Surface Impedance Characterization System · sample[2, 15] or sample film coated on a sm all rod[16], or just a sample on a dielectric holder[17-19] to perturb the field in a cavity

JLAB-TN-09-006 Binping Xiao

Surface Impedance Characterization System:

RF and Calorimeter System Analysis Binping Xiao

February 2009

1. Introduction ................................................................................................................ 2 2. SIC system overview ................................................................................................. 3 3. RF components .......................................................................................................... 5

RF couplers ............................................................................................................ 5 Sapphire ................................................................................................................. 5 TE011 mode identification....................................................................................... 8 RF Choke joint ....................................................................................................... 9

4. Calorimeter components: overview, hardware, simulation and experiments. ......... 10 Overview .............................................................................................................. 10 Hardware .............................................................................................................. 11 Simulation ............................................................................................................ 11 Experiments ......................................................................................................... 13

5. Current status, near-term plans and future ............................................................... 15 Current Status ....................................................................................................... 15 Near-term plans .................................................................................................... 15 Future ................................................................................................................... 16

References: ................................................................................................................... 16


1. Introduction Due to economic reason, enhancing superconducting radiofrequency cavities’ accelerating gradient by surface treatment, and finding different materials, or thin films on cheaper substrate that may be used instead of niobium, is of great interest in recent years. In order to systematically understand the fundamental principle of the radiofrequency behavior of niobium treated in different way, as well as different materials and thin films that fabricated with different methods under different conditions, a facility that can measure small samples’ rf properties in a range of 0~180mT magnetic field and 2~20k temperature is needed. Surface impedance characterization (SIC) system is designed and fabricated to meet this requirement.

In order to measure small samples’ rf properties, it’s necessary to make the sample part of the resonant circuit, normally we use a flat sample as an endplate[1-14], or a part of endplate[2] for a resonant cavity (replacing method), we can also use a small rod sample[2, 15] or sample film coated on a small rod[16], or just a sample on a dielectric holder[17-19] to perturb the field in a cavity (perturbation method), then we can measure the resonant frequency and Q-factor[2, 10-15, 18, 19] change and extract surface impedance from that, we can also measure the rf induced heat on the sample, which normally give us more accuracy than rf measurement, we can get that information by directly measuring the temperature map[1, 3, 5] of the sample, or use a better way, so called “heat substitution method”[4, 6, 7, 9, 16, 17], we will introduce this method later.


2. SIC system overview The basic concept of the SIC system is to put the sample that needs to be measured at the open-end of a TE011 cylindrical niobium cavity with a sapphire rod inside, which can lower the resonant frequency of this cavity significantly to 7.5GHz so that the results are comparable with current srf cavities, which will also give us a relatively low Nb BCS resistance so that we can achieve a reasonably high quality factor. This system can provide a small high-field area on a sample small enough to coordinate with analytical characterization systems, developmental surface treatment processes and thin film deposition equipments. With rf power induced into the cavity from the adjustable couplers, heat will generate on the surface of the sample. By measuring the rf induced heat, we can derive the surface resistance of this sample under certain magnetic field and temperature. The sample is thermally isolated from TE011 cavity and two choke joints are used at the bottom of TE011 cavity to prevent rf power leaking out of the cavity, cavity and thermal system are evacuated so that rf induced heat can be measured accurately. The SIC system can measure a round flat sample (which is easy to prepare) with small size (R=2.5cm, effective rf region R=1cm) on relatively low frequency. Using the TE011 mode, no RF currents cross the gap and no electric field lines terminate on cavity or sample surfaces, thus the multipacting effect can be avoided. Since the sample is thermally isolated from cavity, we have the capability of maintaining constant sample temperature while changing the field, so that surface impedance can be extracted from thermal behavior under constant field.


Fig 1. SIC system overview (Designed by J. Delayen, L. Phillips and H. Wang, modified by H. Wang and B. Xiao) A. Sapphire rod, B. Nb, C. Coupler, D. TE011 cavity, E. Choke joint, F. Nb sample on copper plate with one heater and two thermal sensors underneath

(heater and sensors are not shown) G. Stainless steel thermal insulator H. Copper ring with two heaters connected in parallel and two thermal sensors attached.

