Permittivity of porous granular matter, in relation with Rosettacometary mission

Y. Brouet a,n, A.C. Levasseur-Regourd b, P. Encrenaz a, S. Gulkis c

a Observatoire de Paris, LERMA, 61 Avenue de lObservatoire, 75014 Paris, Franceb UPMC Univ. P. & M. Curie, UMR 8190 (LATMOS-CNRS), 4 place Jussieu, 75005 Paris, Francec JPL, Californian Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

a r t i c l e i n f o

Article history:Received 22 February 2013Received in revised form16 August 2014Accepted 22 August 2014Available online 6 September 2014

Keywords:Rosetta missionMIROCometary nucleiPermittivityPorous matter

a b s t r a c t

We report measurements in laboratory conditions of the relative complex permittivity (hereafterpermittivity) of porous material on a large range of frequencies from 50 MHz to 190 GHz. Suchmeasurements, developed in preparation of the Rosetta mission to comet 67P/Churyumov–Gerasi-menko, specifically for the MIRO radiometric experiment, were obtained with different instrumentationsin three frequency bands: 50–500 MHz, 2.45 – 12 GHz and 190 GHz (center-band frequency of themillimeter receiver of MIRO, specially developed for our purpose). Considering the expected propertiesof cometary nuclei, they were carried out with porous granular materials of volcanic origin, with varioussizes ranging from a few to 500 μm, i.e. Etna's ashes and NASA JSC Mars-1 martian soil simulant. Thesamples were split into several sub-samples with different size ranges and bulk densities. The real partand the imaginary part of the permittivity remain respectively in the 2.1 – 4.0 range and in the 0.05 –

0.31 range. Volume scattering becomes significant for the measurements at 190 GHz when the meangrain size of sub-samples is greater than about 200 μm and implies an increase of the real part and theimaginary part of the permittivity. Without this effect, for any sub-sample, the results are consistent overthe frequency range. From 50 MHz to 190 GHz, evidence is provided for a slight decrease of the real partof the permittivity. Bulk densities of the sub-samples, being in the 800–1300 kg m�3 range, weredetermined during the measurements at 190 GHz. Taking into account the expected bulk density of thenucleus (100–370 kg m�3), as well as temperature for the surface and subsurface (in the 30–300 Krange) and its composition (consisting both of silica-rich dust and ices, mostly of water), these first seriesof results allow an estimate of the real part and the imaginary part of the permittivity of the near-surfaceof the cometary nucleus: the real part is likely to be lower than 1.6 for non-icy regions and lower than1.4 for icy regions; the imaginary part is likely to be below 0.09. These estimates represent upper limitsrelevant for the interpretation of the future data of MIRO.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Motivation

While cometary nuclei are primitive scarcely processed bodiesof the solar system, detailed information about their propertiesand thus about the conditions prevailing in the proto-solar nebulaare still to be revealed by a rendezvous mission. Rosetta, theplanetary cornerstone mission for the long-term programmeHorizon 2000 of the European Space Agency, is planned torendezvous with comet 67P/Churyumov–Gerasimenko (hereafter

67P/C–G) in 2014. Key milestones for the rendezvous are thebeginning of nucleus observations from the orbiter in May 2014 atabout 4.5 AU from the Sun, the delivery of the Philae lander inNovember 2014 at about 3 AU, and the perihelion passage inAugust 2015 near 1.2 AU. A passive radiometric experiment ison-board Rosetta: the Microwave Instrument for the RosettaOrbiter (MIRO; Gulkis et al., 2007). MIRO, devoted to microwavenucleus remote sensing and coma spectroscopy, will measure thenear surface temperature, and temperature gradients through twobroadband continuum channels with center-band frequenciesnear 190 GHz and 563 GHz. It has already provided data duringthe flybys of (2867) Steins and (21) Lutetia (Gulkis et al., 2010,2012). To support the preparation of the MIRO data analysis on thecometary nucleus 67P/C–G, the relative complex permittivity of thenucleus has to be investigated. Propagation of an electromagnetic

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http://dx.doi.org/10.1016/j.pss.2014.08.0120032-0633/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ33 1 40 51 23 58; fax: þ33 1 40 51 20 02.E-mail address: yann.brouet@obspm.fr (Y. Brouet).

Planetary and Space Science 103 (2014) 143–152

wave in a given medium depends on its relative complex permit-tivity ϵr (hereafter permittivity). It corresponds to the ratio of theabsolute permittivity of the material to the vacuum permittivity(equal to 8:854� 10�12 F m�1). It is equal to the sum of ϵ0 (the realpart of the permittivity) and of i ϵ″ (where ϵ″ is the imaginary part).The real part controls the microwave emissivity and the imaginarypart is proportional to the signal attenuation. The permittivity isexpected to depend upon the electromagnetic wave frequency, andalso upon the bulk porosity (i.e. the percentage of the bulk volumeoccupied by empty space), temperature and composition of themedium. It thus needs to be measured (i) for various frequencies,tentatively encompassing the frequencies used by MIRO and otherradiowave experiments aboard the Rosetta spacecraft and (ii) formaterials representative of cometary nuclei, i.e. extremely porousdust or ice–dust mixtures, in order to prepare the inversion of datawhich will be obtained during the Rosetta cometary mission.

