On electromagnetic wave ignited sparks in aqueous dimers

Dimer interactions with electromagnetic waves offer a research tool to obtain microscopic insights into macroscopic matter behavior. They also generate a popularly known household phenomenon in the form of fiery sparks between two closely spaced grapes in a microwave oven. However, the cause has not been scientifically examined until recently. In a detailed study on aqueous dimers,¹ Khattak, Bianucci, and Slepkov concluded that the merging of resonant modes in two closely spaced watery spheres results in a hot electromagnetic spot in their gap, which causes the sparks. This work and the proposed applications have been widely reported^2–5 because of their novelty and public interest, in particular, the claimed demonstration of optical writing with a resolution better than λ₀/80.

In Ref. 1, the authors put a long-standing household puzzle on a rich academic basis. Their work has also motivated the current study on an independent cause of a much different nature. Both theory and experiment indicate that with the wave polarized along the dimer axis (same model as in Ref. 1), mutual enhancement of polarization charges on both sides of the narrow gap can result in an electric field hundreds of times greater than that of the wave, hence triggering the sparks through air arcing. This is evidenced by (1) the predicted and observed sparks in an essentially magnetic-field free environment at 27 MHz, (2) the negligibly small magnetic field in the dimer gap even when the dimer body is in strong electromagnetic resonance with a 2.45-GHz microwave, and (3) a video display of the attraction by electric force between the two spheres of the dimer, rather than the repulsion expected from the radiation pressure of an electromagnetic hotspot.

It is well recognized that bound molecular charges in a dielectric medium will be slightly displaced by an electric field to form polarization charges. The simplest example is a uniform dielectric sphere immersed in a static, uniform, external electric field (E_ext), for which the exact analytical solutions are well-documented (Ref. 6, Sec. 4.4). The main feature is the induced polarization charges (σ_pol) on the spherical surface [see Fig. 1(a)] given by

where ε and ε₀ are the permittivity of the sphere and free space, respectively. θ is the angle between E_ext and the observation direction.

Surface polarization charges partially cancel the E_ext in the interior of the sphere, while still keeping the total interior field (E_in) uniform. The larger the dielectric constant, the greater the cancelation. For example, E_in/E_ext = 0.5 for ε/ε₀ = 4 and E_in/E_ext = 0.037 for ε/ε₀ = 80. Two complementary methods are used for graphic illustrations. Figure 1(a) displays a field-line plot for ε/ε₀ = 4 to show field directions and discontinuities (at σ_pol), while Fig. 1(b) displays a simulated color plot for ε/ε₀ = 80 to show large field variations (see  Appendix A, Part 1, for the software used in all simulations). Here and in all subsequent simulations, air is assumed to be free space.

Consider next a dielectric sphere (of radius R) exposed to an electromagnetic wave with free-space wavelength λ_free. The wavelength in the dielectric (λ_d) is λ_free divided by the index of reflection [= Re(ε/ε₀)^1/2 (Ref. 6, p. 314)]. If λ_d≫ R, the region in and around the sphere falls in the near zone. The induced fields are, thus, dominated by a quasi-static electrical component, which oscillates harmonically in time with a spatial profile well approximated by that of the static equations (Ref. 6, Sec. 10.1), i.e., the fields are essentially the same as in Fig. 1.

Because water has a very large ε/ε₀ at and below microwave frequencies, the induced ±σ_pol cancels most of E_ext in the sphere and approximately doubles it immediately out of the right and left ends of the sphere [Fig. 1(b)]. A weakly loaded, 1-kW microwave oven has a peak electric field (E_ext) of 300–400 V/cm,⁷ while the air breakdown strength is about 3 × 10⁴ V/cm at 1 atm.⁸ So a mere doubling of E_ext in the microwave oven is far from enough to trigger a spark (as pointed out in Ref. 1).

The situation is markedly different in the gap region between two water spheres aligned side-by-side along E_ext [Fig. 2(a)]. First, the induced polarization charges are no longer exactly on the surface. They penetrate slightly into the spheres to form a volume charge density (ρ_pol). However, the penetration is so shallow that ρ_pol still effectively resides on the surface as in Eq. (1). Second and more importantly, ρ_pol on opposite sides of the gap is of opposite signs (denoted below by ±ρ_pol). Facing each other, ±ρ_pol is mutually enhanced, i.e., more molecules are polarized on the +ρ_pol sphere by the action of −ρ_pol on the opposite sphere and vice versa. A narrower gap leads to greater enhancement, consequently a greater gap electric field. Such an effect is well recognized. The relevant question here is whether it can drive up the gap electric field to the air breakdown strength, hence triggering the sparks in a household microwave oven.

