper an instrument is described which affords a means for the accurate and systematic measurement of the intrinsic drag torques of HTS bearings. It uses molecular drag, due to residual gas at medium vacuum, to accelerate the suspended part of the bearing, followed by deceleration measurements in UHX
PRINCIPLE
AND
THEORY
The essential features of the instrument are shown schematically in Fig. 1. It is housed in a stainless steel vacuum vessel Vand consists of a drive unit D which drives a disc S, “the sender” of radius s, at high angular velocity R and a coaxial and parallel “receiver” disc R of radius r. The receiver disc is lolcated at a distance t from the sender and attached to the suspension system J which carries a mirror arrangement 0 for the measurement of rotational frequency. The attractive force allowing free suspension below the superconductor is provided between a permanent magnet M fixed to the top of the suspension and a cooled HTS pellet held outside the vacuum system. The residual gas in the vacuum chamber couples the motion of the sender to the receiver by either viscous or molecular drag forces, depending on the vacuum pressure. The motion of the 327
A, D. CHEW et al.
328
FLV
T
65 00
Fig. 1. Schematic diagram of the essential features of the apparatus.
suspended system about the vertical axis is described by G=Ih,
(1)
where G is the total torque, I is the total moment of inertia of the receiver suspension about the axis of rotation and 61 is the resultant angular acceleration, with w = 2rcf where f is the rotational frequency of the receiver. I is accurately calculable from dimension and mass measurements and h is measured directly. The high speed drive and dynamics of the sender-receiver interspace form the basis of a rotating disc vacuum gauge which has been fully investigated and described by the authors previously [7-131. The Knudsen number Kn relates mean free path I at a particular pressure to some important characteristic dimension, in this case t, by the formula Kn = n/t.
(2)
For Kn c 0.01, molecule-molecule interactions dominate gas behaviour and the transfer of torque is via viscous forces. At low pressures where Kn > 1 molecule-surface collisons dominate and the torque is transferred by molecular drag. The drive torque Gn developed [12] between the
Measurement of the intrinsic drag torques of high temperature superconductor bearings
sender and the stationary or quasi-stationary
329
receiver under viscous conditions is
Go =
;+r4,
(3)
where tl is the coefficient of viscosity, and the other quantities are already defined. Under molecular flow c:onditions, Kn > 1, the torque developed is 10
lW2p,
(4)
where r~is the coefficient of accommodation of tangential momentum of molecules on the receiver surface which may be taken as unity ( f 3%) for a smooth, flat and adsorbate covered surface [9,15,16]. R. is the gas constant, T the thermodynamic temperature, M the molar mass andp the pressure of the residual gas. E is the edge effect loss factor accounting for molecules which leave the discs’ interspace, and is discussed fully in Refs [ 11 and 131. For the conditions of this experiment t R a: c where c = (RoT/M)1’2 is a measure of molecular velocity, and 6 =
[$((3 + (s + r)y2-{t2 + (s - r)2}1/2)]4.
For the particular case T=S equation (5) reduces to
At a typical working separation of t = 12 mm and for I = s = 46 mm, E= 0.59. There are several sources of drag in superconductor magnetic bearings. Intrinsic drag in the bearing results from asymmetries in the magnet/superconductor arrangement which cause the hysteretic loss motion of flux vortices in the superconductors. This produces an intrinsic drag torque Gi which is frequency independent [1,5]. Davis et al. [14] derived an expression for Gi which in this application, of a disc magnet of diameter d or a ring magnet of mean diameter d, magnetized axially with their plane surface parallel to the superconductor’s surface is G, = AB is the twice maximum superconductor’s surface and J, due to eddy current interactions molecules on the various parts
5d2(AlQ3 48p;Jc
*
(7)
variation [1,5] of the magnet’s average field measured at the is the superconductor’s critical current. A drag torque GE may act and a molecular drag torque GM. By considering the impact of gas of the rotating suspension it may be shown that GM = AF’po,
(8)
where A is a constant dependent upon the shape and dimensions, V is the mean thermal velocity of molecules in the gas (464.4 m s-i for air at 295 K) and the pressure p is expressed in mbar. The values of A applicable here are given in Table 1. The angular acceleration of the receiver assembly h is therefore governed by the equation Zc;, = G = Go - G, - GM - GE.
