Experimental Probes of Radio Wave Propagation near Dielectric ...

Experimental Probes of Radio Wave Propagation near Dielectric Boundaries and Implications for Neutrino Detection R. Alvarez, J.C. Hanson, A.M. Johannesen, J. Macy, S. Prohira, J. Stockham, M. Stockham, Al. Zheng, and Am. Zheng

arXiv:1509.04997v1 [astro-ph.IM] 16 Sep 2015

University of Kansas, Lawrence, KS 66045 D.Z. Besson and I. Bikov National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409 Russia (Dated: September 17, 2015)

Abstract Experimental efforts to measure neutrinos by radio-frequency (RF) signals resulting from neutrino interactions in-ice have intensified over the last decade. Recent calculations indicate that one may dramatically improve the sensitivity of ultra-high energy (“UHE”; ≥ 1018 eV) neutrino experiments via detection of radio waves trapped along the air-ice surface. Detectors designed to observe the “Askaryan effect” currently search for RF electromagnetic pulses propagating through bulk ice, and could therefore gain sensitivity if signals are confined to the ice-air boundary. To test the feasibilty of this scenario, measurements of the complex radio-frequency properties of several air-dielectric interfaces were performed for a variety of materials. Two-dimensional surfaces of granulated fused silica (sand), both in the lab as well as occurring naturally, water doped with varying concentrations of salt, natural rock salt formations, granulated salt and ice itself were studied, both in North America and also Antarctica. In no experiment do we observe unambiguous surface wave propagation, as would be evidenced by signals traveling with reduced signal loss and/or superluminal velocities, compared to conventional EM wave propagation. We therefore conclude that the prospects for experimental realization of such detectors are not promising.

I.

INTRODUCTION

Cosmic rays propagating towards Earth from large redshifts can produce neutrinos by interacting with the cosmic microwave background[1–3]. The Aksaryan effect[4] provides an attractive neutrino detection scheme whereby the charged and neutral current neutrino-nucleon interactions in a dielectric material create hadronic and electromagnetic cascades that radiate coherently in the 102 − 103 MHz bandwidth, or wavelengths in the 30-300 cm range[5]. Given its natural abundance in pure form, ice is the most convenient dielectric material, because the long radio attenuation length (≈2 km in the coldest ice) facilitates observation of in-ice neutrino interactions by receivers (Rx) several km distant[6, 7]. The notion of a surface propagating wave has been understood as a special solution to Maxwell’s Equations since the 1800’s, but was first definitively articulated by Jonathan Zenneck over one century ago[8], and also famously considered as a promising avenue for the thenburgeoning wireless industry by Nikolai Tesla1 . Zenneck obtained the dispersion relation for propagation along a boundary with permittivity  in terms of the free-space permittivity 0 as: k 2 = k02 0 /(20 + 2 ), with the standard definition k = ω/c, leading to the expectation that, in so far as dielectrics are characterized by  > 0 , surface waves should propagate with phase velocities exceeding the vacuum velocity of light c0 . We note that this is distinct from superluminal phase velocities propagating along the conducting surface of a waveguide[9], or group velocities propagating at v > c0 in regions of anomalous dispersion. Crudely, such waves represent the solution to Maxwell’s Equations in the limit where the incident angle is equal to the critical angle θcrit – intuitively, surface flux trapping must be the case here since there is neither a transmitted nor a reflected wave. In addition to 2-dimensional rather than 3-dimensional flux spreading, another prediction in this limit is the expectation of waves following the curvature of the surface (or the Earth, as a whole), contrary to the usual expectation that, e.g., radio waves must follow line-of-sight. Upon learning of observations that low-frequency radio waves were detected well beyond simple line-of-sight, Sommerfeld (1909) followed with an expansion of Zenneck’s investigations[10], suspecting that those far-propagating radio waves were carried along the Earth-atmosphere boundary (later it was realized that this phenomena was primarily due to ionospheric reflections), with particular attention given to the vertical vs. horizontally polarized components of surface waves. Sommerfeld concluded that, of the two, the transverse component is most efficiently transported at the interface. More recently, the behavior of waves propagating along a boundary of two dielectrics (characterized by permittivities 0 and 1 ) at near-glancing incidence has been re-visited[11] in the context of neutrino detection, and the qualitative conclusion that RF waves may couple to the interface and travel exclusively along the surface, experiencing flux spreading considerably smaller than in the bulk dielectric, re-derived. That first-principles calculation predicts, specifically, that: • Unlike the well-known evanescent solutions to Maxwell’s equations corresponding to “total internal q reflection” incidence angles, surface waves are superluminal, with phase velocity 1 , corresponding to vp ∼ 1.34c0 at the ice-air boundary typical of Antarctica. vp = 0+ 1 √ • The amplitude attenuation length for a surface wave is intrinsically a factor of 2 2 times longer than the attenuation length in the bulk. This effect is distinct, and augments, the effect of two-dimensional rather than three-dimensional flux spreading, corresponding to power reduction with distance-from-source as 1/r vs. 1/r2 , respectively. In 1