(Heaters and sensors are not shown) I. Coupler near the choke joint to monitor the rf leaking from gap and choke joint.


3. RF components RF couplers Two H-field loop couplers are used in SIC system, they are mechanically adjustable from outside while the cavity is in the dewar. By changing the couplers’ position, their external Q will be changed. In Fig 2 we show the 2k experimental results of couplers’ external Q versus their positions.

Couplers' external Q versus their positions

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+10

0 0.5 1 1.5 2 2.5 3 3.5 4

Coupler's position [mm]

Exte

rnal

Q

Push coupler 2 into the cavityPull coupler 2 out the cavityPush coupler 1 into the cavityPull coupler 1 out the cavity

Fig 2. Couplers’ external Q versus position. The couplers are symmetrically located near the sapphire rod, which leads to cross talk during room temperature measurements and even during 2k measurements because we can’t get loaded Q high enough (now at 107), theoretically cross talk will diminish[20] if we can push loaded Q higher. Sapphire Sapphire is a key component in the SIC system, it can not only reduce the frequency from 34.3GHz to 7.5GHz, which is a reasonably low frequency, but also confines rf power in the sample plate region instead of cavity wall region: from Mathcad simulation we calculate that we can get the power loss sample plate/total ratio can increase from 1.2% to 8.3% by adopting sapphire.


With a sapphire rod inserted into the TE011 cavity, the TE011 mode will propagate along the sapphire and leak from the top end of sapphire. Fig 3 is the simulation result (by Haipeng Wang using HFSS) of radiation loss external Q with different sapphire rod length; the blue curve shows the calculated result, which is limited by the calculation accuracy and shows a lower limitation of 104(A/m)2, red curve shows the linear fitting that can avoid calculating limitation. The previous design with 63.754mm sapphire rod will limit the loaded Q to 2.34*107, with the present design of 105.87mm (114mm in length with 8.13mm inside Nb cap), radiation loss external Q is 1.6*1022, quite negligible comparing with our desired loaded Q (108 to 1010).

Sapphire Rod Length Calculation to the Radiation Loss External Q in SIC Cavity

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

0 10 20 30 40 50 60 70

Sapphire Rod Length z (mm)C

ompl

exM

ag_H

^2 (A

/m)^

2

HFSS 3D simulation, complexMag_H^2

Qext=2.3403e7

63.754mm

linear fit:z (mm)=42.833+2.839*log(Qext)

Fig 3. Sapphire rod length calculation to the radiation loss external Q in SIC cavity However, using sapphire in the SIC system also gives us a problem. We highly suspect that the sapphire rods we used have relatively low loss tangent, which is the main reason that we can’t achieve high enough Q0 (108~109). Fig 4 shows Q0 versus sample temperature for different sapphire materials, here the external Q of both couplers are much higher than loaded Q, so basically the loaded Q we measured is also Q0. A sapphire rod “A” that was annealed in hydrogen and then brazed with Cu/Au gives us 5*105 Q0, a sapphire rod “B” that was annealed in hydrogen and then clamped on a Nb cap gives us 1*106 Q0, a sapphire rod “C” that was not annealed nor brazed or clamped shows 5*106 Q0, recent test shows a higher Q0 of 1*107, which is 20 times higher than “A”. In Fig 4 we noticed the odd effect of an apparent transition temperature between 5 and 6k, which was caused by the temperature difference between the Nb sample and copper plate during the fast cool down procedure.


0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

2 3 4 5 6 7 8 9 10 11 12Sample T [K]

Q_l

oade

d [E

5] (B

lue)

1/24/08 New Sapphire Rod, gap 0.2 mm cool down

8/8/07 Old Sapphire Rod, gap not recorded cool down

9/19/07 Old Sapphire Rod, gap not recorded cooldown9/24/07 Old Sapphire Rod, gap not recorded cooldown

Fig 4. Q0 versus sample temperature In Fig 5 we measured Q0 of SIC system with latest sapphire rod, and compare the results with simulation results with different loss tangent between 10-7 and 2*10-7. We can see most of the experimental results fall into the simulation results with 10-7 and 2*10-7 loss tangent, the exception in 3 to 4k region is caused by the pressure change during the 2k cool down procedure. Because the rf leaking from the choke joint may affect loaded Q, in order to eliminate such an effect from potentially confusing our measurement of the sapphire loss tangent. We use a Cornell shape cavity and put sapphire rod into it. By measuring the loaded Q and comparing with baseline measurement, we can get sapphire’s loss tangent. Based on the test did on Cornell shape cavity, loss tangent is AT MOST 4.762*10-6 for old sapphire, for new sapphire, we designed a test using INFN 6GHz cavity, which is smaller than Cornell shape cavity so that sapphire can play a more important role on cavity’s loaded Q.


