Detection and location of SRF bulk niobium cavities quench using second sound sensitive sensors in superfluid helium

We developed sensors and instrumentation dedicated to detection and location of thermal quenches in SRF cavities via 2nd sound events in HeII. We studied 2 types of Quench Detectors (QD): 1) Oscillating Super leak Transducer (OST), 2) LOw REsponse Time resIstive Thermometers (LORETIT). The QD were characterized in He II bath (Temperature T0 = 1.6 K- Tλ. The SRF cavity quench is experimentally simulated using resistors of different sizes and geometries. High pulsed heat flux qP (qP < 2MW/m2) were applied to these heaters and the dynamic response of QD were investigated as function of several parameters (T0, qP, distance to heater). The OST were used for locating quench on different SRF cavities resonating at 2 frequencies f0 (f0 =88 MHz or f0 =352 MHz). The quench dynamics and critical size of normal resistive area leading to quench were investigated. Furthermore, a Second Sound Resonator (SSR) equipped with a pair of OST at each extremity (2nd sound generator (G) and detector (D)), a low thermal capacity heater (G) and a LORETIT (D), was successfully operated in the resonating and in the pulsed mode. The measured 1st sound and 2nd sound spectra were compared theoretical results and a good agreement is obtained.


Introduction
Thanks to the tremendous R&D effort made by different laboratories and to the use of high purity niobium (e.g. Nb of Residual Resistance Ratio RRR>300), well assessed fabrication techniques and preparation procedures, high accelerating gradient E acc are achieved with SRF bulk Nb cavities. In the framework of the ILC R&D program at KEK (test facility STF-1 [1]), using 9 cells (Fig.1) SRF bulk Nb, =v/c=1 cavities (v: particle velocity, c: speed of the light), operated at a frequency f=1.3 GHz, the achieved E acc was in the range 33.8 MV/m -40.9 MV/m for 13 resonators tested [2]. However, the maximum achieved accelerating gradient in SRF Nb cavities, is often limited the quench. More precisely [2], 51 quench events were observed for 28 9-cells cavities tested at KEK: the observed quench fields are in the range 10 -35 MV/m. The quench is generally due to anomalous RF losses (i.e. Joule heating) of normal-resistive defects or inclusions embedded onto the RF surface [2]. The typical effective radius r D and normal surface resistance R ND of these defects are respectively in the range 1-100 µm and 1-10 m. Considering an ILC cavity (Fig.1), operated at E acc =33 MV/m corresponding to a maximum surface magnetic field H Smax =1.110 5 A/m 2 in the equator region, the local RF losses in defect area are q Defect =0.5.R ND H Smax 2 =31MW/m 2 . Furthermore, unloaded quality factor Q 0 = 2.10 10 was achieved at E acc =20MV/m with a low loss ILC cavities [3]: this value of Q 0 corresponds to a surface resistance R S = 14 n at T 0 =2K in the accelerating mode (frequency f=1.3 GHz). At E acc =33 MV/m, the resulting Joule RF losses in the superconducting surface region are q SRF =0.5 R S H Smax 2 =82 W/m 2 . The cavity could be modeled (Fig. 1b) as a circular Nb plate (radius R>> r D , thickness e =3-4 mm) with the following boundary conditions: 1) RF surface subjected [4] to a non-uniform prescribed heat flux, 2) Heat transfer at the cavity wall cooled by superfluid helium (He II), controlled by the Kapitza conductance at Nb-He II interface, 3) Adiabatic side wall. Using this thermal model, we have solved the steady-state heat equation. The analytical solution obtained [4] were used to compute the variations of the temperature T RF at the center of the defect (radius: R D =10 µm), located on the RF surface of the cavity, as function of E acc . The results (Fig. 2) show a strong increase of T RF with E acc , which is naturally due to the quadratic dependence of RF losses with E acc (e.g. qα R S H S 2 αR S E acc 2 ). Fig. 2 Computation of quench field for ILC cavity-Simulation runs performed for a normal defect (R D =10 µm, R def = 5 m) located at the equator of a ILC cavity (f=1.3GHz) operating at T 0 =2 K.
Furthermore, the cavity is thermally stable (i.e. in superconducting state) if T RF < T C (E acc ), where is T C (E acc ) is the Nb critical temperature. At the quench field Q acc E , the cavity transits to the normal resistive state: Q 0 decreases exponentially dropping by ~3-4 decades, with a time constant  cav 100 s [5]. This decrease of Q 0 is due to the large difference between the surface resistances of normal Nb (R s N~1 0m) and superconducting Nb (R s S ~20n). Considering a SRF cavity with a total RF surface area A C , at the quench field, the area of the normal zone A N [5], which is inversely proportional to R s N , is A N ~ 0.1 A C. Furthermore, the ratio of the quality factors in the superconducting state Q 0 S and in the normal state Q 0 N is given by: , which is close to the observed experimental data (Fig. 4). Further, when Q 0 decreases, the coupling factor =Q 0 /Q F , initially close to 1 decreases: the forward RF power P F is then completely reflected from the cavity, leading to the observed decrease of the RF fields (e.g. E acc (P F . Q F ) 1/2 ). Then the cavity cools down, resulting in a decrease of the hot spot temperature T RF below T C : the cavity is now superconducting and Q 0 increases by factor~10 5 . As the cavity is again matched (e.g. ~1), the RF field could be raised again and a self-sustained cycle is repeated. Obviously, the thermal quench of SRF cavity is easily detectable with RF probes (i.e. transmitted power P t versus time t). But, as P t vs.t curve is an overall measurement, it is insufficient neither to characterize completely the quench, nor to locate the quench source. Local diagnostic tools are then needed for locating and characterizing quench source.