See also Jack and Meg White’s discussion of this phenomena in Jim Jarmusch’s “Coffee and Cigarettes”, also in http://www.youtube.com/watch?v=sL9bq3YmHJo

fact, for so-calledqneutrino-induced “Askaryan” signals, one expects an overall ratio of Esurf ace /Ebulk ∼ ωr/c; taking typical values of ω ∼250 MHz and r=2800 m[11], this results in an enhancement of nearly 300 in the predicted surface electric field amplitude. • Surface coupling is expected when the incidence angle, relative to the surface, is of order one degree or less. The Antarctic ice sheet represents a unique laboratory for surface effects, given the dielectric contrast at the air/snow interface, and the semi-infinite character of the ice sheet. Antartic ice is a remote and largely inaccessible laboratory, however, so we have conducted a series of separate, and somewhat overlapping laboratory measurements to search for evidence of surface excitations. Inherent in each technique are systematic uncertainties, usually due to the finite scale of the measurement apparatus; redundancy is therefore essential in order to derive a composite picture. The techniques can be classified as follows: • Measurement of signal amplitude reduction as a function of distance from a transmitter (Tx) near a dielectric boundary. • Direct measurements of group velocities for waves propagating near a dielectric boundary using signal impulses (in which case direct arrival times are determined), and corresponding determination of the index-of-refraction. • Measurements of phase velocity, by tracking the phase of a continuous-wave (CW) source propagating near that boundary, • Inference of index-of-refraction by measurements of the Voltage Standing Wave Ratio (VSWR) of antennas near a dielectric boundary. Experimentally, systematics are minimized using a propagation medium which is at least several wavelengths thick, and, ideally, semi-infinite in lateral extent. These requirements are not easily satisfied given the typical confines of a standard laboratory, unless the wavelength can be limited to O(1–10 cm). Previous experimental probes of such effects are, correspondingly, not readily found in the literature. Hansen[12] attempted to quantify the effects of rough ocean surfaces by propagating electromagnetic waves between 4 and 32 MHz, over a 235 km path length. In particular, he sought to verify calculations by Barrick[13] that prescribed the numerical loss of signal strength as a function of wave height, and wind and sea state. He observed remarkably good agreement with Barrick’s predictions, up to a frequency of 18 MHz, beyond which his data showed a linearly increasing excess of measured power relative to expectation, rising to a value of 15 dB higher measured power than expected at 30 MHz. Hansen was aware of surface wave propagation and cites work by Wait[14], however, he did not make the explicit connection to Zenneck waves, nor is there explicit measurement of wave velocity. The first unambiguous observation of surface Zenneck waves has been claimed by Soviet groups[15–17] in a serious of experiments beginning in 1980. They measure group velocities exceeding c0 for electromagnetic waves traveling on the surface of high-salinity (35%) water, over the√frequency regime from 700-6000 MHz. Moreover, they also claim observation of the expected 1/ r dimunition of amplitude with distance from the source, as well as the transformation from a surface wave to a bulk wave in the case where the propagating surface wave encounters a surface discontinuity. Mugnai et al[18] observed free space superluminal (by several per cent) wave propagation using a pulsed microwave beam at 8.6 GHz, by measuring the leading edge arrival time between a transmitter and receiver over distances ranging from 30 cm to 130 cm, although the statistical

significance of this result has been contested[19], and a re-analysis of the original data finds inconsistency with v = c0 at less than 2σ significance[20]. Ranfagni et al[21], within the last decade, claimed observation for surface wave excitations at ∼10 GHz frequencies, using custom microwave horns and microwave absorbers to minimize multi-path effects. Their measurements focused on wavespeeds over the frequency range 7.5–10 GHz using a transmitter system stepping through this band at 10 MHz increments. Although their received signals were often evidently contaminated by secondary, downstream interference effects, the ‘leading edge’ of their received signals often indicated phase velocities exceeding c0 , although this was not systematically quantified. No direct study of amplitude was reported in that experiment. II.

MEASUREMENT OF ATTENUATION LENGTH DEPENDENCE ON DISTANCE

The attenuation length is typically defined with respect to the electric field (directly proportional to the voltage measured at the feed point of our receiver dipole antennas). In terms of power transmission, the (modified) Friis transmission equation states that the power received at the receiver after the signal has propagated a distance d through the medium with field attenuation length L is !

Prec /Ptrans

GRx GT x d ∼ exp −2 . 2 d L

(1)

Here, G is a gain factor depending on the angular orientation of the transmitter and receiver. For two aligned dipoles, G is effectively of order unity. Applying equation 1 to two receivers at distances r1 and r2 from the transmitter, we have (in a three-dimensional material), for the voltages V1 and V2 measured at the two points: V2 /V1 =

r1 exp (−(r2 − r1 )/L) r2

(2)

Equation 2 assumes that P ∝ V 2 , and that the antennas are linear devices with a constant effective height converting electric fields into voltages (a standard property of dipole antennas, e.g.). Comparing an antenna measurement in air (with no appreciable attenuation) to the dielectric material, equation 2 becomes rair exp (−(rdiel − rair )/L) (3) rdiel In our case, we seek to investigate ‘trapping’ of electric field flux within a boundary surface layer. In such a case, the dependence of signal power with distance falls more slowly than for flux spreading into the bulk (1/r vs. 1/r2 ), suggesting significantly more advantageous neutrino detection efficiency for near-surface radio receivers rather than englacial radio receivers. Vdiel /Vair =

A.

