Microwave Properties ofRock Salt and Lime Stone

for Detection ofUltra-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 Lα 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 antennasUnderground

rock salt dome

L >> 1-3 km

L

Properties of materials required for UHE Neutrino Detector

Measurement of attenuation length Lα in the material

(a) Measurement of attenuation length Lα in situ ( P. Gorham et al. ) 　 best way

(b) Measurement of complex permittivity ε at laboratory ( our work )

)tan1( jj

Material

Properties

Air

（ STP)

Ice

（ H2

O)

Rock salt

(NaCl)

Lime stone

(CaCO3)

High Density ρ (g/cm3) 0.0012 0.924 2.22 2.7

Small radiation length X0 (cm) 30420 39 10.1 9.0

Large refractive index n 1.000293 1.78 2.43 2.9

Long attenuation length Lα 　

(tanδ)○ ○ ○ △

Large volume V ○ ○ ○ △(?)

tan

1

L

• 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.

tan

2

tan c

)tan1( jj

tan.tan1' jn

)(0

)(0

ztjzzjtj eeEeEE

zeEE 0Ｚ＝ δ= 1/α

E ０ E=E ０・ e － αδ

Ｚ = 0

tan

1

L

Definition of the attenuation length Lα

Ｚ

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

Complex permittivity ε:

Complex refractive index n:

Complex propagation constant γ: tan100 jjj

( for low loss material )

（ Skin depth ）

Lα :The length where the input microwave energy E0 decrease to 1/e times

The methods of measuring complex permittivity at microwave region

Method ε' tanδ material specimen

Cavity

Perturbation

Method1 ~ 20

10-2 ~

10-4 ~ -5

Low ε' material

Low loss material

Separable εand μ

small sample

(rod or stick )

S-parameter

method2 ~ 30

10-1 ~

10-2

High loss materialWide frequency band

toroidal or

plate sample

Dielectric

Resonator

method

10 ~ 100

10-3 ~

10-5

Large ε' material

Low loss materialdisc 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 10-4 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 methodWithout the influence of insertion holes of the cavity resonator

Measurements of complex permittivity of rock salts and lime stones at x-band

• Free Space methodWithout the influence of extraneous waves using movable reference metal plate

Reflection Coefficient

Metal-backed sample

Free space methodMethod ε' tanδ material specimen

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 waveMetal-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 mineAustria

200mm × 200mm × 30

mm

200mm × 200mm ×

10mm

Asse mine Germany

200mm × 200mm × 10

0mm

Rock Salt plate samples for free space method

Real part of the complex permittivities in rock saltsby the free space method at 9.4GHz.

Sample thickness

calculated fr

om Rp

calculated f

rom Rs

(a) Hallstadt 11.1mm

5.9 ± 0.2 6.0 ± 0.2

(b) Hallstadt30.1mm

5.9 ± 0.2 6.0 ± 0.2

(c) Asse Mine 99.0mm

5.9 ± 0.2 5.9 ± 0.2

Metal-backed sample

Measurements of complex permittivity of rock salts and lime stones at x-band

• Cavity perturbation methodWithout the influence of insertion holes of the cavity resonator

Principle of the Cavity Perturbation Method

Measurement of ε using a capacitor at low frequencies

V

V

C

C

)1 (

2

1

20

V

V

Q Q

2

1)]

1( )

1[(

2

1

0

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.

d

SC 0

0

Without sample

sample

metal plate (electrode)

d

SC

0S

With samplemetal plate1

V

V

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.

TE103 Cavity (ASTM, USA)

TM010 Cavity (JIS, Japan)

Insertion Holes in the Cavity Perturbation Method at X-band

Rectangular TE10n 　 Cavity Resonator or Circular TM010

Cavity Resonator are used.

Measurement errors are increased by sample insertion holes.

We made TE10n 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.

V

V

f

f

)1 (

V

V

Q Q Qs

)]

1( )

1[(

2

1

2

1

0

2

Perturbation Formula

For Rectangular TE10n mode Cavity

tan

1

L

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.

V

dV

f

f)1 (

Linearity of the perturbation measurements.

V

dV

f

f)1 (

Linearity of the perturbation measurements.

V

dV

Q Q )]

1( )

1[(

2

1

0

Linearity of the perturbation measurements.

V

dV

Q Q )]

1( )

1[(

2

1

0

tan

1

L

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

Mode number

3 5 7 9 11

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″ , tanε″/ ,α at 9.4GHz, 1/αat 9.4GHz.

Sample ε″ 10-3

tanδ10-4

α at 9.4GHz

(m-1)

L=1/α at

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 SaltAsse, Germany

5.8 ± 0.2

<7.8 <13 <0.31 >3.3

Rock SaltHallstadt, 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

tanδ=1×10-4 in situ measurements by P. Gorham et al.

,2

tan c

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, USANaCl single crystal

Rock salt, Asse mine, Germany

Rock salt, Halstadt mine, Austria Lime stone, Mt. Jura, France

Lime stone, Kamaishi, Japan

tan

1

L

ε'=5.9

Summarized data

Conclusions• The attenuation length of various rock salts and lime stones ar

e 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.