Brief history of thermal diagnostic tools of anomalous rf losses in srf cavities
The first generation of sensors used for quench detection was developed in ~1980. These sensors are surface thermometers sensing the outer surface temperature [5][6][7][8][9] of the cavity cooled by Liquid Helium (LHe). These thermometers operate in sub-cooled, boiling normal LHe or He I and in superfluid helium (HeII, bath temperature T 0 <T  ). Two types of thermometers were used: a) Scanning Surface Thermometers (SST), b) Fixed Surface Thermometers (FST). Due to the cooling medium and the measurement configuration, SST are intrinsically limited [5][6][7][8] when operated in He II: 1) low measurement efficiency (~1-2%), 2) lack of reliability and repeatability. FST are also practically limited because a large number (i.e. >>100) of such sensors is needed [5][6][7][8], in order to ensure a good spatial resolution. Second generation of quench detectors in He II, namely OST (Oscillating Superleak Transducer), were initially developed in 1970 for studies on He II hydrodynamics [10]. The OST are capacitive Quench Detectors (QD), sensing second sound (e.g. temperature wave) events in (He II): they were applied to SRF cavity thermal breakdown studies 7 years ago [11]. Note that LOw REsponse Time (<< 1ms) resIstive Thermometers (LORETIT) could also be used as quench detectors.

Description of OST developed at IPN Orsay
We developed [12]   Compared to the 1 st generation of OST, the 2 nd generation have the following main features: 1) smaller footprint (O.D:13 mm) and better mechanical precision, leading to a higher spatial resolution, 2) nearly unchanged sensitivity, 3) a better reliability and reproducibility of OST mechanical and electrical capacitance.

Test Cells and configuration of Sensors
We have developed a test facility allowing the calibration and full characterization of various quench detectors in LHe bath: the temperature T 0 range is 1.55 K-4.25K. The quench of SRF cavities is experimentally simulated by means of Joule heated resistors. In order to investigate the effect of the heater geometry, and the distance of the sensors to the quench-like source, we performed experimental runs with 6 different configurations (6 test cells) using either cylindrical or flat SMD resistors of different sizes. However, due to space limitation only data obtained with the test-cells #1 and #2 will be reported here. The description of these 2 test-cells is summarized in Table 1 and a photograph of all the 6 test cells used is shown in Fig. 6. Moreover, we used as LOw REsponse Time resIstive Thermometers (LORETIT), two industrial bare ship resistors (Cernox 1050 BC) named CX here after.

Experimental results and discussion
Several experimental runs were performed at different T 0 . The CX resistors were in-situ calibrated (e.g. Resistance vs. Temperature) prior to the measurements of their response to a pulsed heat flux in He II. For the calibration, we used the saturated LHe bath as thermostat: the temperature is regulated to better than 0.2 mK for T 0 < T  =2.1768 K, via precise control of vapour pressure (butterfly valve).

Improvement of the signal conditioner for OST sensors
For OST readout electronics , during the first tests [11] we used, as signal conditioner (SC#1), a basic current amplifier (Fig. 7) similar to that used by other groups. But, the output signal of SC#1 we obtained in characterization experiments or quench detection on cavities were too noisy, which is a limitation for the measurements. In order to increase both the gain of the SC and the output signal to noise ratio (SNR), we developed a new high performance SC (SC#2) for the OST. The two signals recorded by the same OST with the SC#1 and SC#2 are compared in Fig. 7: 1) the signal level is improved by a factor V SC#1 /V SC#2~5 55, 2) The SNR was also improved. Note that in the case of SC#1, due to the low SNR, we have to perform the integration of 200 samples in order to obtain a useful signal.