1.2. Assumed properties of comet 67P/Churyumov–Gerasimenkonucleus

Cometary nuclei are small, irregular and low-albedo bodies.Typically, for 67P/C–G, the size is about 4 km and the geometricalbedo is around 0.04 (Lamy et al., 2008). Comets are composed ofdust (mostly crystalline and glassy silicate minerals) and ices (mostlywater ice) and are rich in organic compounds, such as long-chainhydrocarbons and amino acids (e.g., Kolokova et al., 2004). Althoughtheir masses cannot be directly derived from gravitational perturba-tions, their densities have been estimated to be in the 100–1000 kg m�3 range (e.g., Levasseur-Regourd et al., 2009). The mod-elling of the non-gravitational forces induced by the sublimation ofices, which leads to perihelion advance or delay, suggests very lowdensities (Rickman et al., 1987). The validity of this approach wasconfirmed for comet 9P/Tempel 1 from the analysis of the expansionunder the nucleus gravity of the plume induced by the collision ofthe Deep Impact (DI) probe (Richardson et al., 2007), as well as forcomet 103P/Hartley 2, through a fitting of the potential contours tothe observed geometry of the waste area (A'Hearn et al., 2011).Modelling non-gravitational forces for 67P/C–G has shown that itsbulk density ranges between 100 and 370 kg m�3 (Davidsson andGutiérrez, 2005). Such a low bulk density for an ice–dust mixtureindicates that the bulk porosity is very high, quite likely above 80%. Itmay result from a high macro-porosity, with gravitational aggregatesof sub-nuclei leading to a rubble-pile structure (as suggested for, e.g.,103P/Hartley 2) or from the presence of fractures induced byenergetic impacts. It may also result from a high micro-porosity,originating in voids on the scale of tens of micrometers, in accor-dance with the fact that dust particles seem to mostly consist of fluffyaggregates of grains with sizes in the 0.20–40 μm range (e.g., Fulleet al., 2000; Lasue et al., 2009). A significant amount of the surfaceand subsurface is indeed likely to be built in fluffy dust particles, asillustrated by the analysis of the DI impact crater on 9P/Tempel 1(Schultz et al., 2012). Such porous media are expected, in vacuum, tobe extremely insulating. During Rosetta rendezvous, near-surfacetemperatures in the 30–300 K range are expected, taking intoaccount the variations of illumination. In the deep interior of thecometary nucleus, temperatures are expected of the order of 100 Kand possibly lower (e.g. De Sanctis et al., 2005; Prialnik et al., 2004).

Since laboratory measurements of permittivity are not usuallyobtained for porous materials at millimeter wavelengths, we havechosen here to measure this critical parameter, on ensembles ofmaterials (volcanic ashes of basaltic composition), already porousand relatively well defined. Theymay be considered as a first approachof dust properties within cometary nuclei, in terms of porosity. Thenext section will present the two series of porous samples that havebeen chosen to initiate these studies. The three experiments used toestimate the frequency dependence of the permittivity between

50MHz and 190 GHz (frequency of interest for MIRO experiment)will then be presented. The results will finally be analyzed anddiscussed.

2. Samples

Hundreds of grams of volcanic ashes of basaltic composition,with sizes in the micrometer to centimeter range, were collectedin 2010 on the south side of Etna volcano in Sicily. They mostlyconsist of dark and basaltic porous grains and tiny crystallizedgrains. The mineralogical composition is dominated by olivine. Forthe purpose of this analysis, four sub-samples were prepared aftersieving the sample, with sizes below 50 μm (#1), between 50 and160 μm (#2), between 160 and 355 μm (#3), and finally between355 and 500 μm (#4), as illustrated in Fig. 1a.

We also had access to tens of grams of the NASA JSC Mars-1simulant (e.g., Allen et al., 1998). This sample also corresponds tovolcanic ashes of basaltic composition, collected on the Puu Nenevolcanic cone on Mauna Keas south flank in Hawaii (USA). The maininterest of this sample is that it has already been extensivelydocumented, through a variety of approaches. It mostly consists ofreddish and basaltic porous grains and also tiny crystallized grains,covered by a fine layer of iron oxide, with sizes below 1mm. Moreprecisely, it is composed of olivine, calcium feldspar, titano-magnetite,pyroxene, ferric oxide and basaltic glass. The mean particle density isequal to 1910720 kgm�3 and the mean bulk density is equal to870720 kgm�3, with inferred porosity of about 54% (Allen et al.,1998). For the purpose of this analysis, three sub-samples wereprepared after sieving the sample, with sizes below 80 μm (#5),between 80 and 200 μm (#6), and finally between 200 and 315 μm(#7), as illustrated in Fig. 1b.

Optical microscope images for the seven different sub-samplesshow a difference in the grain texture when the grain size increases.Two main lithologies may be noticed: tiny crystals with very irregularshapes and larger porous irregular grains. The latter, as shown inFig. 2, have a high intrinsic porosity, due to the presence of cavities,the so-called vesicles, formed during outgassing of the initial magma.A significant amount of irregular tiny crystals is present in the lowest-sized sub-samples, typically #1 and #5, whereas the major part of thehighest-sized sub-samples, typically #3, #4 and #7, is composed ofporous grains. The bulk porosity (linked to the bulk density) of thedifferent sub-samples is likely to vary because of the packing effect,which depends on grain shape, and because of the intrinsic porosity,which depends on cavities within the grains. The mean bulk densityof each sub-sample was determined during permittivity measure-ments at millimeter wavelengths, as presented in Section 3.1.

To study the dependence of the permittivity with the grain size,the weighted mean size ϕ (hereafter mean grain size) is estimatedfor each sub-sample. A dimensional analysis by optical microscopywas performed on a given number of grains N (about 100). Theshape of each grain is approximated by a prolate (elongated)spheroid. The diameter Di of the sphere, whose volume is equal tothe prolate spheroid volume of a given grain (where i is thecurrent index for a given grain in a package of N grains), is definedas the mean size of this grain. The size range of a given sub-sampleis divided in J intervals, with j being the current index and Xj themean of a given interval; wj is the weight attributed to eachinterval, otherwise the number of grains with a diameter Di withinthe given interval. The mean grain size ϕ of a given sub-sampleand its standard deviation σϕ are computed as follows:

ϕ¼∑Jj ¼ 1ðwjXjÞ=∑J

j ¼ 1wj ð1Þ

σϕ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑N

i ¼ 1ðDi�ϕÞ2=ðN�1Þq

ð2Þ

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152144

The previously mentioned characteristics are summarized inTable 1 for the seven sub-samples for which measurements areobtained.