We first address this question at 27 MHz, which belongs to an ISM (industrial, scientific, and medical) band. The dimer under study is formed of two identical water spheres with a variable gap width d [Fig. 2(a)]. Here and subsequently, the radius (R) of each sphere is fixed at 7 mm, so λ_d (≈ 124 cm)≫R at 27 MHz and the fields are quasi-static with a negligibly small magnetic component in the near zone.

In the 27 MHz simulation, a voltage is applied to a capacitor formed of two circular plates, 10 cm in radius and 4 cm apart, with their axis coinciding with the x-axis [Fig. 2(b)]. The on-axis electric field, E_ext, is nearly uniform (in the ±x-direction) between the plates. Two water spheres, each with R (radius) = 7 mm and separated by d (gap width) = 0.5 mm, are aligned along E_ext [Fig. 2(b)]. The complex permittivity of water at 27 MHz is assumed to be ε = (78.4 + 0.1i)ε₀.⁹ 

Figure 2(b) shows the simulated x-y plane electric field strength, E(x), of a capacitor loaded with a dimer (d = 0.5 mm) aligned along E_ext, with an instantaneous field strength of 400 V/cm, approximately the maximum field in an 1-kW microwave oven.⁷ The close-up view of the dimer [Fig. 2(c)] features a strong ρ_pol-enhanced electric field in the gap region.

Simulations have also been performed for the dimer in the same instantaneous E_ext for several other gap widths. Figure 2(d) displays the on-axis electric field E_axis along the x-axis, each for a fixed d. In all profiles, E_axis peaks sharply in the gap region where it is much greater than E_ext and more so for a smaller d.

We further define E_gap = E_axis (x = 0) to quantify the gap electric field strength. Figure 2(e) plots E_gap as a function of d for d = 0.005–3 mm. With air modeled as free space, air breakdown cannot be simulated. However, it can be seen that E_gap reaches the air breakdown strength (∼3 × 10⁴ V/cm) at d ≈ 0.13 mm. With d < 0.13 mm, sparking is expected, and the required energy is localized within the gap region [Figs. 2(c) and 2(d)].

As a point of interest, when the two spheres are in contact (d = 0), there is still a gap region around the contact point. Furthermore, bound to their respective molecules, polarization charges are not free to move across the contact point. Hence, the transition from separation to point contact is a smooth one, and the electric field near the contact point is accurately given by the d→0 data in Fig. 2(e).

For the purpose of comparison, in Fig. 2(f), we rotate the dimer in Fig. 2(b) by 90° to make the dimer axis aligned perpendicular to E_ext. Figure 2(g) gives the close-up view of the dimer in Fig. 2(f). It shows no enhancement of the gap electric field. This is expected because |ρ_pol| is now at a minimum near the gap [θ = ±π/2 in Eq. (1)].

This is borne out in experiments at 27 MHz (see  Appendix A, Part 4, for the experimental setup). Figure 3(a) shows a capacitor [same dimensions as in Fig. 2(b)] loaded with two R = 7 mm hydrogel spheres aligned along E_ext. The hydrogel spheres are fixed in a sample holder (see  Appendix A, Part 2, for the sample preparation). The capacitor in Fig. 3 is plotted vertically, so that its E_ext is along the x-axis as in Fig. 2. In actual experiments, the capacitor is horizontal, while the sample holder can be rotated by 90°. An infrared camera is used to obtain thermal images during the experiment (see  Appendix A, Part 3).

The 27 MHz arcing typically started as soon as E_ext = 400 V/cm was applied (the field used in theory), followed shortly by spark ignitions (see supplementary videos). However, the gap surface temperature did not rise as rapidly as the optically bright sparks would suggest. At 27 MHz, the conventional AC circuit theory applies to our circuit dimensions. The impedance between each capacitor plate and the dimer [see Fig. 3(a)] is capacitive (∼1/ω), hence higher at lower frequencies. A relatively high circuit impedance at 27 MHz may have resulted in the slow heating observed.

