DEVELOPMENT OF A NEW 10 GHZ ULTRA-LOW PHASE NOISE OSCILLATOR FOR THE BRAZILIAN GRAVITATIONAL WAVE DETECTOR MARIO SCHENBERG S R Furtado1, O D Aguiar1, M E Tobar2, E N Ivanov2, J. Hartnett2, P J Castro1 1 National Institute for Space Research, São José dos Campos, SP, Brazil. 2 Department of Physics, University of Western Australia, Nedlands, WA, Australia. ABSTRACT

Ministério da Ciência e Tecnologia Instituto Nacional de Pesquisas Espaciais Divisão de Astrofísica

This work describes the development of a new 10GHz ultra-low phase noise oscillator to be operated in the gravitational wave detector Mario Schenberg. This oscillator will be employed to pump a set of high sensitivity klystron cavity-based parametric transducers (Q0 ≈ 2.65x105 and df/dx ≈ 6.0x1013Hz/m) used to monitor the mechanical vibrations of 65cm-diameter CuAl(6%) spherical antenna at 5K. The single sideband phase noise of a free running loop oscillator incorporating the liquid nitrogen-cooled sapphire crystal loaded cavity was measured as -135dBc/Hz at an offset frequency of 3.2kHz, and it was limited both by the sapphire crystal loaded cavity Q-factor (1.3x107) and by the amplifier flicker phase noise (≈-141dBc/[email protected]). The results indicate that the sensitivity of the new transducers will be of about h ≈ 8.0x10-21Hz-1/2 at 5K in a 3.2kHz±40Hz frequency range. The sensitivity of these transducers may be improved replacing the amplifier used in the circuit oscillator by another one with smaller flicker phase noise. In this case, sensitivities around h ≈ 1.0x10-21Hz-1/2 at 5K and h ≈ 9.0x10-22Hz-1/2 at 50mK will be expected in the same frequency range. The experimental tests were performed in the laboratories of the “University of Western Australia”. Details of this work and some recent results are presented here.

Fundação de Amparo à Pesquisa do Estado de São Paulo

INTRODUCTION

OSCILLATOR PHASE NOISE MEASUREMENTS

The gravitational wave detector Mario Schenberg has been constructed in the Physics Institute of the University of São Paulo as programmed by the Brazilian Graviton project, under the full support of FAPESP (the São Paulo State Foundation for Research Support). It is under tests and the initial design sensitivity of h ≈ 2×10−21Hz−1/2 at 4.2K has not been reached so far. This value isrequired to enable the detector to search for core collapses in supernova events, neutron stars going to hydrodynamical instabilities, coalescence of neutron stars and/or black hole systems of 3 solar-masses, among other ‘classical’ astrophysical sources [2,3,4,5,6]. A set of parametric transducers will be used in the Brazilian detector to convert mechanical vibrations of 65cm diameter CuAl(6%) and 1.15ton spherical antenna into electrical signals at the frequency range of 3200 ± 200 Hz, amplifying the signal energy due to the intrinsic parametric gain [7] (see Figure 1). In order to be part of the transducer system, reentrant cavities attached to the resonant mass antenna must be pumped by an ultra-low phase noise microwave oscillator. The main noise sources (the back-action noises, the phase and the electronic series noises due to the effective noise temperature of the readout system, and the Brownian noise) for Schenberg detector may be written as follows [8]:

Oscillator phase noise measurements were accomplished using a high power gain amplifier (Endwave Defense Systems Model JCA812-5021) with phase noise of about -141dBc/[email protected]. The sapphire loaded cavity (maintained at 77K) was used as the frequency discriminator element of the resonant circuit [14].

(1)

(2)

(3)

Figure 4 - The electronic phase noise of the developed oscillator. In red: the experimental measurement of the amplifier phase noise. In blue: the oscillator phase noise according to the Leeson’s Model. In green: the electronic phase noise using the frequency discriminator measurement technique.

(4) Although an oscillator with phase noise of about -100dBc/[email protected] had been used to pump the parametric transducers of Schenberg detector [9], it becomes necessary to minimize this noise source to reach the planned sensibility. To solve this problem it was built and tested a new 10GHz ultra-low phase noise oscillator using a sapphire crystal loaded cavity with high Q-factor (1.5x107) and cooled at the liquid nitrogen temperature (77K) [10].

ELECTROMAGNETIC COUPLING AND Q-FACTOR The sapphire crystal used in the low phase noise microwave oscillator was supplied by Insaco Inc. It was projected to oscillate at 10.24GHz resonance frequency in the high order mode WGM10,1,δ, in order to obtain a high confinement of the electromagnetic field inside the crystal [11] (as shown in Figure 2).

