Breakdown threshold measurement

First, we experimentally measured the threshold electric field for plasma breakdown with and without the radioactive material (0.64 mCi 60Co). Then, we compared the measured values to the theoretical Paschen curves for Ar and air, as illustrated in Fig. 1 (refs 9, 10). The maximum available gyrotron power of 32 kW corresponds to an electric field of 3.49 kV cm−1 (the horizontal dotted green line in Fig. 1). Here, we defined the threshold electric field as the electric field at which 100% breakdown with 20 μs pulse duration of 1 Hz repetition rate occurred in 200 shots experimentally. The distance between the focused spot of the electromagnetic (EM) wave and the radioactive material was set to 20 cm. The measured threshold electric fields without radioactive material are generally in good agreement with the theoretical Paschen curve in the Ar case at pressures between 4 Torr and 100 Torr, the range in which the maximum EM power was above the theoretical threshold breakdown power. In this pressure range, the experimentally measured threshold field in the case in which the 60Co source was present is ∼1.7 times lower than that without the source11. This difference resulted from the generation of a large number of secondary electrons because of the interaction between the gamma rays and the neutral Ar gas molecules, which had low energies (<1 MeV) due to Compton scattering. Discrepancies between the measured and theoretical values are evident at pressures above 100 Torr12. The measured data also show that plasma breakdown occurred at pressures >250 Torr in Ar when the radioactive source was present. Until now, plasma breakdown in an applied electric field significantly lower (∼4 times lower) than the threshold field has not been reported. However, as shown in Fig. 1, plasma breakdown is observable in the presence of radioactive material due to possible plasma formation in this situation in both Ar and air. Specifically, plasma breakdown is evident at 760 Torr (ambient atmospheric pressure) both in Ar and air with 100% probability of plasma occurrence when the radioactive material was present (no breakdown would be observed at this pressure without radioactive material, of course). Neither the photodiode nor the spectroscopic signal probe picked up the emitted light in the 200–1,000 nm wavelength range due to the extremely low photon intensity; however, the delay time was measurable using the radio-frequency (RF) diode signal when the radioactive material was present. In air, the electric field required for breakdown was >3.5 kV cm−1 throughout the pressure range. However, we observed plasma breakdown in air when the radioactive material was present in under-threshold conditions. For the air breakdown experiment, we performed tests at two representative pressures: 60 Torr and 760 Torr (black circles in Fig. 1), corresponding to the pressure applied in the presence of the minimum threshold field and atmospheric pressure, respectively, and observed the RF pulse shapes in the under-threshold and threshold conditions. Figure 2 depicts the RF pulse shapes obtained when breakdown occurred. The RF pulses were not attenuated completely in the cases in which the incident EM field was much lower than the threshold field, that is, in the under-threshold conditions (60 Torr and 760 Torr in air, and 760 Torr in Ar). Meanwhile, the RF pulse corresponding to 30 Torr in Ar is attenuated almost to zero, indicating that these conditions are the threshold conditions. The density of the formed plasma can be estimated by measuring the RF pulse amplitudes shown in Fig. 2. The transmittance of the EM beam was calculated using a plasma slab model, which is described in detail in Supplementary Note 2. The plasma densities were estimated to be 6.44 × 1013cm−3 at 760 Torr in air, 6.23 × 1013cm−3 at 760 Torr in Ar and 5.87 × 1013cm−3 at 60 Torr in air.

Figure 1: Measured threshold fields for breakdown and theoretical Paschen curves for Ar and air. All of the points (blue crosses, red plus signs and black circles) represent measured data, and the lines (black and blue) represent the theoretical curves. For Ar, measured data are depicted for the cases without radioactive material (blue crosses) and with 0.64 mCi of 60Co (red plus signs). The measured threshold electric field had 0.15 kV cm−1 variance. The electromagnetic (EM) wave power was not sufficiently high to induce breakdown in the absence of the external radioactive source at pressures >250 Torr in Ar. However, even though the output power of the gyrotron was insufficient to initiate avalanche ionization, saturation breakdown is observable even at 460 Torr, due to the generation of free electrons by the 60Co source. The maximum output electric field of the gyrotron, ∼3.49 kV cm−1, is below the required threshold electric field (∼15.7 kV cm−1 at 760 Torr in Paschen curve) in Ar and air (black dotted vertical line). However, the observed plasma breakdown indicated by the black circles at 60 Torr and 760 Torr in air and 760 Torr in Ar present the possibility of plasma breakdown in the presence of radioactive material at powers lower than those predicted theoretically. Full size image

