Microwave Properties of Rock Salt and Lime Stone for Detection of Ultra-High Energy Neutrinos

1. Microwave Properties ofRock Salt and Lime Stonefor Detection ofUltra-High Energy Neutrinos ToshioKamijo and Masami Chiba Tokyo Metropolitan University, Tokyo Japan 22 August, 2002 Hilton Waikoloa Village Hotel, Waikoloa, Hawaii USA AS26, SPIE Astronomical Telescopes and Instrumentation, Hawaii

2. Excess electrons in the shower from the UHE neutrino interaction generate coherent Cherenkov radiation with an emission angle of 66. Underground Salt Neutrino Detector. L Array of the antennas Underground rock salt dome L >> 1-3 km Hockley salt mine, USA If the attenuation lengthLαof the rock salt would be large, we would be able to decrease the numbers of antennas for detectors.

3. Properties of materials required for UHE Neutrino Detector • Rock salt has higher density, larger refractive index and smaller radiation length than air and ice. In practice, attenuation length of materials must be long, because we want to decrease the number of antennas. Measurement of attenuation lengthLα in the material (a) Measurement of attenuation lengthLαin situ( P. Gorham et al. )best way (b) Measurement of complex permittivityε at laboratory ( our work )

4. Definition of theattenuation lengthLα Complex permittivityε: Complex refractive indexn: Complex propagation constant γ: Lα :The length where the input microwave energy E0 decrease to 1/e times ( for low loss material ) E０ E=E０・e－αδ Ｚ Ｚ = 0 （Skin depth） Ｚ＝δ= 1/α Example for NaCl single crystal at 9.4GHz ε' = 5.9 , tanδ = (1 ~ 5) × 10-4 Lα= 8.4m ~ 42m If the tanδ is constant, Lα= 180m ~ 790m at 500MHz

5. The methods of measuring complex permittivity at microwave region Cavity perturbation method was adopted.

6. Measurements of complex permittivity of rock salts and lime stones at x-band • Free Space method Without the influence of extraneous waves using movable reference metal plate • Cavity perturbation method Without the influence of insertion holes of the cavity resonator

7. Measurements of complex permittivity of rock salts and lime stones at x-band • Free Space method Without the influence of extraneous waves using movable reference metal plate Metal-backed sample Reflection Coefficient

8. Free space method Extraneous direct wave Extraneous direct wave Extraneous scattered wave Metal-backed sample Transmittion and Reflection Coefficient Reflection Coefficient • Complex permittivity are derived from reflection or transmittion coefficients of a sheet sample. • Measurements are troubled with extraneous direct wave and scattered wave from various surrounding objects as indicated by red arrows.

9. The principle of the measurement of the free space method. Metal-backed sample Reflected wave Movable Input wave Reference metal plate Movable sample Extraneous waves are cancelled vectorically by moving reference metal plate on the specimen, so that only the phases of the reflected wave change.

10. Radio Wave Scattering Coefficient Measuring System Directed wave Up and Down

11. Sound Wave Scattering Coefficient Measuring System

12. An example of vector diagram of received wave signals.

13. Rock Salt plate samples for free space method Hallstadt mineAustria Asse mine Germany 200mm × 200mm × 30mm 200mm × 200mm × 10mm 200mm × 200mm × 100mm

14. Sample thickness  calculated from Rp  calculated from Rs (a) Hallstadt 11.1mm 5.9 ± 0.2 6.0 ± 0.2 (b) Hallstadt 30.1mm 5.9 ± 0.2 6.0 ± 0.2 (c) Asse Mine 99.0mm 5.9 ± 0.2 5.9 ± 0.2 Real part of the complex permittivities  in rock saltsby the free space method at 9.4GHz. Metal-backed sample

15. Measurements of complex permittivity of rock salts and lime stones at x-band • Cavity perturbation method Without the influence of insertion holes of the cavity resonator

16. Principle of the Cavity Perturbation Method Measurement of ε using a capacitor at low frequencies metal plate (electrode) S sample metal plate With sample Without sample The changes of complex admittances ( capacitance C and Q of the capacitor ) are measured with and without sample by a impedance meter or a Q-meter with LC-Resonator Circuit.