Figure 1 - Schematic view of the gravitational wave detector Mario Schenberg. The spherical resonant mass will be kept in vacuum and isolated from mechanical noises. Nine parametric transducers will monitor their fundamental modes of vibration. When coupled to the antenna, the transducer–sphere system will work as a mass–spring system with three modes, where the first one will be constituted of the antenna effective mass (287.5kg), the second one will be constituted of the mechanical structure of the transducer (53g), and the third one will be constituted of a membrane (10mg) that will close the transducer microwave cavity and modulate it around 3.2kHz.

Magnetic Probe

f0 (GHz)

∆f (kHz)

QL

β1

β2

Q0

9.446301145

1.452

6.5x106

0.24

0.70

1.3x107

9.446309631

1.297

7.3x106

0.96

6.8x10-3

1.5x107

The single sideband phase noise of a free running loop oscillator incorporating the liquid nitrogen-cooled sapphire crystal loaded cavity was measured as -135dBc/Hz at an offset frequency of 3.2kHz, and it was limited both by the sapphire crystal loaded cavity Q-factor (1.3x107) and by the amplifier flicker phase noise (≈-141dBc/[email protected]). The oscillator phase noise measurements were accomplished using the frequency discriminator technique, and the results were coherent with the Leeson’s Model. Figure 5 shows the strain noise power spectral density of Schenberg detector considering the new oscillator phase noise and the experimental results (see Table 2) obtained for niobium superconducting reentrant cavities (maintained at 4K) to be used in parametric transducers of Schenberg detector [10]. Schenberg detector sensitivity will be of about 5x10-21Hz-1/2 in 3200±40Hz frequency range (red curve), being limited by the series noise which is directly proportional to the noise temperature Tamp(f) of the first microwave amplifier in the readout chain and inversely proportional to the df/dx factor of the transducer reentrant cavities, as showed in Eq. 1-3. Table 2 - Input parameters used at the simulation of Schenberg detector performance [10]. Antenna Thermodynamic Temperature

Strain Noise Power Spectral Density (Hz-1/2)

The sapphire crystal was loaded inside a copper cavity designed not to possess spurious modes [12], and every measurements has been taken at 77K in order to achieve very high Q-factors. The electric coupling measurements were accomplished by a reflection technique using a method developed by Munro et al. (2004) [13]. The resonant frequencies were detected by the transmission technique, using a vetorial network analyzer (VNA) and an arrangement for the field probes inside the cavity (see Figure 3), and the loaded Q-factors were evaluated based on bandwidth measurements at the half-power resonance frequency of the cavities. The electromagnetic sign provided by the VNA in a pre-defined range was injected into the sapphire loaded cavity by a magnetic probe, being detected by an electric probe coupled to WGM's of the resonator. In order to make possible the insertion of the sapphire loaded cavity inside a liquid nitrogen tank, a cryostat composed by a vacuum chamber (where the resonator was kept inside) joined to a long stainless steel tube connected to a vacuum pump was constructed.

Electric Probe

CONCLUSION

Figure 3 - The sapphire crystal loaded inside the metallic cavity with two field probes.

Figure 2 - The electromagnetic energy distribution of the WGM8,1,δ in a sapphire resonator with 10.0836 GHz resonance frequency. The red region presents high concentration of electromagnetic energy showing that most of the energy is stored inside the sapphire crystal (images obtained from the CST Microwave Studio software).

Figure 4 shows the electronic phase noise of the developed oscillator, where the experimental measurement of the amplifier phase noise is represented by the red curve and the oscillator phase noise of about -140dBc/[email protected] is shown in blue color, according to the Leeson’s Model and the results presented in Table 1. The green curve represents the result obtained from the frequency discriminator technique, indicating that the phase noise of the developed oscillator is of about -135dBc/[email protected]. Table 1 - Experimental results of the sapphire resonator WGM10,1,δ (at 77K)

Oscillator Frequency

5K 10 GHz

Reentrant Cavity Electric coupling Frequency variation df/dx of Reentrant Cavity Parametric Transducer Input power Amplifier Noise Temperature Reentrant Cavity Electric Q-factor

1 Hz/m -70dBm ou 10-10 Watts 10K 2.65x105

Oscillator Phase noise

-135dBc/[email protected] kHz

Oscillator Amplitude noise

-150dBc/[email protected] kHz

The parametric transducer sensitivity of Schenberg detector may be improved replacing the amplifier used in the circuit oscillator by another one with smaller flicker phase noise. In this case, sensitivities will be expected around h ≈ 1.0x10-21Hz-1/2 at 5K and h ≈ 9.0x10-22Hz-1/2 at 50mK in the frequency range of 3200±40Hz, as shown in Figure 5 with blue and green dot lines, respectively. Frequency (Hz)

Figure 5 – The strain noise power spectral density of Schenberg detector using the 10 GHz ultra-low phase noise oscillator developed.

ACKNOWLEDGMENTS This work has been supported by FAPESP (under grants No. 1998/13468-9 and 2006/56041-3), CAPES, INPE and UWA.

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