Figure 2: RF diode signal waveforms attenuated due to plasma formation in the path of the RF beam. Typically, the radio-frequency (RF) pulse is turned on at around 15 μs and maintained for 20 μs, as indicated by the black curve, which was obtained without a source. The RF pulses drop quickly because they are attenuated immediately upon plasma formation. The RF signals do not completely drop to zero in air at 60 Torr or 760 Torr or in Ar at 760 Torr, enabling estimation of the plasma density. (For comparison, in Ar at 30 Torr, the RF diode signal represented by the pink dotted line drops almost to zero since the incident RF power is above the threshold power for breakdown, and the plasma density reaches the critical density). Full size image

Ar plasma with radioactive material

Next, we focus on the Ar gas experiment conducted in the presence of the radioactive material since the gyrotron output power was sufficient to form Ar plasma at pressures between ∼2 Torr and 250 Torr, as shown in Fig. 1, which enabled us to study the plasma formation in the presence of the radioactive material in greater detail. A distinct difference between the delay times obtained in the presence and absence of the radioactive material is evident. The probability of no breakdown for the formative delay time can be expressed as7,13

where (cm−3) is the average value of the number of electrons per volume. Further, the electron density approaches the critical density (n cr ≈1014 cm−3) at 95 GHz when the plasma frequency is the same as the angular frequency. P 1 (N) represents the formative delay time, which is the probability of an avalanche reaching a size corresponding to an electron density n.

The probability distribution for the statistical waiting time for the avalanche such that zero electrons are found until per volume up to time, t, can be formulated

where S is the average generation rate of initial electrons owing to the stochastic seeding source in the volume12. We assume that the density of free electrons generated by the decay of 60Co in the breakdown volume is constant and that the source term S is independent of the inner pressure of the chamber, as the primary seed electrons from the radioactive material have high average energies (∼0.44 MeV). Hence, the rate of attachment to the molecules can be considered to be the same under all pressures. By combining the two probabilities, that is, those for the formative and statistical delay times, the fitting curve can be obtained by changing the source S for the radioactive material case (black dashed line in Fig. 3) (Supplementary Note 3).

Figure 3: Probability of no breakdown as a function of the delay time. (a–c) At each pressure, the delay time was measured when the threshold RF electric field was applied. The threshold RF electric field amplitude was defined as the applied RF electric field amplitude at which 100% plasma breakdown with 20 μs pulse duration occurred over 200 shots at a repetition rate of 1 Hz. The measured electric field variance was 0.15 kV cm−1. The red crosses and blue circles indicate the experimental data obtained with and without the radioactive source, respectively. The theoretical curves (black dashed line) were calculated using the Laue plots in combination with the formative and statistical waiting times, as described in Supplementary Note 3 (refs 7, 13, 14). Full size image

Figure 3 depicts the probability of no breakdown as a function of the delay time. The experiment used to obtain these data was performed using an electric field with an amplitude equal to the threshold value necessary for plasma breakdown at each of the pressures. The black dashed lines indicate the theoretically calculated delay times described above. The delay times represented by the absence of the radioactive material (blue circles) increase as the pressure increases from 30 to 250 Torr. It is evident that the statistical plasma formation delay time distributions extend to longer times in the absence of the radioactive source. The measured minimum delay time in the presence of the radioactive material is <2.4 μs for each of the pressures, as shown in Fig. 3. At 250 Torr, not only the statistical delay time, but also the formative delay time, is reduced significantly in the presence of the radioactive source. These characteristics are strong indicators of the presence of a radioactive source nearby.

With increased confidence that the existence of radioactive material significantly changes the delay time before breakdown, we evaluated the ability of the proposed method to indicate the presence of radioactive material in real time. A remotely controllable gate was mounted on the chamber containing the radioactive material. We monitored the delay time before plasma breakdown for each EM pulse and performed real-time measurements as a function of time with (gate open) and without (gate closed) the radioactive source, as well as with different distances between the radioactive source and the EM beam focal point. Figure 4a shows that the gyrotron’s ability to indicate the presence of radioactive material in real time is strong. The delay time is markedly shorter in the presence of the radioactive material; thus, it could be detected in real time. Comparison of the data obtained with (red circles) and without (blue squares) the radiation source indicates that the delay time distribution in the ordinary state is significantly wider than that in the presence of the radioactive source, since the free electrons present in this case have a more random distribution in time. In addition, the average delay time and the width of the delay time distribution both increase in the presence of radioactive material as the distance increases from 20 to 120 cm (given the limitations of the laboratory setup, the distance could be at most 120 cm), as shown in Fig. 4b. The centres of the delay time distributions obtained with the radioactive material present, which are indicated by the red dotted line, shift to the right and become closer to those of the distributions obtained without the radioactive material, which are indicated by the blue dotted line in Fig. 4b. The delay time distributions over 200 shots with and without the radioactive material are distinctly separated when the detector is close to the source. Although they start to overlap when the distance is 120 cm, they are still discernable, which demonstrates the sensitivity of the measurement technique. As shown in Fig. 4b, the delay times with and without radioactive material can be distinguished from one another up to ∼120 cm.