(9)
Consequently Gi can be determined from acceleration measurements if Z, GM, GE and Gn are known. The undriven and decelerating system with Gn = 0 allows an alternative means for the determination of Gi by deceleration measurements. Equation (9) becomes Zc;, = -G, - GM - GE.
(10)
Gi is not frequency dependent but GM and GE depend linearly with frequency. Writing GM = uw and GE = /IO, equation (10) becomes ZcL=--Gi-aw-/3w.
(11)
A. D. CHEWet al.
330
Table 1. Details of the three suspension apparatus used Suspension 2
Suspension 1
Property Receiver surface
Total suspension mass Total moment of inertia I Molecular drag constant A Permanent magnet
46.00 f 0.02 mm radius polished aluminium disc
46.00 f 0.02 mm radius machined silicon wafer; smooth surface face downwards 34.8 g 1.228f0.004 x IO-‘kg m2 1.001 f0.002 x 10e3 m4 Nd-Fe-B ring IRner radius: 13.75 mm Outer radius: 17.25 mm Depth: 4.00 mm Pole face field: 0.05 T
75.4 g 3.325 f0.002 x IO-’ kg m2 9.77 f 0.03 x 10e4 m4 Nd-Fe-B disc Radius: 12.5 mm Depth: 7.06 mm Pole face field: 0.11 T
Suspension 3 42.32 f 0.2 mm radius machined silicon wafer; smooth surface face downwards 33.6 g 9.91 f0.04 x 1O-6 kg m2 7.42 f0.02 x 10d4 m4 Nd-Fe-B ring Inner radius: 13.75 mm Outer radius: 17.25 mm Depth: 4.00 mm Pole face field: 0.05 T
When GE is negligible, as was arranged to be the case in the experiments equation (11) simplifies to Ib = -Gr - CIW,
reported here, (12)
which has the solution o(t) =
w,+z
exp(-:?
(
-4,
>
(13)
where t is the time and o. is the starting frequency. In the case of Gr,,,= 0 the solution to the above differential equation is o(t) =
00
-
GI
yt,
(14)
i.e. there is a linear decay of the rotational speed with time. APPARATUS
AND EXPERIMENTAL
PROCEDURE
The instrument is shown schematically in Fig. 1 and in a photograph in Fig. 2. The vacuum is maintained by a turbomolecular pump and pressure is controlled from lo- lo up to 10-i mbar by using a fine-leak valve FLV to admit gas; laboratory air was used exclusively in the experiments reported here. The drive unit D is a modified Edwards High Vacuum International EXT250M turbomolecular pump in which the blades have been replaced by an aluminium alloy disc of radius s = 46 mm. It operates in the frequency range 0 < R < 1000 Hz. The plate H is a pneumatically operated, and rapidly removable, aluminium shield located between the sender and the receiver, which enables the receiver to be exposed to a near step-function of molecular torque from the high speed sender or shielded from its influence. A Leybold VM2 12 second generation spinning rotor gauge (SRG) was used for accurate measurement of vacuum pressures in the range 2 x 10B2 to 4 x 10m6 mbar. Hot and cold cathode ionization gauges were used to measure lower pressures and a residual gas analyser was used to monitor the vacuum composition. Three different receiver suspensions were used in order to facilitate various comparisons and their dimensions and details of the associated disc and ring permanent magnets are given in Table 1. The highly polished side of a silicon wafer was used as the receiver surface in suspensions 1 and 3 and a highly polished aluminium disc was used in suspension 2. The value of 0 on similar receiver surfaces has been measured [9,15,16] to be unity. The receiver disc was attached to the magnet in each suspension via an ahnninium spindle J. Three YBazCuaOr HTS pellets, made and investigated in the chronological order A, B, C, whose details are given in Table 2 were supplied by the Forschungszentrum, Karlsruhe [ 171. They were produced by the melt texturation process and the sequence A-B-C had an improved grain structure with the aim to reduce the internal losses giving rise to the intrinsic drag torque. The HTS pellets were seated in a flat-bottomed re-entrant Kodial glass tube which also served as a dewar vessel enabling the pellet to be immersed in liquid nitrogen LN outside the vacuum chamber with the magnet and shaft arrangement suspended
Measurement of the intrinsic drag torques of high temperature superconductor bearings
Fig. 2. Photograph of the apparatus showing suspension 1 suspended below HTS pellet A.