3. Instrumentation

Measurements of the permittivity were performed in 2011–2013, for the two porous materials of volcanic origin previouslydescribed. Measurements at 190 GHz were made at LERMAlaboratory (Observatoire de Paris, France) with a quasi-opticalbench. Measurements at 2.45 GHz, 5.6 GHz, 8 GHz, and 12 GHzwere made at IMS laboratory (Bordeaux, France), with resonantcavities. Measurements at 0.05, 0.10 and 0.50 GHz were also madeat IMS, with an open coaxial cell. All the measurements wereperformed under laboratory conditions (discussed in Section 3.5).

3.1. Measurements with a quasi-optical bench at 190 GHz

We have used a quasi-optical bench to characterize the permit-tivity of samples at 190 GHz. The bench is mounted in transmissionas shown in Fig. 3 under ambient conditions of the laboratory. Amillimeter Vector Network Analyzer (VNA) generates the electro-magnetic signal to the emitter. Firstly, the VNA, connected to thereceiver, analyzes the phase and the amplitude versus frequency

#3

Fig. 2. Scanning electron microscope image of dark porous grains, with sizes of theorder of a few hundred micrometers, belonging to the sub-sample #3 from Etna.They have a high intrinsic porosity due to the presence of vesicles.

Table 1Main characteristics of the seven sub-samples from Etna and JSC Mars-1 simulant.m is the total available mass, N the number of grains used for dimensional analysis,ϕ the mean grain size and σϕ its standard deviation.

Sample # m (g) Ng ϕ7σϕ ðμmÞ

Etna 1 3 81 367152 14 80 1157353 48 84 2837674 64 96 506760

JSC Mars-1 5 3 100 427216 10 99 1577367 8 81 272746

Fig. 3. Schematic of the free-space quasi-optical bench sketch mounted intransmission at 190 GHz. Signal emitted by the first horn (H) is focused a firsttime before it reaches the sample and a second time before it reaches the secondhorn. SH: Sample Holder; AS: Absorbent Screen; L: Lens; H: Horn; HG: HarmonicGenerator; HR: Harmonic Receiver.

300 µm

#1 #2

#3 #4

50 µm

500 µm

100 µm #5 #6

#7

80 µm 200 µm

315 µm

Fig. 1. Optical microscope images of the 4 sub-samples from Etna (a) and of the 3 subsamples of JSC Mars-1 simulant (b).

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152 145

(in the 170–200 GHz range) of a signal passing through an emptysample holder placed at a Gaussian beam waist within the system.The mass of this empty sample holder is determined. A secondanalysis is made with the same holder filled with the sample. Itsmass is also determined in order to estimate the bulk density of thesample, knowing the filled volume. Inside two wooden pieces, twocylindrical holes are used as sample holders, with thicknesses (Z) ofabout 3.1 mm and 9.8 mm and a diameter of 20 mm. A material witha negligible absorption in the radiowave domain (o0:1 dB=mm) isused to maintain the sample inside the cylindrical hole. In order toavoid power coming from the secondary lobes of the radio signalthrough the holder, an efficient absorbing material for microwaves(about 4 dB/mm) covers the previous material without affecting theprimary lobe (cf. Fig. 3).

ϵ0 is deduced from the refractive index n (equal toffiffiffiffiϵ0

p), derived

from the determination of the slope of the signal phase rota-tion Δφ, induced by the thickness of the sample Z, versus thefrequency ν, assuming that n remains constant in the range offrequency swept, as shown by the following equation (Goy et al.,2006):

ν� ðn�1Þ � Z=c¼Δφ=360 ð3ÞThe loss tangent, tan δ (equal to ϵ″/ϵ0), is deduced from theanalysis of the amplitude damping (i.e. the signal attenuation)induced by the thickness of the sample (Fox, 2010):

tan δ¼ cα=2πνmn ð4Þwhere c is the velocity of light (in mm/s), α is the absorptioncoefficient (in dB/mm), related to the signal attenuation measuredby the VNA (in dB), and νm is the mean frequency of themeasurement (in Hz). Finally, taking into account Eqs. (3) and(4), the real and imaginary parts of the permittivity are deducedfrom

ϵ0 ¼ n2 ð5Þand

ϵ″¼ tan δ � ϵ0 ð6ÞFor all sub-samples, except #4, a sweeping of frequencies was

performed between 180 GHz and 200 GHz to determine thepermittivity at 190 GHz. The permittivity of the sub-sample #4was determined at 180 GHz with a sweeping frequency between175 and 185 GHz. The high signal attenuation due to this sub-sample and the degraded performances of the measurement setupat higher frequencies did not allow the determination of thepermittivity with a frequency sweeping between 180 GHz and200 GHz. The validation of the measurement was performed witha standard material such as PolyTetraFluoroEthylene (PTFE), with areal part of the permittivity around 2.05 at millimeter wavelengths(e.g. Birch, 1981).