T versus Q

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

1.6E+07

2 3 4 5 6 7 8 9

T [K]

Q

3/7 2008 warm up, sample T versus Measured QQ simulated from mathcad without gap, loss tangent=2*10^-7Q simulated from mathcad without gap, loss tangent=10^-7Q simulated from mathcad without gap, loss tangent=1.5*10^-73/19 2008 cooldown, cavity T versus Measured Q3/19 2008 warm up, cavity T versus Measured Q

Fig 5. Experimental and simulation (with different loss tangent) loaded Q. TE011 mode identification SIC system uses an “open gap” design to separate the sample plate from the Nb cavity, so that we can measure rf induced heat accurately, this also gives us benefit on TE011 mode identification. By tuning the gap between cavity and sample plate, the resonant frequency can be tuned. Based on MAFIA simulation (by Haipeng Wang) and MWS simulation (by Frank Marhauser), we get the value of tuning sensitivity is 30kHz/µm. Fig 6 shows the simulation and experimental (room temperature and 4k) results of tuning sensitivity of TE011 mode.


Tuning Sensitivity of TE011 mode

7.43

7.44

7.45

7.46

7.47

7.48

7.49

7.5

7.51

0 0.2 0.4 0.6 0.8 1 1.2

gap [mm]

frequ

ency

[GH

z]

Simulation result from MWS

Experimental result at 4k

Experimental result at Room T

Fig 6. Tuning sensitivity of TE011 mode: simulation, room temperature and 4k measurement. RF Choke joint In order to prevent rf power leaking from the gap between sample plate and cavity, two

choke joints are used. The choke joints are designed for 7.5GHz, with 4λ (1cm) in

depth. During the procedure that we measured tuning sensitivity of TE011 mode at room temperature and 4k, we also measured transmitted power from coupler C to coupler I (marked in Fig 1.), it changed a lot while we change the gap, however loaded Q didn’t change much, which means RF leaking from choke joint didn’t affect loaded Q significantly in this case.


4. Calorimeter components: overview, hardware, simulation and experiments. Overview Calorimeter system consists of a copper plate at the top, a stainless steel ring, a copper calorimeter ring, and another stainless steel ring at the bottom, all of them are brazed together and then brazed on a 6” conflat.

Fig 7. Calorimeter part of SIC system A. Nb Sample on copper plate, Ga is used to combine them. B. Stainless steel thermal insulator C. Copper ring D. Heater E. Cernox thermal sensor A 25 ohm heater and two thermometers are attached to the copper plate, two 50 ohm heaters that have been connected in parallel and two thermometers are attached to the copper ring, they are used to precisely control the temperature of the copper plate and copper ring. Two temperature controllers are used to control the temperature of the copper ring and copper plate separately. Normally we will set the temperature of the copper plate at the temperature that we want to measure surface resistance. Then we set the temperature of copper ring at a reasonably lower temperature than copper plate. When we increase the rf power from the coupler, the rf induced heat on the sample will also be increased, because the temperature on the copper plate and copper ring are both fixed, which can ensure that bath temperature fluctuation can be neglected. By measuring power change of the heater on the copper plate, we can get the rf induced heat that generate on the copper plate, we call this “heat substitution method”.