Table 2. Details of the thnx superconductors
Diameter (mm) Depth (nW Density (kg me3)
Pellet A
Pellet B
Pellet C
42.30 10.40 6.2 x 10’
42.72 13.10 6.2 x lo3
42.10 12.54 6.7 x lo3
331
332
A. D. CHEW et al.
below it inside the chamber, as shown in Fig. 2. An automatic filler was used to keep the liquid nitrogen level constant. The experimental procedure was as follows. The fork F, machined from a non-conducting vacuum-compatible ceramic, was used to align the receiver and the sender discs and then to place the magnet within the vicinty of the HTS pellet under investigation prior to field cooling. The fork also served as a safety device. Following the cooling of the pellet by LN the HTS pelletmagnet distance y and the disc-separation t were measured with a travelling microscope. The sender was run up to speed, the pressure raised and the shield H then withdrawn. Small increments in pressure were made to determine the threshold pressure, and hence the molecular drive starting torque GDs at which the suspension could be continuously accelerated; below this threshold the suspension would oscillate but not rotate continuously. The pressure required to achieve acceleration was about 10B3 mbar which is in the molecular flow regime where equation (4) applies. The suspension was accelerated to a low frequency, typically 90 rpm, to keep the effects of molecular and eddy current drag small and the shield was then replaced. The frequency of the receiver rotation ( f 0.001 rpm) was measured using a commercially available tachometer whose internal laser was reflected from a polished and machined flat 0 on the shaft of the suspension apparatus. Early trials indicated that there was an accelerating interaction between the rotating magnetic field of the sender and the magnetic field of the receiver suspension 2. To avoid this problem, when the shutter had been replaced, the rotor was turned off and measurements were taken only after the drive unit had come to rest and power to its drive magnets turned off. The simple geometry of the apparatus and experimental procedure and the application of equations (9) and (10) to interpret acceleration and deceleration allowed an efficient method for the investigation of the effects of residual gas pressure and the properties of individual HTS-magnet combinations. RESULTS
AND ANALYSIS
Figure 3 shows the deceleration of suspension 3, using HTS pellet A with frequency measured as a function of time for vacuum pressures in the range 2 x IO-* to 1.7 x lo-* mbar and a constant value of the HTS pellet-magnet distance y of 2.9 mm. The slowing rate is strongly pressure dependent. At higher pressures the decay curve has a general exponential-like form; at the lower pressures it approaches a simple linear form. It is evident that at the lowest pressure (1.7 x IO-* mbar) the deceleration rate becomes almost independent of pressure. The pressure dependence evident in Fig. 3 is also shown in Fig. 4 as a plot of the time to slow to half the initial speed or,/2 vs pressure. At the lowest pressure the almost perfect linearity of the curve in Fig. 3 indicates, in the light of equation (14), that eddy current and molecular contributions to the drag are negligible. Using a least squares fit to the data at this pressure and then equation (14) gives a value of Gi of 8.82 f 0.04 x lo-’ Nm. (The value of GM at this pressure and 80 rpm is 2.3 x lo-l3 Nm and therefore negligible in comparison.) A theoretical estimate of Gi using equation (7) and values [l] of Jc = lo7 A m-* and AB = 0.001 T (which are subject to an unknown uncertainty) is 9.6 x lo-’ Nm, in reasonable agreement with the measured value. In Fig. 5 the deceleration of suspension 1 using HTS pellet A at a pressure of 1.5 x lo-* mbar is shown for a range of HTS pellet-magnet distances y. The minimum value ofy was limited by the thickness (2.5 mm) of the Kodial tube. At the larger values of y the suspension was (unavoidably) slightly tilted. As above, using a least squares fit to the linear data of the curves at y = 5.2-5.5 mm and 2.8 mm gives the lowest and highest values of Gi of 2.65 f 0.03 x lo-’ Nm and 9.13 f 0.07 x lo-’ Nm, respectively. This is as expected since the highest magnetic field intensity at the pellet, and hence larger value of AB, occurs at the smallest value of y. The theoretical estimates of Gi are 4.8 x lo-’ Nm, and 1.O x lo-* Nm, respectively. A comparison of the deceleration using two different magnets at the same pellet-magnet distance (3.0 mm) and the same HTS pellet A is shown in Fig. 6 for suspensions 1 and 2 and a pressure of 1.2 x lo-* mbar. Using a least squares fit to the linear part of the curves gives Gi values of 8.67 f 0.04 x lo-’ Nm and 4.20 f0.02 x lo-* Nm for suspension 1 and 2, respectively, and the respective theoretical estimates are 9.3 x lo-’ Nm and 6.4 x lo-* Nm. Another effect to be noted is the increased curvature of the data of suspension 2 which has a much