3.2. Measurements with resonant cavities at 2.45, 5.6, 8, and 12 GHz

The perturbation theory of resonant cavities (Bethe andSchwinger, 1943) was used to perform permittivity measurementsat 2.45, 5.6, 8, and 12 GHz with rectangular cavities. The methodrelies on the measurement of the slight perturbations of theresonance modes of the cavity, induced by the insertion of thesub-sample. Then, the signal passes through a small amount ofdust (from a given sub-sample) contained in a cylinder of 8 mm ofdiameter and of about 5 cm of height. An empty cylinder is used todetermine the resonant frequency and the quality factor of thecavity. Once a material is introduced at the center of the cavity,where the electrical field strength of the standing wave is max-imum, the resonant frequency and the quality factor of the cavityare weakly shifted. Real and imaginary parts of the permittivity are

obtained by measuring these modifications with a VNA connectedto the cavity which provides a resonance curve.

Under the assumptions that the electromagnetic field is essen-tially uniform within the sample and weakly changed over most ofthe cavity volume by the insertion of the sample, the real andimaginary parts of the permittivity are determined by the follow-ing equations (Altschuler, 1963):

ϵ0 ¼ 1þð2=τÞ � ðν0�ν1Þ=ν0 ð7Þ

ϵ″¼ ð1=τÞ � ½ð1=Q1Þ�ð1=Q0Þ� ð8Þ(ν0,Q0) and (ν1,Q1) are respectively the resonant frequency and thequality factor of the empty cavity and the filled cavity. τ is thefilling factor expressed by the ratio of the integral of the power ofthe electric field on the sample volume to the similar integral onthe cavity volume. It is derived from a calibration of a given cavitywith standard material (as PTFE).

3.3. Measurements with an open coaxial cell at 0.05, 0.10 and0.50 GHz

At 0.05, 0.10 and 0.50 GHz, permittivity measurements wereperformed with an open coaxial cell connected to an impedanceanalyzer. During the measurement, a signal passes through a smallamount of dust (from a given sub-sample) with a thickness of about15 mm, inside the cylindrical cavity of the cell with a diameter ofabout 5 mm. The real part and the imaginary part of the permittiv-ity are deduced from the variation of the complex admittance, equalto ðGþ iBÞ, measured by the analyzer, between the empty cell andthe filled cell. They are respectively deduced from the imaginarypart and the real part of the admittance, taking into account the cellcalibration, by the following relations (Colin, 1997):

ϵ0 ¼ ðB=ω�C0Þ=Ca ð9Þ

ϵ″¼ G=Caω ð10Þwhere C0 and Ca are respectively the residual capacity and the activecapacity of the cell and ω is the pulsation. These coefficients aredetermined during the calibration of the cell with standardmaterials.

3.4. Error bars estimation

The results relevant to millimeter wavelengths obtained withthe quasi-optical bench, presented in Sections 4.1 and 4.2, arepresented as the mean of 5 individual measurements. The absoluteerrors on each measurement on a given sub-sample, taking intoaccount the standard deviation (cf. Table 2) and the instrumentalerrors, are estimated to be below 11% for ϵ0 and below 2% for ϵ″.Instrumental errors on the determination of ϵ0 and ϵ″ are expectedto be below 1% using the method of error propagation and takinginto account the errors on the thickness measurements of samples,the signal phase measurements by the VNA and the attenuationmeasurement. The stability of the frequency delivered by the VNAis very high, 710�7 GHz, so its participation to the error propaga-tion may be considered as negligible.

For measurements using resonant cavities and an open coaxialcell, only one permittivity measurement was performed by sub-sample. Absolute errors on the real part and the imaginary part ofthe permittivity, mainly due to instrumentation, are estimated tobe about 5%.

3.5. Temperature and humidity conditions

All the measurements were performed under temperature andhumidity conditions of the laboratory. Measurements at 2 MHz ona non-compacted basaltic powder (with a bulk porosity of about

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152146

50%), as performed under variable temperature conditions, haveshown that ϵ0 and ϵ″ decrease respectively by about 6% and 17%with the temperature decreasing from 300 K to 230 K (Heggyet al., 2001). During the measurements with the quasi-opticalbench, the variations in temperature comprised in the 293–301 Krange are supposed not to be critical.

Grains may trap water molecules of ambient air by capillarity.Then, the permittivity increases with the moisture of the sample(Sabouroux and Ba, 2011). In order to remove some possiblemoisture, all the sub-samples were dried in a heater for 24 h at100 1C at room pressure before any measurements. Because theprinciples of measurement of the three instrumentations arebased on a differential measurement, the variations in relativehumidity of ambient air, comprised between 35% and 48% formeasurements with the quasi-optical bench, equal to 54% with theresonant cavities, and equal to 53% with the open coaxial cell,should be unimportant for the comparison of the currentmeasurements.

4. Results and discussion

Results of permittivity measurements performed with thequasi-optical bench at 180 GHz and 190 GHz are summarized inTable 2. Results of permittivity measurements performed at 2.45,5.6, 8 and 12 GHz (hereafter medium frequencies) with resonantcavities and at 0.05, 0.10 and 0.50 GHz (hereafter low frequencies)with an open coaxial cell are respectively summarized inTables 3 and 4.

4.1. Size dependence of permittivity

4.1.1. Results for Etna sub-samplesFig. 4 shows the real part and the imaginary part of the

permittivity of the Etna sub-samples as a function of the meangrain size ϕ for the three series of frequencies corresponding tothe three instrumentations mentioned above. The real part of thepermittivity (ϵ0) remains in the 2.60 – 4.00 range. At 190 GHz, ϵ0

increases with the increasing mean grain size from 2.66 (sub-sample #1) to 3.15 (sub-sample #3) and is equal to 3.92 for sub-sample #4 measured at 180 GHz. No significant variations arenoticed at medium frequencies where the values are about 3.10.For low frequencies, ϵ0 seems to decrease slowly with the increas-ing mean grain size from about 3.60 to 3.10.