17. Insertion Holes in the Cavity Perturbation Method at X-band Rectangular TE10nCavity Resonator or Circular TM010 Cavity Resonator are used. The sample is inserted through insertion holes, located in the place where only the electric fields exist. This place is looks like acapacitor at low frequency. TE103 Cavity (ASTM, USA) Why do the sample insertion holes exist in the place of electrodes ? Measurement errors are increased by sample insertion holes. We made TE10n cavity resonator without sample insertion holes at 9.4GHz. TM010 Cavity (JIS, Japan)

18. Cavity Perturbation Method at X-band The changes of the resonance frequency and the Q of the cavity are measured with and without a sample by a Scalar- or Vector- Network Analyzer. Perturbation Formula For Rectangular TE10n mode Cavity • Small rod or stick samples are needed so that the the linearity of the perturbation formula holds.

19. Exploded view of the cavity X-band perturbed cavity resonator without insertion holes

20. Samples measured with the perturbative cavity resonator • Natural rock salt samples are very fragile, so that it is difficult to make small stick samples ( 1mm x 1mm x 10.2mm ). • Lime stone samples (especially Jura lime stone ) are rigid. The small stick samples are obtained by grinded using a milling machine.

21. Linearity of the perturbation measurements.

22. Linearity of the perturbation measurements.

23. Linearity of the perturbation measurements.

24. Linearity of the perturbation measurements.

25. Real part of the permittivity vs. filling factor for the rock salt and lime stone samples.

26. Imaginary part of the permittivity vs. filling factor for the rock salt and lime stone samples.

27. Sample  ε″10-3 tanδ 10-4 α at 9.4GHz (m-1) La=1/αat 9.4GHz (m) Single crystal (NaCl) 5.8 ± 0.2 3.2 ± 0.3 5.5 ± 0.5 0.13 ± .01 7.7±0.7 Rock Salt Asse, Germany 5.8 ± 0.2 <7.8 <13 <0.31 >3.3 Rock Salt Hallstadt, Austria 5.8 ± 0.2 <44 <76 <1.8 >0.56 Lime stone Kamaishi, Japan 9.0 ± 0.2 20 22 0.54 1.9 Lime stone Mt. Jura, France 8.7 ± 0.2 60 69 1.7 0.59 Comparison among single crystal NaCl, Asse rock salt, Hallstadt rock salt, Kamaishi lime stone and Jura lime stone in , ε″ , tand =ε″/ ,α at 9.4GHz, 1/αat 9.4GHz.

28. Summarized data NaCl, Dielectric Materials and Applications (A. R. von Hippel ed.), 1954 in situmeasurements by P. Gorham et al. tanδ=1×10-4 Purest natural salt Typical good salt dome (GPR) Best salt bed halite (GPR) NaCl single crystal Rock salt Hockley mine, USA NaCl, Hippel 25GHz Rock salt, Asse mine, Germany Lime stone, Kamaishi, Japan Rock salt, Halstadt mine, Austria Lime stone, Mt. Jura, France ε'=5.9

29. Conclusions • The attenuation length of various rock salts and lime stones are measured by the cavity perturbation method at 9.4GHz and frequency dependence in 7-12GHz. • The attenuation length of rock salts in Hockley mine, USA and Asse mine, Germany are long, they are over 100 m at 500MHz if the tanδ is constant with respect to the frequency, so that they would become a candidate for UHE Neutrino Detector site. • The attenuation length of these rock salts below X-band frequency are required in order to seek the optimum frequency of the Neutrino detector. We have a plan to make cavity resonators without insertion holes operated below X-band.