Measurement
of the intrinsic drag torques of high temperature
superconductor
bearings
333
Pressure v 1.78-8 mbar 0
l.le-7
nlhar
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4.6e-4 mbar
0
1.2e-3 mbar
0
3.4e-3 mbar
.
1 .Oe.2 mbar
[3
20
0
40
60
80
2 S-2
100
tnbar
120
140
160
Time (minutes) Fig. 3. Deceleration of receiver suspension 3, using HTS pellet A, for a range of vacuum pressures and a constant HTS pellet-magnet distance y of 2.9 mm.
80.
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Pressure (mbd Fig. 4,. Half speed decay time plotted as a function of pressure for the data in Fig. 3.
la'
A. D. CHEW et al.
334
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I
I
I
I
I
I
I
2
4
6
8
10
12
14
I 16
I
I
I
I
18
20
22
24
Time (minutes) Fig. 5. Deceleration of receiver suspension 1, using HTS pellet A, for a range of HTS pellet-magnet distances y and a pressure of 1.5 x 10e8 mbar. The full lines are a least squares fit to the data.
L t
A?+
I
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A
suspemiw12 suspensim1 I
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++ +
h
40
+
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60
80
100
120
140
160
Time (minutes) Fig. 6. Deceleration of receiver suspensions 1 and 2, using HT.9 pellet A, at a HTS pellet-magnet distance y of 3.0 mm and a pressure of 1.2 x lo-* mbar.
Measurement
of the intrinsic drag torques of high temperature
superconductor
bearings
335
stronger magnet of 0.11 T compared to 0.05 T for suspension 1. Since the vacua are the same, this implies that eddy current interactions with surroundings are not negligible for suspension 2. The effect of the improvement in the grain structure in the HTS pellets is shown in Fig. 7 where the deceleration of suspension 3 is measured at a pressure of 1.3 x 10d8 mbar for the three HTS pellets at the same value of y = 2.7 mm. The data are linear and again using a least squares fit the values of Gi for the pellets A, B and C are measured as 8.70 f0.03 x 10m9 Nm, 2.65 fO.O1 x 10M9 Nm and 1.191 ho.005 x 10M9 Nm, respectively. It can be seen that an improvement in lthe fabrication process has decreased the intrinsic drag torque by a factor of seven. The measured and predicted values of Gi for the above experiments are summarised in Table 3 which also gives the measured starting torque Gus calculated from equations (4) and (5) using the threshold pressure needed to continuously accelerate the suspension. The uncertainty in Gus includes a f 4% uncertainty [9] in the threshold pressure measured using the SRG. In all cases, there is a marked difference between the Gi and GDs values such that Gns is between 100 and 1600Gi. This is possibly due to a “potential well” type of phenomenon in which a threshold kinetic energy is needed to overcome a starting potential barrier in the magnet-pellet bearing; below the threshold the suspension would only oscillate. In all experiments a sharp fall of frequency at the end of each deceleration curves was observed as is shown in Figs 3 and 6. On each occasion the last recorded frequency was about 3 rpm, after which continuous rotation ceased and oscillation occurred as though a potential barrier could no longer be surmounted. The fact that Gi does not equal Gns is an important observation and shows that Gr can only be evaluated above 10 rpm and beyond an effective potential barrier. These phenomena remain to be investigated further. Spontaneous reacceleration was observed on one occasion when the deceleration of suspension 1, using HTS pellet A, was measured as a function of time at a pressure of 1.5 x 10m3 mbar and y = 4-5 mm. The deceleration was in accord with that of other experiments until a frequency of approximately 7 r]pm at which point deceleration ceased and spontaneous reacceleration occurred, 90. LL
65. 0
5
10
15
20
25
30
35
Time (minutes) Fig. 7. Decelemtion of receiver suspension 3 using HTS pellets A, B and C at a HTS pellet-magnet distancey of 2.7 mm and a pressure of 1.3 x 10m8 mbar. The full lines are a least squares fit to tbe data.