Figure 4: Experimentally determined real-time ability to detect the presence of radioactive material. The experiment was implemented at 19 kW and 250 Torr. (a) Real-time measurement of the total delay time with and without the radioactive source. The source was in a lead box 20 cm from the focal point, and the lead box was opened and closed every 50 shots by an autocontrolled gate. The minimum delay times required for discharge with and without the source were ∼2.2 μs and 4.1 μs, respectively. (b) Delay time distributions measured with the 60Co source 20–120 cm from the EM beam focal point. The delay time distributions obtained with and without the radioactive source are distinct from one another at each of the distances. Full size image

Detection sensitivity

Experimentally, we could detect 0.5 μg (equivalent to 0.64 mCi activity) of 60Co up to ∼120 cm away from the focus of the incident EM wave, as shown in Fig. 4b. Now, we compare these experimentally obtained detection sensitivities to the theoretical results calculated based on plasma on/off phenomena. The theory assumes that the incident EM beam is focused and that there is rarely a free electron present in the breakdown-prone volume in the absence of radioactive material within the pulse duration of the incident EM wave, resulting in close to zero probability of breakdown. The theoretically detectable mass (M(g)) of 60Co can be calculated using the following previously reported formula14:

where L γ,a =1/n a σ a (=280 m, n a is the density of air) is the range of gamma ray propagation and is determined by the average absorption cross-section, σ a ; d is the distance from the radioactive source to the focused beam spot; A is the specific activity, which is 1.1 × 103 Ci g−1 for 60Co; V=0.17 cm3 is the breakdown-prone volume corresponding to , the ratio of the wave power to the threshold power in the focal plane; τ THz is the pulse duration (s); is the ratio of the energy required to produce one secondary electron–ion pair to that of the primary electrons generated by the gamma rays; is the ratio of the ionization frequency to the effective ionization (net ionization) frequency; and L γ =1/n a σ T (=130 m) is the gamma ray propagation distance and is determined by the total interaction cross-section, σ T , in air. Using equation (3), the detectable masses of 60Co at 20 and 120 cm were calculated to be 0.067 mg and 2.4 mg, respectively. Considering that there are distinct differences between the delay times with and without radioactive material that were measured at distances of 20–60 cm (Fig. 4b), the experimentally detectable mass of 0.5 μg corresponds to a sensitivity at least 130 times greater than the theoretical sensitivity determined based on plasma on/off phenomena. The delay times with and without radioactive material those were measured at 120 cm still exhibit noticeable differences (Fig. 4b), in which case the sensitivity increases to 4,800 times the theoretical sensitivity. The discrepancies between the experimentally determined and theoretically predicted minimum detectable masses are attributed to the fact that our experiment was based on using plasma delay time measurements to discern the presence of the radioactive material, whereas the theory was based on plasma on/off phenomena. Thus, plasma breakdown delay time measurements result in more sensitive detection than does reliance on plasma on/off phenomena. Our increased sensitivity may also relax the frequency requirement of the millimetre/THz-wave source.

Under-threshold breakdown with radioactivity in Ar and air

In the previous subsections, we discussed the breakdown of Ar in the presence of radioactive material. An air breakdown study with radioactive material at atmospheric pressure was also necessary to prove the effectiveness of the proposed idea in a real environment. However, the maximum possible electric field intensity for the gyrotron was lower than that according to the theoretical Paschen curve of air, as shown in Fig. 1. Nonetheless, very interestingly, we experimentally observed under-threshold breakdowns, that is, breakdowns that occurred in applied electric fields much weaker (more than four times weaker) than the threshold field necessary for plasma formation in the vicinity of the radioactive material. Of course, no plasma breakdown occurred in the absence of radioactive material in this electric field.