Hardware We use stainless steel 304A here as the thermal insulator, the properties (thermal conductivity, thermal diffusivity and density) of stainless steel 304A are obtained from http://www.bnl.gov/magnets/Staff/gupta/cryogenic-data-handbook/. Five thermometers have been used in the SIC system: two cernox 1050 (CX#1 1050 38126 on copper plate, CX#3 1050 38134 on copper ring) are connected to temperature controller 332, one cernox 1050(CX#5 1050 33688 on cavity) and two cernox 1010 (CX#2 1010 38591 on copper plate, CX#4 1010 36895 on copper ring) are connected to temperature monitor 218. These thermometers, temperature controller and temperature monitor are made by Lake Shore Cryotronics, Inc.. Simulation BCS resistance of Nb sample at less than 4.6k (Tc/2) is given by the formula below[21]:

)/2.992.1exp(2.910643.1),( 20

50 Tf

TfTRBCS ×−××××= −

H field distribution can be get from MathCAD and MWS simulations. Fig 8 is the MathCAD simulation result (by Haipeng Wang) of H field distribution.

Fig 8. H field on sample plate from J. Delayen and H. Wang’s simulation


RF induced heat on sample plate:

∫= dSHRP BCSrf2

21

If we treat the above curve as two linear parts divided by peak at r/R=0.4, H is 170mT = 170*795.77A/m in Vacuum, we can roughly get:

622

01.0

004.0

004.0

0

22 10*30**

21

006.0006.001.0

004.02*

21 −=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛= ∫∫ ππ HRrdrrrdrrHRP BCSBCSrf

(H is in A*m, Prf is in Watt)

27622 10310*30**)7.795774(*21 HRHRP BCSBCSrf ×== −π

Prf is in Watt and H is in Tesla. To simplify the calculation, we assume that BCS resistance is field independent.

We can compare this result with 27107.3 HRP BCSrf ×=

Prf is in Watt and H is in Tesla. Based on Frank’s open gap simulation in file mode20HFieldOnSample.xls, we also

get the same result ( ). 710624.3 ×

(Prf is in Wattt, not W/m^2) Fig 9. Power dissipated (W) versus T (K) on BCS Nb Sample at 170mT peak field


From the plot above we can get some useful information: at 170mT and 4.5k, power dissipation on the sample is 31.8W, at 2k it is 0.53W. Using the same method we can also get that at 10mT and 4.5k, power dissipation on the sample is 0.11W, at 2k it is 1.834mW. With the current stainless steel thermal insulators in the calorimeter, 2mW power dissipation on Nb sample at 1.8K bath temperature will cause the sample temperature increase to 3.3K, which means it can measure Nb sample at 10mT weak peak field at 1.8k~2k range in CW mode, and for 170mT. at 4.5K Nb sample temperature, we must work in pulse mode, and duty factor is in 10-4~10-5 (0.002W/31.8W) range. However with the stainless steel insulator, Nb sample will be hard to cool down from 4k to 2k, it will take at least 2 hours after bath temperature cool down to 2k, that’s one of the reasons we plan to use copper as the thermal insulator in the next generation SIC system.

Fig 10. Power dissipated on Nb sample (mW) versus equilibrium sample temperature (K) with (a) stainless steel insulator (b) copper insulator We can see from Fig 10 above that with a copper insulator, a 500mW power dissipation on the sample will cause the sample temperature to increase from 1.8K to a little less than 2K, which means we can work in CW mode at 170mT, high peak field. While the sample is at 4.5K, peak field remain at 170mT, we should use pulse mode and duty factor will be 0.5/31.8 at 10-2 range. Experiments Theoretically under current status with 107 loaded Q, we are able to generate rf induced heat on the sample and measure the temperature change on the sample plate, or use the designed “heat substitution method”. We can also directly add power to the heater and


measure the temperature increasing and then compare the experimental result with our simulation. Fig 11 is the experimental results of plate and ring temperature change while put 10.97mW power on plate heater with 2K bath temperature. We can compare it with ANSYS simulation results, which gives us 7.7426K plate temperature and 5.39919K ring temperature, a little higher than the experimental results, which is caused by the inaccuracy of power measurement, because we use two wires measurement, the real heater’s power is lower than 10.97mW, another two wires will be added to each heater in the next generation SIC system so we can accurately measure their power in the future.