Response of cernox thermometers at T 0 = 1.9 K
Using the cell #2 (SMD heater #1, heater area: 2.5 mm 2 ), we succeeded to measure at T 0 = 1.9 K, the response of CX#1 and CX# 2 to a pulsed heat flux applied to the heater (Peak value: q P 15.2 MW/m 2 , pulse duration:  P =100 µs). The corresponding results are shown in Fig. 7. It should be stressed that it was really challenging to perform such measurement of fast and weak transient thermometric signals in He II with a small heater (e.g area=2.5 mm 2 ) in a large bath (I.D: 350 mm, Height: 100 mm-750 mm). Note that, for the above data, we achieved a resolution better than 2µV at a sampling rate of 100 kHz with a baseline signals ~100 mV. Moreover, for a sensing current of 20 µA, the measured peak values are ~100 µV-300 µV leading to a peak transient heating~100 µK: our results are in good agreement with the few data, in our knowledge, previously reported [13]. Furthermore, the observed time lag between the first observed signal peaks of the sensors CX#1 and CX#2 is t=770 µs, resulting in a second sound velocity u 2 =20 m/s, measured by a pulse method at T=1.9 K: this value is close (e.g. 6.1%) to the data (e.g. u 2 =18.77 m/s) reported previously by Donnelly team [14] using a 2 nd sound resonator.

Response of OST sensors to pulsed heat flux
Using the heater #1 (heater area: 2.5 mm 2 ) of cell#1, we thoroughly investigated at 1.9K, the response of OST#8 and OST #7 to various pulsed heat flux: we varied the peak value q P , while the pulse duration was kept constant  P =100 µs. The results are illustrated in Fig. 8. These data clearly show a linear behavior with respect to q P : the peak amplitude of OST signal V OST is proportional to q P (Fig.8-Fig. 9). These behavior were observed for both OST sensors, located respectively at r=35.7 mm and r=60.8 mm as illustrated in Fig. 9. For the SMD resistors (e.g. heaters configuration corresponding to a spherical symmetry), one expects a quadratic decrease of the heat flux with the distance r to the heater (e.g. q r -2 ) as it is clearly observed in Fig. 9.

Quench detection on SRF cavities
In this paper, we will present on test performed on Quarter-Wave Resonator (QWR, frequency: 5 ICECICMC IOP Publishing IOP Conf. Series: Materials Science and Engineering 171 (2017) 012110 doi:10.1088/1757-899X/171/1/012110 88MHz) prototype (Fig. 10) developed at IPNO for SPIRAL2 (SP2) project. The RF parameters of the SP2 cavity are: a) particle velocity =v/c=0.12, b) E acc =6.5 MV/m, c) peak surface magnetic field B pk = 65 mT, d) quality factor Q 0 =1.510 9 at 2 K, corresponding to a heat load of 10W. The cavity is equipped with its LHe tank. Four OST fabricated at IPNO were used for quench location (Fig. 10). At T 0 =1.8 K, the cavity Tokyo quenched at E acc Q = 8.8 MV/m: Q 0 =1.3 10 10 at the quench field. Second sound signals induced by the quench were recorded by the OST assembly (Fig. 11). Fig. 11 Measured 2 nd sound events during the quench of the SP2 prototype cavity Tokyo The x-axis, which is usually time, was converted in distance using 2 nd velocity Ué=19.87 m/s at 1.8 K The analysis of OST signals lead to the following conclusion : 1) as expected, the quench source is located on the critical welding [2] between the cavity dome and the tube, where the surface magnetic field is high, 2) as expected the adiabatic walls reflect the 2 nd sound wave, 3) as 2 nd sound wave is attenuated, no sizable signal is recorded by the OST#3 located at 70 cm from the quench source.

Description of the second sound resonator
In order to perform precise measurements of the 2 nd sound velocity u 2 in He II, we developed a Second Sound Resonator (SSR). This SSR (Fig. 12) is equipped with a pair of OST at its 2 extremities as thermal source (OST#1) and sensor (OST#2), and a low thermal capacity heater with 2 thermometers CX#1and CX#2. This SSR could be operated in the standard standing wave mode or in pulsed mode (i.e. thermal shock waves). Further 2 nd sound could either thermally generated (e.g. Joule heating) or via the normal fluid flow induced by the motion the OST#1 membrane (e.g. mechanic-heat effect). Conversely, 2 nd sound could be detected either with the thermometer or with OST#2.

Theory
The second-sound velocity u 2 will be determined experimentally as a function of temperature by measuring the frequency of one of resonant modes of the SSR. The resonance frequencies f mnp of the different modes of the cylindrical SSR are given by: Where u is the sound velocity, the integer p is the mode number (p th harmonic) and R the radius of the resonator. The parameter a mn is the n th root the equation: Where J m is the Bessel function of the first kind and of order m.

Results and discussion
The SSR was first tested as first sound resonator in gaseous helium (pressure: 1013 mbar, T~300 K) then in LHe at 4.2 K. The measured and computed spectra using equation 1 are in very good agreement: more than 11 resonating mode were compared and the relative difference between measured and calculation results was less than 4.5 % (Fig. 13). Fig. 14 Effect of temperature on the measured second sound spectrum in superfluid helium at T=1.7K The measured 2 nd sound spectra at T=1.7 K, 1.9 K and 2.1 K are presented in Fig. 14. The data clearly show an increase of resonant frequencies f for all the modes when T is decreased. This is simply due to the temperature dependence [12,14] of the 2 nd sound velocity u 2 : as f is proportional to u 2 , f increases when T is lowered because u 2 increases when T decreases.