Laboratory Amplitude Measurements in Sand

On the University of Kansas campus, we have attempted to discern surface wave effects using the sand volleyball courts located at the University’s gym and recreational facilities. These have the advantage of close proximity to the KU Physics Department, but the disadvantage of limited depth (typically 30 cm of dry sand, followed by a deeper layer susceptible to increasing moisture). Our measurements consisted of a series of peak voltages for impulses, measured as a function of separation distance between transmitter and receiver; for these measurements, both transmitter and receiver were half-buried in the sand. Each of the 5 cm diameter, 30 cm long RICE[22] neutrino detection experiment’s half-wave “fat” dipole antennas offers good reception

FIG. 1: Near-surface amplitude measurements made in sand volleyball courts at University of Kansas. √ Data points shown as circles overlaid with fits to 1/r (red) vs. 1/ r (blue) functional forms. Errors represent error on average value displayed in each bin, and are therefore proportional to the square root of the inverse of the number of trials.

over the range 0.2–1 GHz. The peak response of the antenna is measured to be at ∼450 MHz in air (or 450 MHz/n in a medium characterized by index-of-refraction n) with a fractional ∼0.2. Figure 1 shows the result of this exercise. Although the data quality are bandwidth ∆f f reasonably good √ and favor the 1/r fit, we cannot conclusively discriminate between V (r) ∝ 1/r vs. V (r) ∝ 1/ r, corresponding to spherical vs. planar flux-spreading, respectively. B.

Amplitude Measurements at South Pole with the RICE Experiment

As an alternative, we have attempted to quantify planar signal flux trapping directly from data taken using a fat dipole antenna transmitter/receiver pair lowered into two neighboring iceholes drilled for the RICE experiment at the South Pole in 1998. Each of these mechanically holes is approximately 180 m deep and 12 cm in diameter. Two different trials were carried out in the original experiment, conducted in 2003, which we have recently re-analyzed. That experiment targeted a measurement of the index-of-refraction dependence with depth, rather than measurement of surface waves, so control of systematics were designed with the former goal in mind. In each trial, two antennas were placed near-surface, and the propagation time, as well as the signal voltage registered at the receiver recorded. Next, the two antennas were co-lowered into parallel iceholes with a horizontal separation of order 50 m. Of interest here is the signal amplitude after the antennas have descended several wavelengths into the ice, at which point the received signal voltage can be compared with the near-surface measurements. If signal has been trapped in the boundary layer in the latter case, then, given the negligible radio-frequency signal absorption in the near-surface ice firn,

FIG. 2: RICE Tx→Rx waveforms obtained at varying depths (1m or 15m) for both Tx and Rx.

FIG. 3: RICE hole B2 Tx→RICE hole B4 waveform comparison.

theqratio of signal amplitude relative to the in-ice signal amplitude should vary q the near-surface√ 2 as 1/r/ 1/r , or simply r. I.e., the near-surface received amplitudes should be markedly larger than the sub-surface received amplitudes. Ralston’s calculations[11], in fact, predict an √ additional enhancement by a factor of 2 2. The results of this exercise are shown in Figures 2 and 3, for broadcasts between a) the South Pole Station (SPS) rodwell hole (evacuated volume remaining after melted ice has been extracted for general SPS use) and RICE hole B2 and b) RICE hole B2 and RICE hole B4, respectively. Although there is some moderate change in the waveform shapes of the near-surface vs. the deep-ice received signals, the overall received power in the first ∼100 ns of the initial pulse emission is comparable in the in-ice vs. the near-surface √ transmission cases, and inconsistent with the expected enhancement by a factor of > 50 m that would be expected for the case of surface signal flux trapping. C.

Complementary Investigation of Flux Spreading using Variable Transmitter Depth

We can also investigate possible surface flux trapping using an approach complementary to the one just described. To the extent that flux is trapped on the surface, of course, it can therefore no longer be measured within the bulk ice. I.e., the near-constancy of received signal by the preexisting englacial RICE receiver array, comparing the case where the transmitter is near-surface, and therefore more likely to excite surface coupling, to the case where the transmitter is fully submerged, similarly implies a near-constant signal flux spreading. As a transmitter antenna is lowered into a borehole, we have therefore measured the peak amplitude of the signal received in several of the RICE channels 0–4, themselves varying between 110 m and 200 m depths. Knowing the geometry of the transmitter and receiver, correcting for the dipole beam pattern of the dipole antennas (G(θ) ∝ cosθ), and assuming bulk electric field spreading varying as 1/r, we observe reasonable agreement (Fig. 4), down to the bottom of the transmitter borehole, between the signal received at the surface compared to the signal received at depth, consistent with the expected volumetric flux dimunition for all tested depths, and inconsistent with significant fluxtrapping for near-surface transmitter depths. We note that a follow-up experiment proposed for South Pole will instead scan over a range of radial separations for transmitter depths in the near-surface regime (–50 cm< z