Response of an oscillating superleak transducer to a pointlike heat source

A new technique of superconducting cavity diagnostics has been introduced by D. L. Hartill at Cornell University, Ithaca, New York. It uses oscillating superleak transducers (OST) which detect the heat transferred from a cavity’s quench point via Second Sound through the superfluid He bath, needed to cool the superconducting cavity. The localization of the quench point is done by triangulation. The observed response of an OST is a nontrivial, but reproducible pattern of oscillations. A small helium evaporation cryostat was built which allows the investigation of the response of an OST in greater detail. The distance between a pointlike electrical heater and the OST can be varied. The OST can be mounted either parallel or perpendicular to the plate that houses the heat source. If the artificial quench point releases an amount of energy compatible to a real quench spot on a cavity’s surface, the OST signal starts with a negative pulse, which is usually strong enough to allow automatic detection. Furthermore, the reflection of the Second Sound on the wall is observed. A reflection coefficient $R=0.39\pm 0.05$ of the glass wall is measured. This excludes a strong influence of multiple reflections in the complex OST response. Fourier analyses show three main frequencies, found in all OST spectra. They can be interpreted as modes of an oscillating circular membrane.

Figure 1

Helium phase diagram [10]. Cooling down helium under normal pressure the liquid phase occurs at 4.2 K. Reduction of the pressure to 49 hPa cools the liquid to the triple point where superfluidity occurs.

Figure 2

Relative density versus temperature below the $\lambda$ point in helium.

Figure 3

Second Sound velocity $v_{\mathrm{SeSo}}$ versus temperature [14].

Figure 4

TESLA cavity in the simulation with $2\times 6$ OSTs (red squares). A three signal event is shown.

Figure 5

Sketch of the He evaporation cryostat with mounted OST and heat source.

Figure 6

OST mounted horizontally on the support tube (left) and detail drawing (right) with $H=\mathrm{\text{housing}}$, $M=\mathrm{\text{porous}}$ membrane, and $P=\mathrm{\text{immobile}}$ brass plate.

Figure 7

Readout circuit for the OST.

Figure 8

12 OST signals recorded in high resolution mode with increasing distance (given on the right side of each signal). The He level was 19.5 cm above the resistor. The red crosses mark the earliest and latest expected point for the Second Sound to reach the OST; the kink in the red dotted line is due to the change in the step size. All 12 signals are shown with the same scale for the amplitude, from $-5\mathrm{mV}$ to $+5\mathrm{mV}$.

Figure 9

Signal amplitude at the OST depending on the traveling path $z_{\mathrm{OST}}$ of the Second Sound wave. Three different shapes of the heating pulse are compared.

Figure 10

Starting region of an OST signal. In green the noise band is given, calculated from the measured OST signal prior firing the resistor. The first red line ($t_{\mathrm{calc}}$) indicates the position, where the signal is expected theoretically; the second one ($t_{\mathrm{meas}}$) gives the position where at first the OST signal crosses the noise band.

Figure 11

Distances obtained from data analysis of a full series of OST spectra versus the distance obtained from the mechanical setup.

Figure 12

Drawing of the vertical mounting of the OST. In red are shown the shortest distances for the Second Sound to reach the OST with and without reflection. The heat source is plotted in scale.

Figure 13

Without reflection (red crosses) the path length $P_{\mathrm{SoSe}}$ follows the expected linear behavior (see also Fig. 10). Reflected Second Sound (black crosses) has a longer path length $P_{\mathrm{SoSe}}$, according to the distance to the wall. The difference in the path length’s $P_{\mathrm{SoSe}}$ shrinks with increasing $z_{\mathrm{OST}}$, as the direct and reflected path length gets more similar.

Figure 14

The 3D diagram shows how the Fourier amplitudes of the three typical frequency distributions decaying in time.

Figure 15

Graphic representation of the eigenmodes of an oscillating circular membrane with the smallest frequencies; figure adopted according to 7.

Figure 16

Exponential decay of the OST signal amplitude (absolute value), measured over a full second.