First, we investigated the under-threshold breakdown with radioactive material in Ar at 760 Torr. As shown in Fig. 5a, the delay time is not widely distributed as it was in Fig. 3 (the delay times are not statistically distributed) since the existence of radioactive material eliminates the statistical nature of the delay time distribution. The delay time decreases significantly as the output power increases. Figure 5b demonstrates the feasibility of using the proposed method for real-time radioactive material detection and shows that the delay time is dependent upon the EM power. The delay times were measured in real time with and without the radioactive material as the incident EM power was varied. No breakdown was observed at either 30 or 32 kW when the radioactive material was absent, as indicated by the hatched regions in Fig. 5b. Clear differences are evident between Figs 4a and 5b; both cases indicate that the presence of the radioactive material caused the statistical nature of the delay time distributions to disappear in real time, but under-threshold breakdown (Fig. 5b) is impossible without exposure to radioactive material.

Figure 5: Experimental delay time measurements in the presence of radioactive material in Ar gas. (a) Probability of no breakdown versus delay time. (b) Real-time measurements of delay time variations at output powers of 30 and 32 kW. No breakdown is observed in the absence of radioactive material, as indicated by the grey hatched regions. Full size image

The theoretical Paschen curve (Fig. 1) predicts that almost the same threshold electric field is required for plasma breakdown at atmospheric pressure in air and in Ar when there is no radioactive material12. However, with radioactive material nearby, the threshold electric field is significantly reduced, according to the Ar gas experiment. The experimental results obtained using Ar gas suggest that plasma breakdown may be possible in air at 760 Torr, even if the incident EM power is much lower than the threshold power. Therefore, we performed the air breakdown experiment in the presence of the radioactive material. The output power of the gyrotron was varied between 29 and 32 kW at 60 Torr and 760 Torr in air. According to the Paschen curve, 60 Torr is the minimum threshold pressure for pressurized air breakdown (Fig. 1). The distance between the radioactive source and the focal point of the incident EM beam was set to 20 cm for the experiment, which was performed in ambient air at a temperature of 23 °C (±0.5 °C) and a humidity of 62% (±2%).

We successfully observed plasma breakdown in air at 60 Torr and 760 Torr in the presence of 0.64 mCi of 60Co with incident EM powers of ∼30 kW, that is, around ten times smaller than the power required for plasma breakdown without radioactive material. Figure 6a,b depict the probabilities of no breakdown at different incident EM powers in the presence of radioactive material at 60 Torr and 760 Torr, respectively. The breakdown delay times shown in Fig. 6c,d were measured in real time, similarly to in the Ar experiment. Breakdown cannot occur without radioactive material, as indicated by the hatched regions in Fig. 6c,d. The measured delay times as well as the dispersions of the delay times in Ar and air at 760 are in close agreement with one another (Fig. 5b for Ar at 760 Torr versus Fig. 6d for air at 760 Torr). These results represent the clear experimental demonstration of the real-time monitoring of radioactive material in ambient air by using a low EM power (∼30 kW) to initiate the plasma. We also observed the dependence of the delay time on the incident power, as shown in Fig. 6e. As the pressure increases, the delay time increases accordingly due to the increase in the power required for plasma breakdown. Also, the delay time becomes shorter as the incident EM power increases at a fixed pressure.

Figure 6: Delay times experimentally measured in the presence of radioactive material in Air. (a,b) Probability of no breakdown versus delay time at 60 Torr and 760 Torr, respectively. (c,d) Real-time delay time measurements obtained at 60 Torr and 760 Torr, respectively, along with 50% of the cumulative data measured with respect to the initial delay time. A gate on the lead box enclosing the radioactive source was opened and closed every 30 s by an autocontrolled gate. (e) Dependence of delay time on pressure at various EM powers. Full size image

The considerable reduction observed in the measured threshold electric field (∼3.5 kV cm−1 during the experiment performed in the presence of radioactive material versus ∼16 kV cm−1 in theory in the absence of radioactive material) necessary to initiate plasma breakdown in air at atmospheric pressure in the presence of radioactive material requires further analysis. We postulate that the increased conductivity in the breakdown-prone volume leads to the reduction in the electric field amplitude necessary for breakdown. We introduce a field-reduction factor, β, to express the reduced electric field required for breakdown owing to the presence of radioactive material:

where (Supplementary Note 4). Here, n 0 is the seed electron density when there is no radioactive material; for typical atmospheric cases, a seed electron number density of 1–10 cm−3 is widely accepted. n 0 * is the seed electron density in the presence of radioactive material, and n cr is the critical plasma density at 95 GHz. Because the radioactive material generates high-energy gamma photons, high-energy electrons are produced in turn. The initial high-energy electrons with a density of n 0e produce secondary knock-on electrons via collisions with the molecules present in the breakdown-prone volume. To produce one secondary electron–ion pair, an average energy of ∼34 eV is needed11. The energy distribution of the gamma photons and high-energy electrons of 0.64 mCi 60Co at 20 cm from the source can be determined using Monte Carlo N-Particle eXtended (MCNPX ver. 2.50) code (Supplementary Fig. 2). The calculated number of secondary knock-on electrons produced by a single high-energy electron is ∼12,600 (Supplementary Note 4). Considering the pulse length of the applied RF field (∼1 μs) before the formation of the plasma, the total secondary knock-on electron number density attributable to the high-energy electrons is ∼1.3 × 108cm−3 (Supplementary Note 4). The significant increase in the number of background-free electrons owing to the high-energy electrons generated by the radioactive material results in an increase in the conductivity of the RF-focused volume, resulting in breakdown in the area. The field-reduction factor increases gradually as the number of background-free electrons increases (Supplementary Fig. 3). For an initial seed electron number density of 1.3 × 108cm−3, the calculated value of β is ∼2.5, which means that the required electric field is reduced by a factor of 2.5 as compared to the field required when a radioactive material is not present. On the basis of this analysis, the reduction in the electric field required for breakdown (experimentally determined reduction factor of 4 versus theoretical reduction factor of 2.5) can be understood to a certain extent, although a slight discrepancy still exists between the experimental and theoretical observations. The additional reduction observed experimentally may be due to uncontrollable experimental conditions, including the fact that the exact molecular contents are unknown and an aerosol may be present11,12.

Sensitivity and detection range limitation

Finally, we determined the detection range of the setup by measuring the plasma breakdown probability as a function of the distance. For these measurements, the incident gyrotron beam was irradiated 300 times with a repetition rate of 1 Hz at each pressure. The measurements were performed at a pressure of 400 Torr in Ar with an incident EM wave power of 28 kW, in which case plasma breakdown did not occur in the absence of the radioactive material. Figure 7a shows that the probability of a plasma avalanche occurring decreases d increases. To investigate this phenomenon, we simulated the generation of free electrons by applying the same conditions that were employed in our experiment and using the MCNPX code (data denoted by red circles in Fig. 7a). The average number of free electrons in a volume of 1 cm3 decreases with increasing distance, with the number eventually decreasing to 1 electron cm−3 at a distance of 270 cm from the beam focal point; this value is approximately the same as the number of background electrons. In the short-distance (d<<L γ ) approximation, the photon density decreases with 1/d2 (ref. 14). The simulated average numbers of free electrons that are presented in Fig. 7b closely follow the expected trend. In addition, the exponential decay of the probability as a function of distance was observed, and the results are shown in Fig. 7c. The probability of plasma breakdown becomes <20% at distances >220 cm, at which the average number of free electrons is <2.

Figure 7: The probability of plasma breakdown and MCNPX results. Experimentally determined plasma breakdown probability and MCNPX-simulation-based average number of free electrons as functions of distance. Under normal conditions (that is, in the absence of the radioactive source), plasma breakdown is not observable for an incident power of 28 kW in Ar at 400 Torr. (a) Plasma formation probability, which decreases exponentially with increasing distance, and average number of free electrons, which decreases in proportion to 1/d2. The circles and diamonds represent the MCNPX simulation results and the experimentally measured data, respectively, and the dotted curves are the fit curves. (b) Linear fit of the average number of electrons to 1/d2. (c) Linear fit of the logarithm of the probability to d. The linear fits are in excellent agreement with the experimental data. The R2 values represent how close the data are to the regression lines. Full size image

In an actual situation, the incident EM wave can be emitted from far away (at a distance R) by using an antenna, as shown in Fig. 8. The location of breakdown due to the radioactive source can be adjusted to increase the detection sensitivity. At 95 GHz, an antenna size of 1.2 m enables the detection range to be 1 km from the source. However, air turbulence may limit the maximum focal location. Let us consider the effect of beam wander on the detection range15. For the weak turbulence case, the detection range R is

Figure 8: Schematic of a possible setup for the detection of radioactive material inside a container. The distance from the high-power EM source to the breakdown point is , where D is the size of the antenna’s aperture, and λ is the wavelength of the incident beam. Full size image