Figure 3(b) displays the thermal images of the dimer surface for three gap widths, taken in situ by an infrared camera after a 35-sec exposure to E_ext (peak) = 400 V/cm. The initial dimer temperature is 23.7 °C. For d = 0.7 mm, the gap is too far apart to trigger an arc. For d = 0.2 mm, the gap starts to arc/spark with T_max (spatial maximum) = 41.3 °C on the gap surfaces. For d = 0, the gap arcs/sparks strongly with T_max = 72.1 °C.

Assuming an air breakdown strength of 3 × 10⁴ V/cm,⁸ the simulated threshold (i.e., longest) d for arcing is 0.13 mm [Fig. 2(e)], while the measured value is 0.2 mm [Fig. 3(b)], indicating a lower actual air breakdown strength. There is a ±10% uncertainty in the capacitor voltage measurement. On the other hand, the AC air breakdown strength is significantly lower than the DC value (by as much as 20% at 30 kHz as shown in Ref. 10, which also reports a weaker dependence on humidity). Considering these factors, the measured threshold d for arcing (∼0.2 mm) is in reasonable agreement with the prediction (0.13 mm).

To further confirm that the gap electric field originates from the ± ρ_pol buildup, we rotate the dimer by 90° with respect to the E_ext [Fig. 3(c)]. As expected, no arcing is observed [Fig. 3(d)] since |ρ_pol| is now at a minimum near the gap [θ = ±π/2 in Eq. (1)].

To conclude, the electrical origin for gap sparks has, thus, been established in an essentially magnetic-field free environment at 27 MHz.

It should be pointed out that the effect under study is not specific to aqueous dimers. E-field intensification in dielectric or conducting dimers has been commonly studied to explain rapid or non-uniform processing of materials by microwaves.^11–15 The treated systems are rather complex, and multiple effects are involved in addition to electrical polarization. The current model of an isolated dimer allows a detailed quantitative study on various effects such as the polarization-charge enhancement.

An important issue to address is the frequency range for the validity of the electrical mechanism, especially when the dimer is in strong electromagnetic resonances with the incident wave.

As an electromagnetic wave enters a dielectric object, multiple reflections off the inside walls can constructively superpose into a resonant standing wave at certain discrete frequencies. In 1908, Mie developed the analytical theory for a plane wave incident onto a dielectric sphere.¹⁶ A dielectric sphere of radius R is known to exhibit Mie resonances in an electromagnetic wave if λ_d ≤ 2 R. For example, at 2.45 GHz, water has a dielectric constant of ε/ε₀ = 77.5 + 10i.¹⁷ Thus, λ_free = 12.25 cm is shortened to λ_d ≈ 1.39 cm in water. By documented formula,¹⁸ at 2.45 GHz, the lowest-order water sphere resonance occurs at R ≈ 6.9 mm and the second resonance at R ≈ 9.8 mm, each with a rather broad resonant width due to the large loss tangent [see, for example, Fig. 5(b) of Ref. 1].

Instead of varying R to bring out the electromagnetic resonances, we may equivalently vary the incident wave frequency (f) at the fixed sphere radius of R = 7 mm. In this case, the first resonance occurs at ∼2.4 GHz and the second resonance at ∼3.4 GHz. Assume that a plane wave with electric field linearly polarized in the x-direction is propagating in the z-direction. We denote the electric field amplitude of the incident plane wave by E_ext. The magnetic field H_ext is in phase with the electric field with an amplitude given by H_ext = E_ext/377 in SI unit (377 being the impedance of free space in Ohm).

Let the wave be incident on a dimer of two R = 7 mm water spheres on the x-y plane with its axis aligned along E_ext (the most favorable orientation for polarization charge formation across the gap). As in the 27 MHz simulation, we assume E_ext = 400 V/cm for all frequencies simulations. However, the dimer has a frequency-dependent complex permittivity given by the Debye function,¹⁹ 

for exp(−ωt) time dependence, where τ is the temperature-dependent relaxation time. Value of ε(ω = $∞$⁠), ε(ω = 0), and τ can be obtained by a fitting procedure with measured values.²⁰ For water at 25 °C, ε(ω = $∞$⁠) = 5.2ε₀, ε(ω = 0) = 78.36ε₀, and τ = 8.27 × 10⁻¹² (Ref. 20, Table III).