Measured plate and ring temperature

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0:00:00 0:01:26 0:02:53 0:04:19 0:05:46 0:07:12 0:08:38 0:10:05 0:11:31 0:12:58 0:14:24

Time

Tem

pera

ture

[K]

Ansys results: Tplate Tring 7.74260 5.39919

Tplate

Tring

Fig 11. Plate and ring temperature change while put 10.97mW power on plate heater with 2K bath temperature.


5. Current status, near-term plans and future Current Status

Haipeng’s closed gap simulation gives us that =U

H pk 5300, while Hpk is in Oe and U

is in Joule, and based on Frank’s open gap simulation, with normalized stored energy (U = 1 Joule) and 0.2mm gap, Hpk = 2.67*105 A/m, while gap is 0.5mm, Hpk =

1.88*105 A/m, here 1 Oe = 79.58 A/m, we have =U

H pk 3355 at 0.2mm gap, while Hpk

is in Oe and U is in Joule. Currently we can achieve 107 loaded Q. We are working on the rf power and trying to get 10W power at 7.5GHz from that, in this case the highest magnetic field we can achieve with critical coupling is:

)(5.23110*5.7*2

10*10*4.50262

**4.5026*4.5026 9

7

Oef

QPUH diss

pk ====ππ

If we want to get 2000 Oe magnetic field with 107 Q, the rf power should be:

)(1.74610

10*5.7*2*4.5026

20002*4.5026 7

922

WQ

fHPP pk

dissin =⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛==

ππ

If we can get 108 Q, then we would need 74.6 Watts to reach 2000 Oe. Near-term plans With INFN 6GHz small cavity, we expect to obtain more accurate loss tangent of sapphire rod material than that of Cornell shape cavity, we can also try different surface and bulk treatment methods[16, 22] and we can measure how loss tangent changes with different methods. We adopted Nb flange on both sides of INFN cavity so the whole rf system is made by Nb, except two copper couplers. Work on the rf power source at 7.5GHz, try to find VCO with the right tuning sensitivity that required by SIC system and get 10W cw rf power from it. With 10W rf power and the present cavity Q0, we can generate up to 23mT peak field and 10mW rf induced heat at 2k on the sample surface. With 10mW heat, sample temperature should increase to about 7K with 2K bath temperature. We should notice here the sample temperature increase will cause Nb surface resistance increase, thus the rf induced heat will also increase, which will finally make sample temperature more than 7k.


Future Continue to push Q0 higher. The SIC maximum field should be determined by the primary cavity structure material and its temperature. For Nb, we want to push peak field on sample surface forward 180mT Systematically investigate the changing of gap (gap distance and tilting). With experience gained from the present structure, we plan to refine the design of the second-generation SIC and construct it with improved coupling characteristic and adopt large-grain high purity Nb to replace present reactive-grade Nb. Our aim is to make SIC system the standard method to evaluate rf property of superconducting radiofrequency materials. References: [1] P. Kneisel, G. Muller, and C. Reece, "INVESTIGATION OF THE SURFACE RESISTANCE

OF SUPERCONDUCTING NIOBIUM USING THERMOMETRY IN SUPERFLUID HEL IUM," IEEE TRANSACTIONS ON MAGNETICS, vol. MAG-23, NO: 2, p. 5, March 1987.

[2] J. R. Delayen, C. L. Bohn, and C. T. Roche, "Measurements of the Surface Resistance of High-Tc Superconductors at High RF Fields," Journal of Superconductivity, vol. 3, No. 3, p. 8, 1990.

[3] M. Juillard, B. Anne, B. Bonin, and L. Wartski, "SUPERCONDUCTING SURFACE RESISTANCE MEASUREMENTS WITH A TE011 CAVITY," EPAC 1990, 1990.

[4] C. Liang, "A New Surface Resistance Measurement Method with Ultrahigh Sensitivity," p. 167, 1993.

[5] M.Ribeaudeau, JP.Charrier, S.Chel, M.Juillard, M.Fouaidy, and M.Caruette, "RF SURFACE RESISTANCE MEASUREMENTS OF SUPERCONDUCTING SAMPLES WITH VACUUM INSULATED THERMOMETERS," EPAC 1998.

[6] M. Fouaidy, P. Bosland, M. Ribeaudeau, S. Chel, and M. Juillard, "NEW RESULTS ON RF PROPERTIES OF SUPERCONDUCTING NIOBIUM FILMS USING A THERMOMETRIC SYSTEM," EPAC 2002, 2002.