The imaginary part of the permittivity (ϵ″) remains within 0.05and 0.31. Regarding the measurements at 180 GHz and 190 GHz,an increase of ϵ″ is noticed with an increasing mean grain size,whereas at medium and low frequencies, ϵ″ is relatively stablewhen the mean grain size increases. Actually, ϵ″ increases from0.05 to 0.14 at 190 GHz and is equal to 0.31 at 180 GHz for sub-sample #4 while ϵ″ is about 0.10 from 0.05 to 12 GHz.

4.1.2. Results for JSC Mars-1 simulantFig. 5 shows the real part and the imaginary part of the

permittivity of the JSC Mars-1 simulant as a function of the meangrain size ϕ for the three series of frequencies. ϵ0 remains within2.1 and 3.9. At 190 GHz, ϵ0 increases with the increasing meangrain size from about 2.1 for the sub-sample #5 to about 2.4 forthe sub-samples #6 and #7. At medium and low frequencies, aslight decrease of ϵ’ is noticed when the mean grain size increases.

For any frequency, no significant change of ϵ″ is noticed whenthe mean grain size increases. ϵ″ remains between 0.16 and 0.30.At 190 GHz, ϵ″ is about 0.20.

To summarize, regarding the measurements at 180 GHz and190 GHz, an increase of the real and imaginary parts of thepermittivity as a function of the increasing mean grain size isnoticed for the sub-samples from Etna, while an increase of ϵ0

between sub-sample #5 and sub-samples #6 and #7 and nosignificant variation of ϵ″ are noticed for the JSC Mars-1 simulant.At medium frequencies, a slight decrease of ϵ’and no significantvariation of ϵ″ are noticed for the JSC Mars-1 simulant, whereas no

Table 3Permittivity measurements at 12, 8, 5.6 and 2.45 GHz (temperature ¼ 294 K;relative humidity ¼ 53%). n.m.: not measured; the small masses available for sub-samples #1 and #5 (cf. Table 1) prevented measurements to be done. La=λ is theabsorption length normalized to the wavelength (discussed in Section 4.3.2).

Sample ν¼12 GHz 8 GHz 5.6 GHz 2.45 GHz

ϵ0 ϵ″ La=λ ϵ0 ϵ″ La=λ ϵ0 ϵ″ La=λ ϵ0 ϵ″ La=λ

#1 n.m. n.m. n.m. n.m. n.m. n.m. n.m. n.m.#2 3.05 0.09 3.1 3.05 0.09 3.1 3.05 0.08 3.5 3.10 0.07 4.0#3 3.05 0.09 3.1 3.05 0.09 3.1 3.05 0.09 3.3 3.10 0.08 3.5#4 3.05 0.10 2.8 3.05 0.10 2.8 3.05 0.09 3.1 3.10 0.08 3.5

#5 n.m. n.m. n.m. n.m. n.m. n.m. n.m. n.m.#6 2.85 0.29 0.9 2.90 0.28 1.0 3.00 0.26 1.1 3.10 0.22 1.3#7 2.70 0.26 1.0 2.70 0.23 1.1 2.80 0.21 1.3 2.90 0.18 1.5

Table 4Permittivity measurements at 0.50, 0.10 and 0.05 GHz (temperature¼293 K;relative humidity ¼54%). La=λ is the absorption length normalized to the wave-length (discussed in Section 4.3.2).

Sample 0.50 GHz 0.10 GHz 0.05 GHz

ϵ0 ϵ″ La=λ ϵ0 ϵ″ La=λ ϵ0 ϵ″ La=λ

#1 3.56 0.09 3.3 3.58 0.09 3.5 3.60 0.09 3.4#2 3.50 0.09 3.3 3.51 0.08 3.6 3.54 0.08 3.7#3 3.48 0.10 3.0 3.49 0.10 3.0 3.52 0.10 3.0#4 3.14 0.09 3.1 3.15 0.09 3.2 3.20 0.09 3.1

#5 3.66 0.23 1.3 3.75 0.25 1.2 3.86 0.30 1.0#6 3.50 0.21 1.4 3.60 0.24 1.3 3.70 0.28 1.1#7 3.30 0.21 1.4 3.40 0.24 1.2 3.50 0.28 1.1

Table 2Permittivity measurements at 190 GHz (and at 180 GHz for sub-sample #4). Ta and Ha are respectively the mean temperature and the mean relative humidity of the airobtained from the temperatures and relative hygrometry recorded during the measurements. La=λ is the absorption length normalized to the wavelength (discussed inSection 4.3.2).

Sample ν (GHz) ϕ7σϕ ðμmÞ ρ7σρ (kg m�3) ϵ0 7σϵ0 ϵ″7σϵ″ La=λ Ta (K) Ha (%)

#1 190 36715 1085714 2.6670.05 0.05170.010 5.1 297 35#2 190 115735 1236710 2.9270.04 0.09170.007 3.0 298 38#3 190 283767 1190715 3.1570.06 0.14470.010 2.0 298 38#4 180 506760 1207713 3.9270.10 0.30570.013 1.0 298 48

#5 190 42721 804722 2.1370.04 0.17470.016 1.3 297 37#6 190 157736 86478 2.4270.01 0.16770.005 1.5 298 38#7 190 272746 84979 2.4270.04 0.16570.004 1.5 298 38

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152 147

significant variations are noticed for the Etna sub-samples. Thetrends for Etna sub-samples and the JSC Mars-1 sub-samples aresimilar at low frequencies, with a slight decrease of ϵ0 and nosignificant variation for ϵ″.