For water, we have used ε/ε₀ = 78.4 + 0.1i for 27 MHz (Refs. 9 and ε/ε₀ = 77.5 + 10i for 2.45 GHz.¹⁷ Question arises as to whether Eq. (2) can yield similar ε/ε₀ at these two frequencies. Simple substitutions give ε/ε₀ = 78.36 + 0.10i for 27 MHz and ε/ε₀ = 77.19 + 9.17i for 2.45 GHz, both being very close to what we used in single-frequency cases.

When the quasi-static condition (λ_d ≫ R) is not satisfied at high frequencies, fields at different points will not oscillate in phase. However, the peak value (amplitude) is of primary interest. Hence, we denote the on-axis electric and magnetic field amplitudes by E_axis and H_axis, respectively. Figure 4(a) plots E_axis (left figure) and H_axis (right figure), normalized to the incident E_axis and H_ext, respectively, as functions of x for f = 10 MHz, 1 GHz, and 1.5 GHz for a dimer with d = 0.2 mm. The x-coordinate range covers the whole dimer, so the gap appears as a narrow region in the figure. It is seen that E_axis/E_ext peaks sharply in the gap region, where we also find E_axis/E_ext≫ H_axis/H_ext.

The frequency range considered in Fig. 4(a) (f < 1.5 GHz) has an in-water wavelength (λ_d > 23 mm) satisfying λ_d ≫ R (= 7 mm). Thus, the dimer falls in the quasi-static near zone and is dominated by the electric field. The quasi-static regime is characterized by a spatial electric field profile essentially independent of f. For example, 27 MHz is deep in the quasi-static regime. It is indistinguishable from the 10 MHz curve in Fig. 4(a) (also true in Fig. 5 below).

Figures 4(b)–4(d) plot E_axis/E_ext (left column) and H_axis/H_ext (right column) for f = 2.45, 6, and 10 GHz for the same gap width of 0.2 mm. As f rises above ∼1.5 GHz, electromagnetic resonances start to appear one after another (band edge first). The x-axis profiles of these resonant modes in the two spheres can be seen in Figs. 4(b)–4(d). In the presence of resonances, the gap electric field is a mixture of polarization-charge field and fringe electric fields of the resonances. However, we may readily identify the polarization-charge part of the field. The steep drop of the electric field on both sides of the gap [Figs. 4(a)–4(d)] indicates a large x-gradient of E_axis; hence, a concentration of polarization charges on the gap surfaces. In other words, the sharp peak of E_axis in the gap region is predominantly due to surface polarizations charges.

Figure 4 also shows a rather broad frequency range of the polarization-charge effect. E_axis/E_ext in the gap decreases from 40 at f < 2.45 GHz, to 30 at f = 6 GHz, then to 12 at f = 10 GHz, an indication that the polarization-charge effect rapidly fades away beyond 10 GHz.

We may look at the problem from a different angle to find the influence of sphere resonances on the polarization-charge field. For simplicity, we quantify the gap electric and magnetic fields by a single value, E_gap and H_gap, respectively, where E_gap = E_axis (x = 0) and H_gap = H_axis (x = 0). Figures 5(a) and 5(b) plot, respectively, E_gap/E_ext (in log scale) and H_gap/H_ext (in linear scale) as a function of f from 10 MHz to 10 GHz for four gap distances d. It can be seen that E_gap/E_ext is the superposition of a smooth polarization-charge field and a much smaller, fluctuating fringe electric field of the resonances. The smallness and fluctuating behavior of the fringe fields are evidenced by H_gap/H_ext in Fig. 5(b).

In Fig. 5(a), E_gap/E_ext at low frequencies (<1.5 GHz) is independent of f, as is consistent with the quasi-static data in Fig. 4(a). As resonances set in at higher frequencies, the fringe fields influence the polarization-charge field positively or negatively. If suffices to focus on the region (∼3 GHz), where the maximum E_gap/E_ext occurs. The fringe fields are seen to add a d-dependent, 0.45–3.4% positive contribution to the quasi-static polarization charge field. Thus, even the strong electromagnetic resonances contribute to the gap electric field in a minor way.