40
A. D. CHEW et al.
336
Table 3. Summary of measured drag torques y (f0.1
Graph 3 5 5 6 6 7 7 7
mm)
2.9 2.8 5.2-5.5 3.0 3.0 2.7 2.7 2.7
Suspension
Pellet
G, measured x 10’ Nm
G, predicted x 10’ Nm
3 1 1 2 1 3 3 3
A A A A A A B
8.82 f 0.04 [9.13 rto.071 2.65 f 0.03 42.0 f 0.2 8.67 f0.04 8.70f0.03 2.65 f 0.01 1.191 f0.005
9.6 10.0 4.8 64.4 9.3 10.3
C
Gas measured x lo6 Nm 1.52f0.08
1.47f 0.07 4.47 f 0.22 1.05f0.05 1.92f0.10
as is shown in Fig. 8. At points A on the graph the pressure was rapidly reduced to 1.4 x 10B7 mbar and deceleration recommenced, but acceleration could then be induced by raising the pressure to 1.5 x low3 mbar. A similar observation has been reported by other workers who attributed the phenomenon to a temperature gradient in the magnet [ 181 giving rise to a change in magnetization, but this explanation does not easily accord with observations made here, which remain puzzling. This phenomenon was not reproducible. The dependence of deceleration on vacuum pressure is clearly shown in Fig. 4 and demonstrates a way of using the instrument to measure pressure by utilising equation (12). If, as is shown in Fig. 9, the system is driven up to a certain frequency and the drive disconnected (at point X) the acceleration is controlled by Zci,= Go - GA and the deceleration by I&’ = - GA, where GA represents the sum of the retarding torques which operate over a small frequency range. Thus GD = Z(b - ~7) and pressure may be deduced by equation (4). The example of Fig. 9 is for suspension 3 using pellet A. Substituting the values $2= 4 18.8 Hz, c = 1.00, E =0.58, r=42.32 x 10T3 m and M=28.96 x 10V3 kg in equation (4) and combining with the measured torque values, from a least squares fit to the data, gives a measured
a3
b
300
350
400
O” 0
500 450 Time (minutes)
0
550
600
Fig. 8. Frequency of receiver suspension 1, using HTS pellet A, at a HTS pellet-magnet distance y of 4-5 mm, showing spontaneous reacceleration. The pressure was reduced from 1.5 x 10e3 mbar to 1.4 x lo-’ mbar at point A.
650
Measurement of the intrinsic drag torques of high temperature superconductor bearings
T
A
A
A
A
A
AA
337
AAA
A A A \
X
LfhA A A A AA A
I
0
50
I
loo
I
150
I
200
I
260
I
I
I
300
350
400
I
450
500
Time (secondsl Fig. 9. Accele:ration and deceleration of receiver suspension 3, using HT.5 pellet A, for the case of nonzero (before point X) and zero drive torque Go, respectively. The HTS pellet-magnet distance y was 2.9 mm and the spinning rotor gauge reading was 3.97 x 10m4 mbar. pressure
3.97 f0.16
of 3.60 SO.18 x 10m4 mbar in reasonable x 10e4 mbar.