4.2. Frequency dependence of permittivity

Figs. 6 and 7 show the permittivity (real and imaginary parts)of the Etna sub-samples and the JSC Mars-1 sub-samples, respec-tively, as a function of the measurement frequency on a logarith-mic scale. The frequency dependence of the real part of thepermittivity from 0.05 to 190 GHz exhibits similar trends ofdecrease for all sub-samples except for #3 and #4 for which ϵ0

respectively increases at 190 GHz and 180 GHz. It may be due tothe fact that a permittivity measurement is dependent on thevolume scattering, which becomes significant when the grain sizeis comparable to the wavelength. Such is the case for sub-sample#3 for a frequency of 190 GHz and for sub-sample #4 for afrequency of 180 GHz. With the increasing frequency, ϵ0 decreasesin the 3.9–2.1 range. For the sub-sample #4, ϵ0 is relatively stableand remains in the 3.0–3.2 range. For sub-samples from Etna, ϵ″ isrelatively stable whereas it decreases between 0.05 and 0.50 GHzand increases between 2.45 and 12 GHz for sub-samples of the JSCMars-1 simulant. The imaginary part of the permittivity is higherfor the JSC Mars-1 sub-samples than for the Etna sub-samples,with values respectively in the 0.18–0.30 range and in the 0.08–

0.10 range up to 12 GHz. At 190 GHz, measurements of ϵ″ aresimilar for the sub-samples #3, #5, #6 and #7 but differ for thelowest-sized sub-samples #1 and #2 and the highest-sized sub-sample #4 (may be due to the volume scattering as previouslymentioned).

4.3. Discussion

4.3.1. Influence of the bulk density (linked to the bulk porosity)The mixing formulae, which describe the variation of the

permittivity of a mixture of air and solid material as a functionof the volume fraction (defined as the ratio of the bulk density tothe intrinsic density), predict that the real and imaginary parts ofthe permittivity linearly decrease with the decreasing bulk density(Campbell and Ulrichs, 1969). Moreover, at 2 MHz, by working ondifferent controlled compactions of powdered Djiboutian basalt,Heggy et al. (2001) have provided evidence for a decrease of ϵ0 andϵ″ from about 8 to 3 and from about 0.060 to 0.025, respectively,for a bulk porosity increasing from 31% to 50%.

At 190 GHz, the increase of the real part of the permittivitybetween the sub-samples #1 and #2 and between the sub-samples #5 and #6 is consistent with the increase of the bulkdensity determined during the measurements (cf. Table 2). Theincrease of the imaginary part is also consistent with the increaseof the bulk density between the Etna sub-samples #1 and #2whereas there is no variation of the imaginary part between the

Fig. 4. Real part (a) and imaginary part (b) of the permittivity, respectively ϵ0 and ϵ″, versus mean grain size Φ at all measurement frequencies for the 4 sub-samplesfrom Etna.

Fig. 5. Real part (a) and imaginary part (b) of the permittivity, respectively ϵ0 and ϵ″, versus mean grain size Φ at all measurement frequencies for the 3 sub-samples of JSCMars-1 simulant.

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152148

JSC Mars-1 sub-samples #5 and #6. It may be due to the fact thatthe high iron oxide content of the JSC Mars-1 sub-samples,implying high dielectric losses, dominates the bulk density effect.The increase of the real and imaginary parts of the permittivitymeasured for Etna sub-samples with a mean grain size greaterthan about 200 μm originates in volume scattering. The high ironoxide content seems to dominate the volume scattering effect forthe JSC Mars-1 sub-sample #7 for which no increase of the realand imaginary parts is noticed.

4.3.2. Comparison with other measurementsAlthough our samples are subdivided into sub-samples with

different grain size distributions, the results may be compared toprevious measurements on samples of basaltic composition atnear frequencies or comprised within the large frequency rangestudied here.

As far as comparisons for the sub-samples from Etna areconcerned, it may be interesting to still mention the permittivitymeasurements obtained by Heggy et al. (2001) at 2 MHz. For anon-compacted powdered basalt with a bulk porosity of 50%,corresponding to a bulk density of 1350 kg m�3 and with atemperature of 300 K, they obtained a real part of the permittivityequal to 3.2070.03 and an imaginary part equal to 0.1870.03.

With a comparable grain size, ϵ0 of the sub-sample #1 measured atlow frequencies is greater of about 13%. The imaginary partobtained by Heggy et al. (2001) is at least two times higher thanfor the sub-samples #1. Between 4 and 19 GHz, Adams et al. (1996)obtained a real part of the permittivity in the 3.45–3.70 range andan imaginary part in the 0.06–0.11 range for volcanic ashes ofbasaltic composition. These results are consistent with our mea-surements at medium frequencies of ϵ″ for all sub-samples fromEtna, while lower values are obtained for ϵ0.

Previous measurements on a sample of JSC Mars-1 simulantwere performed between 0.01 and 1 GHz using a coaxial transmis-sion line technique (Leuschen, 1999). At 0.05, 0.10 and 0.50 GHz, ϵ0

is respectively equal to 3.55, 3.50 and 3.20 and ϵ″ is respectivelyequal to 0.10, 0.15 and 0.18. Our results for ϵ0 are consistent withthese measurements, whereas we find somewhat larger values forϵ″ for all frequencies and grain size ranges. Measurements havealso been made between 0.20 and 1.30 GHz using three radaremitter/receiver sets mounted in transmission (Williams andGreeley, 2004). These measurements are in agreement with ourmeasurements, with ϵ0 equal to about 3.18 at 0.50 GHz and 3.09 at1.24 GHz, and with rather stable high values of ϵ″, around 0.20.Williams and Greeley (2004) mentioned that the high values of ϵ″measured for the JSC Mars-1 simulant, that we also obtained, maybe due to the relatively high content of the Mars simulant in iron

Fig. 6. Real part (a) and imaginary part (b) of the permittivity versus frequency for the 4 sub-samples from Etna.

