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

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

Properties of materials required for UHE Neutrino Detector Measurement of attenuation length L α in the material (a) Measurement of attenuation length L α in situ ( P. Gorham et al. ) best way (b) Measurement of complex permittivity ε at laboratory ( our work ) Material Properties Air （ STP) Ice （ H 2 O ) Rock salt (NaCl) Lime stone (CaCO 3 ) High Density ρ (g/cm 3 ) Small radiation length X 0 (cm) Large refractive index n Long attenuation length L α (tanδ) ○○○ △ Large volume V ○○○ △ (?) 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.

Ｚ＝ δ= 1/α E０E０ E=E ０ ・ e － αδ Ｚ =0Ｚ =0 Definition of the attenuation length Lα Ｚ Example for NaCl single crystal at 9.4GHz ε' = 5.9, tanδ = (1 ~ 5) × L α = 8.4m ~ 42m If the tanδ is constant, L α = 180m ~ 790m at 500MHz Complex permittivity ε: Complex refractive index n: Complex propagation constant γ: ( for low loss material ) （ Skin depth ） L α :The length where the input microwave energy E 0 decrease to 1/e times

The methods of measuring complex permittivity at microwave region Methodε'ε'tanδmaterialspecimen Cavity Perturbation Method 1 ~ ~ ~ -5 Low ε' material Low loss material Separable εand μ small sample (rod or stick ) S-parameter method 2 ~ ~ High loss material Wide frequency band toroidal or plate sample Dielectric Resonator method 10 ~ ~ Large ε' material Low loss material disc sample Free space method - Measurement in situ ( non-destructive ) large sample long sample for low loss material Pure Rock Salt: ε' = 5.9, tanδ = (1-5) x Cavity perturbation method was adopted.

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

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 Reflection Coefficient Metal-backed sample

Free space method Methodε'ε'tanδmaterialspecimen Free space method - Measurements in situ ( non-destructive ) large sample long sample for low loss material Transmittion and Reflection Coefficient Reflection Coefficient Metal-backed sample Extraneous direct wave 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. Extraneous scattered wave Extraneous direct wave

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

Radio Wave Scattering Coefficient Measuring System Directed wave Up and Down

Sound Wave Scattering Coefficient Measuring System

An example of vector diagram of received wave signals.

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

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

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

Principle of the Cavity Perturbation Method Measurement of ε using a capacitor at low frequencies 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. Without sample sample metal plate (electrode) S With sample metal plate

Why do the sample insertion holes exist in the place of electrodes ? The sample is inserted through insertion holes, located in the place where only the electric fields exist. This place is looks like a capacitor at low frequency. TE 103 Cavity (ASTM, USA) TM 010 Cavity (JIS, Japan) Insertion Holes in the Cavity Perturbation Method at X-band Rectangular TE 10n Cavity Resonator or Circular TM 010 Cavity Resonator are used. Measurement errors are increased by sample insertion holes. We made TE 10n cavity resonator without sample insertion holes at 9.4GHz.

Cavity Perturbation Method at X-band Small rod or stick samples are needed so that the the linearity of the perturbation formula holds. 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 TE 10n mode Cavity

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

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.

Linearity of the perturbation measurements.

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

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

Comparison among single crystal NaCl, Asse rock salt, Hallstadt rock salt, Kamaishi lime stone and Jura lime stone in , ε″, tan   ε″/ ,  α at 9.4GHz, 1/α  at 9.4GHz. Sample  ε″  tanδ  α at 9.4GHz (m -1 ) L  =1/α at 9.4GHz (m) Single crystal (NaCl) 5.8 ± ± ± ± ±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 ± Lime stone Mt. Jura, France 8.7 ±

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

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.