For a detailed simulation of the electrical origin in the presence of electromagnetic resonances in the dimer body, we again consider a dimer oriented parallel to E_ext. To relate to the subsequent experiment, a 2.45-GHz microwave linearly polarized in the x-direction is inputted via a rectangular horn antenna to propagate in the z-direction onto the sample [Fig. 6(a)]. Two R = 7 mm water spheres with a variable gap width are placed side by side along the incident E_ext at a distance of 13 cm in front of the antenna opening. At this position, the incident power varies by ∼1% from the center to the far edge of the dimer. So, the E_ext on the dimer is well represented by its value at the dimer center.

The simulated instantaneous electric field pattern is shown on the x-z plane in Fig. 6(a). The x-y plane electric field amplitude patterns around the dimer are shown in Fig. 6(b) for d = 2, 1, and 0.2 mm. As expected, an electromagnetic resonant mode now appears in each sphere, and there are two important features as discussed below.

First, as the gap width d narrows, there is no observable change of the resonant field profiles (pattern and strength) within each sphere [Figs. 6(b)–6(e)], and the gap magnetic field remains negligibly small [Figs. 6(c) and 6(e)]. Thus, there is no evidence of mode coupling into an electromagnetic hotspot in the gap. This is because the resonant mode under study is formed of a standing wave in the body of the sphere and fringe fields on the outside. The body field of one sphere can hardly be affected by the fringe fields of a neighboring sphere.

Second, in contrast to the gap magnetic field, the gap electric field rises sharply with a decreasing d to values far greater than the body field [Figs. 6(b) and 6(d)], which again shows the polarization charges effect. Thus, in addition to generating electromagnetic resonances in the two spheres, the incident traveling wave has also induced a large polarization-charge electric field in their gap, which can cause an AC air breakdown similar to that in a capacitor.

As an additional note, these results are obtained with the dimer axis aligned along E_ext. We have examined other relative orientations between the dimer and E_ext. The gap electric field always maximizes when the dimer is aligned along E_ext.

In a multimode cavity, the magnitude and polarization of E_ext vary spatially and are highly load-dependent (see Fig. 2 of Ref. 7), which explains the stochastic nature of the sparks taking place in a microwave oven.¹ The resulting difficulty in data reproducibility can be remedied by traveling-wave irradiation [see Fig. 6(a)], which is ∼99% uniform on the sample with a known magnitude and polarization.

For a traveling-wave experiment at 2.45 GHz (see  Appendix A, Part 5, for the experimental setup) in the same configuration as in Fig. 6(a), two R = 7 mm hydrogel spheres are aligned along E_ext and placed 13 cm in front of the antenna opening, where the magnetron power is only sufficient to produce an E_ext (peak) of 100 V/cm (instead of 400 V/cm as in the simulation). Extrapolating from Fig. 5(a), we find that arcing occurs only when the two spheres are almost in contact.

Figure 7(a) displays thermal image of the dimer surface for d = 0.7, 0.1 mm, and 0 after a 10-s exposure to E_ext (peak) ≈ 100 V/cm, which is incident along the z-direction and linearly polarized in the x-direction. Arcing barely starts at d = 0.1 mm and becomes stronger at d = 0. The maximum temperature measured in situ by an IR camera on the side surfaces of the gap is 52.7 °C for d = 0.1 mm and 83.2 °C for d = 0 vs an initial temperature of 22 °C. Because of insufficient magnetron power, no sparks have been observed for both d = 0.1 mm and d = 0. However, arcing is witnessed by the thermal hotspots on gap surfaces.

To check the wave polarization effect, we rotate the dimer in Fig. 7(a) by 90° on the x-y plane, so that its axis is aligned perpendicular to the E_ext. As in the 27 MHz experiment in Fig. 3(d), no temperature rise has been observed after a 10-s exposure [Fig. 7(b)].

As a final note, the infrared camera gives the thermal image of the surface temperature. While a hotspot on gap surfaces can provide evidence of arcing, the surface temperature profile (especially after arcing) by no means represents the actual electromagnetic field distribution [e.g., Fig. 7(b) above or Figs. 3(b), 3(e), and 3(h) in Ref. 1]. For a direct display of field profiles, numerical simulations should be resorted to [e.g., Figs. 6(b)–6(e) above or Figs. 3(c), 3(f), and 3(i) in Ref. 1].