Fig. 7. Real part (a) and imaginary part (b) of the permittivity versus frequency for the 3 sub-samples of JSC Mars-1 simulant.

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152 149

oxide which is a lossy material (involving a greater attenuation ofthe signal).

In preparation for the CONSERT radar experiment on boardRosetta spacecraft (Kofman et al., 2007), Heggy et al. (2012) havemade permittivity measurements between 5 and 100 MHz onthree ordinary chondrites and of a mesosiderite reduced in finepowders with a bulk porosity of about 30%. The loss tangent valuesobtained for the three ordinary chondrites samples, approxima-tively equal to 0.004, are an order of magnitude lower than thoseobtained from the results reported in Table 4 of the current paper.The higher metallic content of the current samples may beresponsible for such a difference. This hypothesis is supported bythe results obtained by Heggy et al. (2012) for the mesosideritesample, mostly composed of kamacite and taenite, for which theloss tangent values are approximatively equal to 0.012, three timeshigher than for the ordinary chondrites samples. The loss tangentvalues obtained for the mesosiderite sample are lower than thoseobtained for the current samples. It is not excluded that a residualmoisture effect may affect the measurements at low frequencies.Nevertheless, Heggy et al. (2012)'s samples are rocks reduced inpowders, so that one should be careful when comparing themeasurements obtained for these samples to measurementsperformed on samples obtained without crushing.

The results can also be expressed in terms of the absorptionlength La, i.e. the distance over which a collimated power fluxdecreases by a factor e. It is a crucial parameter for the interpreta-tion of radar remote sensing. Assuming tan δ to be much lowerthan 1, La=λ can be approximated as (Campbell and Ulrichs, 1969)

Laλ¼

ffiffiffiffiϵ0

p

2πϵ″ð11Þ

La=λ remains in the 1.0–5.1 for Etna sub-samples and remains inthe 1.0–1.5 range for JSC Mars-1 sub-samples (cf. Tables 2–4). Lowvalues obtained for JSC Mars-1 sub-samples are likely due to thehigh content in iron oxide. At 0.45 GHz, Campbell and Ulrichs(1969) obtained absorption lengths normalized by the wavelengthin the 5–30 range for basalts reduced in powders with bulkdensities equal to 1000 kg m�3. Their results contrast with thelower values obtained here for Etna sub-samples, in the 3.0 – 3.3range, at a comparable frequency (0.50 GHz). These low valuescould be due to a residual moisture effect. Otherwise, as Heggyet al. (2012)'s samples, Campbell and Ulrichs (1969)'s samples arerocks reduced in powders and their chemical composition, grainsize and bulk density are different, thus it is not surprising to getdifferent results in terms of absorption length.

4.3.3. Significance for future observations of MIRO experiment onboard Rosetta

Estimations of the permittivity of the surface and subsurface ofthe nucleus of comet 67P/C–G are needed for interpretation of theMIRO measurements. Once the expected bulk density and tem-perature of the nucleus are taken into account, our measurementsperformed at the center-band frequency of the millimeter receiverof MIRO, on tentatively appropriate analogs for the refractorycomponent of a cometary nucleus, should provide relevant infor-mation on the permittivity of suspected non-icy regions (Beltonet al., 2007).

The bulk density of the cometary nucleus is expected, asalready mentioned, to be lower than our samples, i.e. in the100–370 kg m�3 range. Our measurements at 190 GHz of the realpart of the permittivity reported in Fig. 8, without those affectedby the volume scattering, suggest, as a first approximation, that ϵ0

decreases quasi-linearly with the decreasing bulk density. Theextrapolation of ϵ0 obtained for the bulk density range expectedfor the cometary nucleus suggests that ϵ0 is likely to be in the 1.15–1.56 range. Also, one would expect that ϵ″ decreases quasi-linearly

with the decreasing bulk density. Therefore, our measurements ofϵ″, without those affected by the volume scattering, only providean upper limit equal to 0.09.

Our measurements were made for temperatures between 293and 301 K. Near-surface temperatures of the cometary nucleus areexpected to vary in the range 30–300 K, due to the illuminationvariation during its orbital period and the night/day differences.Relations between the permittivity and the temperature wereobtained at 1.7, 2.6, 6.6 and 31.6 GHz on a sample of JSC-1A lunarmare simulant, build up of volcanic ashes (Calla and Rathore,2012). With a temperature decreasing from 303 K to 83 K, ϵ’ and ϵ″ linearly decrease. Results show that the higher the frequency, theweaker is the temperature dependence. The slope varies from(2.670.2)�10�3 K �1 at 1.7 GHz to (4.770.7)�10�4 K�1 at31.6 GHz for ϵ0 and from (6.574)�10�4 K�1 at 1.7 GHz to(872)�10�5 K�1 at 31.6 GHz for ϵ″. Assuming thus that theslope at 190 GHz is close to what it is obtained at 31.6 GHz, andtaking into account the estimation of the permittivity for non-icyregions at 300 K, the range of the real part and the upper limit forthe imaginary part of the permittivity can be estimated for lowertemperature. At 30 K, ϵ’ is estimated to be in the 1.02–1.43 rangeand ϵ″ is likely to be below 0.07 for non-icy regions of the nucleusof 67P/C–G.

Ice–dust mixtures must also be considered on the nucleussurface. Heggy et al. (2012) have also made permittivity measure-ments at 90 MHz for temperature in the 113–233 K range on waterice–dust mixtures, with a bulk density close to that of our samples.These complementary results suggest that ϵ0 decreases from 6 to20% between a pure dust sample and a dirty ice sample with adust-to-ice mass ratio equal to 50%. Assuming that the ice contenteffect on the permittivity is the same at 90 MHz and at 190 GHz,that icy regions are composed of ice and dust mixture, then thereal part of the permittivity is likely to be below 1.4. Ice contenteffect on the imaginary part of the permittivity of a ice–dustmixture is currently not well known.