agreement
with the SRG reading
of
CONCLUSIONS
A new technique for the systematic measurement of the intrinsic drag torques Gt of HTS bearings with high accuracy has been developed. The results show that an ultra high vacuum environment is required to make residual gas effects negligible. Careful construction of the apparatus made eddy current drag effects negligible in most cases. The lowest value of Gr measured using a YBCO pellet of high quality with large grain structure was 1.2 x 10d9 Nm at a HTS pellet-magnet distance of 2.7 mm. Theoretical estimates of Gr are in reasonable accord with the measured values. The threshold torque needed to continuously accelerate the suspension was 100-l 600Gt. A non-reproducible phenomenon of spontaneous reacceleration was observed at a pressure of 1.5 x 10m3 mbar. Using the accelerating mode of the instrument enabled measurement of vacuum pressure in reasonable agreement with a spinning rotor gauge value; further pressure measurements will be reported in a separate article. Acknowledgements-The authors would like to record thanks to Thomas Burghardt, Wolfgang Hennig and Hans Bornemann of the Forschungszentrum, Karlsruhe for the provision of HTS pellets and useful discussion on this work. Technical assistance at the University of York was provided by Ian Wright. This work was jointly funded by the EPSRC (award GR/J07105) and Edwards High Vacuum International. REFERENCES 1. H. J. Bomemann, T. Ritter, C. Urban, 0. Zaitsev, K. Weber and H. Rietschel, Appl. Supercond. 2, 439 (1994). 2. F. C. Moon, C. Golkowski and D. Kuppennann, Appl. Supercond. 1, 1175(1993). 3. H. Ogiwara, T. Azukizawa and M. Morishita, Appl. Supercond. 1, 1185 (1993).
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4. B. R. Weinberger, L. Lynds, J. Van Valzah, H. E. Eaton, J. R. Hull, T. M. Mulcahy ++ndS. A. Basinger, IEEE Trans. Magn. 27, 2415 (1991). 5. D. E. Weeks, 1 Appl. Phys. 70, 1820 (1991). 6. B. R. Weinberger, L. Lynds, J. R. Hull and U. Balachandran, Appl. Phys. Lett. 59, 1132 (1991). 7. A. Chambers, A. D. Chew and A. P. Troup, Vacuum 43, 9 (1992). 8. A. Chambers. A. D. Chew and A. P Trouu, 1 Vat. Sci. Technol. A 10, 2655 (1992). 9. A. D. Chew, A. Chambers and A. P Troup, Vacuum44, 583 (1993). ’ ’ 10. A. D. Chew, Doctor of Philosophy thesis, University of York, U.K. February (1993). 11. G. J. Pert, A. Chambers and A. D. Chew, Vacuum45, 937 (1994). 12. A. D. Chew, A. Chambers, G. J. Pert, S. L. Bastow and A. P. Troup, kuum 46, 773 (1995). 13. A. D. Chew, A. Chambers, G. J. Pert and A. P Troup, J kc. Sci. Technol. A 13, 2271 (1995). 14. L. C. Davis, E. M. Logothetis and R. E. Soltis, J Appl. Phys. 64, 4212 (1988). 15. G. Comsa, J. K. Fremerey and B. Lindenau, in Proceedings ofthe Eighth International kcuum Congress, Vol. II (Edited by J. P Langeron and L. Maurice), p. 218. Societe Fratqaise du Vide, Paris (1981). 16. L. B. Thomas, in Rarefield Gas Dynamics-Proceedings of the lbelfrh International Symposium, Part 1 (Edited by S. S. Fisher), p. 83. American Institue of Aeronautics and Astronautics, New York (1981). 17. Pellets manufactured and supplied by Forschungszentrum Karlsruhe GmbH, Institut filr Nukleare Festkiirperphysik, PO. Box 3640, 76021 Karlsruhe, Germany. 18. K. B. Ma, J. R. Liu, C. McMichael, R. Bruce, D. Mims and W. K. Chu, 1 Appl. Phys. 70, 3961 (1991).