The observation of sparks in aqueous dimers in a dominantly electrical environment at 27 MHz proves the existence of an electrical origin for the phenomenon. Specifically, the strong electric field required for air arcing comes from a 2–3 orders-of-magnitude buildup of ±ρ_pol on opposite sides of the dimer gap. This is supported by the consistency of predicted and observed threshold conditions as well as by the absence of sparks upon a 90° rotation of the dimer relative to E_ext. Further simulations over a broad frequency range as well as the observed gap arcing and sphere attraction at 2.45 GHz indicate the viability of the electrical origin even in the presence of the first few electromagnetic resonances in the dimer. These results, to our knowledge, shed new light into the basic properties of isolated dimers. It may hopefully be a useful reference for current investigation of the electromagnetic behavior of complex systems.

See the supplementary material for optical movies showing the sparks for the d = 0.2 mm and d = 0 at 27 MHz with the legends “Real-time sparks between two R = 7 mm hydrogel spheres with 0.2 mm gap in a 27 MHz capacitor” and “Real-time sparks between two R = 7 mm hydrogel spheres with 0 gap in a 27 MHz capacitor,” respectively. An optical movie showing the attractive motion and the eventual sparks is presented in a supplementary movie with the legend “Real-time attraction between two R = 10 mm hydrogel spheres on a flat surface, d (initial) =1.5 mm and f = 2.45 GHz.” Two larger-radius (R = 10 mm) spheres on a flat horizontal surface were placed 2 cm from the horn opening for a greater attractive force and clearer attractive motion. The sphere attraction at 2.45 GHz serves as further evidence for the electrical nature of the gap field. The R = 10 mm spheres are in strong electromagnetic resonance in the second mode. If an electromagnetic hotspot were present in the gap, its radiation pressure would have generated a repulsive force.

Another point of interest concerns the role of water vapor under 2.45 GHz radiation. The heating rate is proportional to f, ε″ (imaginary part of ε) and the square of the local electric field (Ref. 6, Chap. 7). Heating of the hydrogel spheres at 2.45 GHz, thus, evaporates far more water vapor than at 27 MHz. Either the E_ext or air arcing can subsequently create a water vapor plasma, which then plays a role commensurate with its density. An experimental resolution of the water vapor effect is beyond the capability of our facility.

The authors are grateful to ANSYS, Inc. for generously providing the HFSS software used throughout this research, to Wave Power Technology for providing technical assistance on their 2.45 GHz magnetron, and to H. H. Teng for helpful discussions on the HFSS software. This work was funded by the Ministry of Science and Technology, Taiwan, under Grant No. MOST109–2112-M-002–018.

The authors have no conflicts to disclose.

K.R.C. conceived the idea and wrote the manuscript with input from all authors. L.C.L. and M.S.L., who contributed equally to this work, performed the simulation and experimental research. L.R.B. designed and fabricated the 27 MHz experimental system and supervised its use. Y.F.T. refined the experimental systems and participated in the measurements.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

All simulations were performed using the Ansys HFSS (high-frequency structure simulator) software, which solves the full set of Maxwell equations by the finite element method (http://anlage.umd.edu/HFSSv10UserGuide.pdf). In our simulations, PMLs (perfectly matched layers) are assumed on a closed boundary, which encloses the entire simulated structure. PMLs are fictitious materials that fully absorb the electromagnetic fields acting upon them. This is consistent with the rapidly decaying fringe fields out of the 27 MHz capacitor and the absorbing walls of the anechoic chamber in the 2.45 GHz experiment.

The only samples used in the experiment are the commonly available hydrogel spheres, which are polymer networks extensively swollen with water. The average weight of each is 0.019 g (dry) and 1.437 g (swollen with water to 7 mm radius). So, the water content is ∼99% by weight. Dry polymer networks were placed in tap water at room temperature for about 2 days before the experiment. The hydrogel spheres were taken out for the experiment as soon as they had expanded to the desired radius. Each sphere was used only once. Figure 8(a) shows the relative sizes of the dry polymer network and the swollen hydrogel sphere.