Variations of the permittivity mentioned above, taking intoaccount the expected bulk density, temperature variations andcomposition of the cometary nucleus, suggest that our resultsrepresent upper limits for the permittivity of the surface and thesubsurface of the 67P/C–G nucleus.

1

1.5

2

2.5

3

3.5

4

0 200 400 600 800 1000 1200 1400 1600

ε’

ρ (kg/m3)

#1 #2

#5

#6

67P/C-G

f(ρ)EtnaJSC Mars-1

Fig. 8. Real part of the permittivity ϵ0 versus bulk density ρ (kg/m3). Resultsobtained on sub-samples #1 and #2 from Etna and #5 and #6 from JSC Mars-1simulant are presented. Results obtained from measurements affected by thevolume scattering are not presented. The solid line represents the linear regressionf(ρ) of the measured points; f ðρÞ ¼ A� ρþ1 with A¼ ð1570:04Þ � 10�3. The linearregression, as a first approximation, allows us to provide a first estimation of thereal part of the permittivity of non-icy regions on the surface of the nucleus ofcomet 67P/C–G for a temperature equal to 300 K and for a frequency equal to 190GHz: 1:15rϵ0r1:56.

Y. Brouet et al. / Planetary and Space Science 103 (2014) 143–152150

5. Conclusion

We report permittivity measurements of the JSC Mars-1simulant and of volcanic ashes from Etna, on a range of wave-length from the meter to the millimeter domain, encompassingthose of the MIRO and CONSERT experiments aboard Rosetta.Their high natural porosity makes them suitable samples toinvestigate the permittivity of porous cometary dust. Moreoverthey provide several sub-samples with a natural broad range ofgrain size, typically between a few and hundreds of microns, andwith different bulk densities. The real part of the permittivityremains between 2.6 and 4.0 and between 2.1 and 3.9 respectivelyfor the Etna sub-samples and the JSC Mars-1 sub-samples. Theimaginary part of the permittivity remains respectively between0.05 and 0.31 and between 0.16 and 0.30. For all sub-samples, ϵ0

tends to decrease with the increasing mean grain size at lowfrequencies (0.05, 0.10 and 0.50 GHz). At medium frequencies(2.45, 5.6, 8 and 12 GHz), ϵ0 tends to remain constant with theincreasing mean grain size for the Etna sub-samples and tends todecrease for the JSC Mars-1 sub-samples. For both samples, ϵ″does not vary significantly with the increasing mean grain size atlow and medium frequencies. At 190 GHz, variations of ϵ0 and ϵ″are consistent with the variations of the bulk density for the sub-samples whose the mean grain size is smaller than 200 μm (λ=8).For sub-samples with a mean grain size larger than 200 μm,measurements are affected by volume scattering and not takeninto account. It is the first time that the permittivity of identicalsamples is studied on such a wide frequency range from 0.05 GHzto 190 GHz. Results are consistent along the frequency range,although three different instrumentations were used. Overall, ϵ0

decreases with the increasing frequency. The imaginary part of thepermittivity is relatively stable with the increasing frequency forthe sub-samples from Etna, while it varies for the JSC Mars-1 sub-samples.

The bulk density of the sub-samples was determined duringmeasurements at 190 GHz. The results reported here are currentlythe only data measured on porous matter relevant for the milli-meter wave radiometer of the MIRO instrument. Investigationsand predictions of the permittivity of the near-surface of thecometary nucleus 67P/C–G have to take into account the bulkdensity, the temperature variations and the composition of thecometary material. Therefore, in the context of the in situ proper-ties mentioned above, our permittivity measurements at 190 GHzrepresent upper-limits for the interpretation of the future data ofMIRO. From the extrapolation of our data giving the bulk densitydependence of the permittivity at 190 GHz, for a temperature ofthe order of 300 K, the real part of the permittivity for non-icyregions on the cometary surface is likely to be in the 1.15–1.56range and the upper limit of the imaginary part is equal to 0.09.For a temperature of the order of 30 K, ϵ0 is likely to be in the 1.02–1.43 range and the upper limit of ϵ″ is equal to 0.07. For icy regions,whose expected permittivity is dependent on the ice content foran ice–dust mixture and on the temperature, ϵ0 is likely to bebelow 1.4. These estimations will be directly applicable to thefuture interpretation of data from MIRO experiment.

The results reported in this paper may have applications for themicrowave observations of solar system objects: remote sensing ofthe Earth, observations of TNOs (Trans-Neptunian Objects) assecondary calibrators for Herschel and Planck, dunes, ices andvolcanoes on Titan and the saturnian moons.

Acknowledgments

Support from CNES is acknowledged, as well as support fromUniversité Pierre et Marie Curie. We warmly acknowledge Valérie

Ciarletti from the LATMOS laboratory (Paris, France) who gave us theEtna's ashes and Michel Cabane from the LATMOS laboratory whoallowed us to make measurements on the JSC Mars-1 simulantsample. We also acknowledge Gilles Ruffié and Fabrice Bonnaudinfrom the IMS laboratory (Bordeaux, France) and Maurice Gheudin,Gérard Beaudin, Patrice Landry, Jean-Marie Munier and MicheleBatrung from the LERMA laboratory (Paris, France) for their supportto the measurements. We warmly thank Stefano Bertone (Universityof Bern, Switzerland) for his useful comments. We acknowledge theMIRO Team for its support to this work. And finally we acknowledgeJacques Thibieroz from the Sisyphe laboratory (Paris, France) for hissupport to the samples characterization.

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