[7] E. Mahner, S. Calatroni, E. Chiaveri, E. Haebel, and J. M. Tessier, "A new instrument to measure the surface resistance of superconducting samples at 400 MHz," Review of Scientific Instruments, vol. 74, Number 7, p. 5, July 2003.

[8] C. Nantista, S. Tantawi, J. Weisend, R. Siemann, V. Dolgashev, and I. Campisi, "Test Bed for Superconducting Materials," PAC 2005, p. 3, 2005.

[9] G. K. D. L. Phillips, J. R. Delayen, J. P. Ozelis, T. Plawski, H. Wang, G. Wu, "A SAPPHIRE LOADED TE011 CAVITY FOR SURFACE IMPEDANCE MEASUREMENTS – DESIGN, CONSTRUCTION, AND COMMISSIONING STATUS," SRF2005, 2005.

[10] G. M. N. Klei, H. Piel, B. Roas, L. Schultz, U. Klein, M. Peiniger, "Millimeter wave surface resistance of epitaxially grown YBa2Cu3O7–x thin films," Applied Physics Letter, vol. 54, p. 3, February 20 1989.

[11] Y. G. P. B. A. Tonkin, "modular system for microwave surface impedance measurement of high temperature superconductors," Superconductor Science and Technology, vol. 6, p. 7, Februray 2 1993.


[12] M. Misra, N. D. Kataria, and G. P. Srivastava, "Sensitivity in the measurement of microwave surface resistance of high Tc superconducting samples of differnet sizes by the cavity method," Superconductor Science and Technology, vol. 12, p. 6, October 7 1998.

[13] M. Misra, N. D. Kataria, and G. P. Srivastava, "Laterally resolved microwave surface-resistance measurement of high-Tc superconductor Samples by Cavity Substitution Technique," IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, vol. 48, No. 5, p. 11, May 2000.

[14] N. D. KATARIA, M. MISRA, and R. PINTO, "Sensitivity of surface resistance measurement of HTS thin films by cavity resonator, dielectric resonator and microstrip line resonator," PRAMANA - journal of physics, vol. 58, p. 7, May & June 2002.

[15] J. R. Delayen and C. L. Bohn, "Temperature, Frequency, and RF Field Dependence of the Surface Resistance of Polycrystalline YBCO," Physical Review B, vol. 40, Number 7, p. 4, September 1 1989.

[16] L. H. Allen, "The Surface Resistance of Superconducting A15 Niobium-Tin Films at 8.6 GHz," p. 98, 1986.

[17] D. L. Rubin, K. Green, J. Gruschus, J. Kirchgessner, D. Moffat, H. Padamsee, J. Sears, Q. S. Shu, L. F. Schneemeyer, and J. V. Waszczak, "Observation of a narrow superconducting transition at 6GHz in crystals of YBCO," Physical Review B, vol. 38, Number 10, p. 5, October 1 1988.

[18] C. Zuccaro, M. Winter, N. Klein, and K. Urban, "Microwave absorption in single crystals of lanthanum aluminate," Journal of Applied Physics, vol. 82, p. 10, December 1 1997.

[19] D. C. M. R. J. Ormeno, D. M. Broun, S F. Lee, and J. R. Waldram, "Sapphire resonator for the measurement of surface impedance of high-temperature superconducting thin films," Review of Scientific Instruments, vol. 68, p. 6, January 22 1997.

[20] Y. Zhao and M. D. Cole, "The analysis of the cross-talk in a RF gun superconducting cavity," PAC 2003, 2003.

[21] P. Bauer, "Review of Models of RF Surface Resistance in High Gradient Niobium Cavities for Particle Accelerators Revision 1," 2004.

[22] A. N. Luiten, A. G. Mann, A. J. Giles, and D. G. Blair, "Ultra-Stable Sapphire Resonator-Oscillator," IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT,, vol. 42, NO. 2, p. 5, April 1993.

Documents

Surface Impedance Characterization System · sample[2, 15] or sample film coated on a sm all rod[16], or just a sample on a dielectric holder[17-19] to perturb the field in a cavity