Figures 8(b) and 8(c) show two hydrogel spheres placed in the sample holder for the 27 MHz and 2.45 GHz experiment, respectively. The sample holder for the 27 MHz experiments [Fig. 8(b)] is 4 cm in height, 4 cm in width, and 2 cm in thickness. It can be inserted between the capacitor plates (4 cm in separation) in either parallel or perpendicular orientation to E_ext. The sample holder for the 2.45 GHz experiments is shown in Fig. 8(c). The radiation (with E_ext parallel or perpendicular to the dimer axis) comes vertically down from the horn antenna.

The sample holder is made of a rigid polyurethane foam (Eccostock SH4). According to the manufacturer's data sheet, it is a heat insulating material that can withstand a temperature up to 135 °C. It has a density of ∼0.08 g/cc, dielectric constant of ∼1.08 (at 1 MHz), loss tangent of ∼0.0015 (at 1 MHz), and dielectric strength of ∼1.6 × 10⁴ V/cm. For the dielectric constant and loss tangent, the manufacturer gives only 1 MHz data, but General Plastics tested their polyurethane foam at 1, 5, and 10 GHz (https://docplayer.net/50164587-Polyurethane-foam-dielectric-materials-for-use-in-radomes-and-other-applications.html), which fall within ±5% of the 1 MHz data for Eccostock SH4.

We used a Flir Tau2 336 infrared camera to obtain thermal images of the sample during the experiment. The infrared camera has a 35 mm lens, a resolution of 336 × 256 pixels, a sensitivity of <60 mK, and a 30 Hz maximum frame rate (https://www.flir.com/products/tau-2/?model=46336035H). It is always placed in a weak field area and is also enclosed in a shielded aluminum box (except for an aperture for an observation port) for extra protection [see Figs. 9(c) and 10(b)]. We have never observed any effect by RF or microwaves on our IR camera.

An overview of the 27-MHz applicator system is shown in Fig. 9(a). The applicator shielding box with tuner controls is on the right. A 1.5 kW CW power tube amplifier is on the left. A power meter measures forward and reflected powers with a trip relay for system protection. A 5-W transmitter source, a variable attenuator, and a 300-W solid state amplifier are used to drive the power tube amplifier. An rf SPDT switch connects the power source to the applicator or a load. All power transmission lines are LMR-400 type low loss coaxial cable with 100% shield coverage.

Figure 9(b) shows the inside of the applicator box with capacitor plates. The rf matching configuration is a pi C-L-C matching circuit that can transform 50 Ω impedance power up to at least 10⁵ Ω. The input variable capacitor is 25 to 800 pF rated for 1 kV peak, and the variable rf power inductor is 0–15 μH modified to withstand 15 kV peak. The unloaded Q of this circuit is ∼150 but varies with the capacitor size and spacing. When there is no rf absorbing material between the capacitor plates, nearly 100% of the rf loss is in the inductor. The blower-cooled inductor can handle 300 W of power absorption. When an rf absorbing load is placed between the plates, higher input power can be applied. A capacitor divider probe in the bottom plate is calibrated by applying a few watts of rf power and measuring the total capacitor voltage at a particular plate spacing with a high frequency 300+ MHz scope probe. The estimated measurement error is ±10%. All components inside the shielding box [Fig. 9(b)] are rigidly fixed. The box can be rotated by 90°, so that the capacitor becomes vertical.

The 2.45 GHz experimental system (Fig. 10) is the modified version of a 24 GHz system.²¹ The microwave source is a commercial 3-kW, 2.45-GHz magnetron. The 2.45 GHz wave passes through a protection device (a circulator) and a diagnostic circuit for power and frequency measurements [Fig. 10(a)] before entering into a 60 × 60 × 60 cm³ anechoic chamber [Fig. 10(b)] via a rectangular horn antenna [same dimensions as in Fig. 6(a)].

The chamber walls are lined with pyramid-shaped radiation C-RAM SFC-HC-3 absorbers (>99% absorption) to prevent reflections [Fig. 10(b)]. So, the sample is irradiated by a nearly un-interfered traveling wave. A height-adjustable infrared camera is mounted outside the chamber wall to take thermal images of the sample during the experiment.

Compared with the multimode standing waves in a cavity, the traveling wave allows polarization and magnitude control of the fields on the sample, hence much higher data reproducibility. However, this is at the expense of field strength. For the same input power, the field strength of a traveling wave can be much weaker than that of a standing wave in an unloaded resonant structure.