Remote Detection of Radioactive Material on the Basis of the Plasma Breakdown Using High-Power Millimeter-Wave Source

Introduction

Breakdown discharge

In the 1900s, the gas discharge field was established as a school of physics by John Sealy E. Herlin introduced gas discharge into the microwave regime, and the beginning of the decomposition experiments were performed with noble gases instead of air due to the complex chemical structure and physical reaction of air molecules. In the microwave regime, theoretical and experimental approaches to gaseous plasma breakdown in the atmosphere were improved by A.D.

Gyrotron oscillator

Motivation

Near the hazardous source, a high-intensity EM beam is emitted, resulting in immediate plasma breakdown at the focal point due to the high average number of free electrons generated by the radioactive material [12].

Thesis outline

The derived probability based on the formative delay time is a function of electric field amplitude and pressure. Latency analysis for plasma breakdown is another outstanding piece of evidence for the existence of radioactive material. A new finding of this study was the reduced required electric field with the presence of radioactive material.

Theoretical & Mathematical Development

Estimation of plasma density for under-threshold condition

There are two types of plasma structure; the plasma behaves as a mirror in the overdense case where the angular frequency (ω) is less than the plasma frequency (ωp). The other is the subdense structure when the angular frequency is greater than the plasma density, so the plasma acts as a nonlinear refractive medium. Here, we introduce the low plasma state to consider the attenuated RF wave between two dielectric media [17].

The incident EM wave is a layered dielectric medium and is not completely absorbed by the conductor. The following expression is given to calculate the refractive index of the conducting medium. For a TE wave, the reflection and transmission coefficients at the first interface are given by

Similarly, the amplitudes ρ23 and τ23 are amplitudes, and ϕ23 and χ23 are phase changes at the second boundary for the reflection and transmission coefficients given by. By combining the equations of (2.9) to (2.14), the solution for the reflection and transmission is written as. Based on the formalism described in this section, the plasma density will be calculated using the measured transmission values ​​during the experiment in section 4.2.1.

Theoretical derivation of delay time for Ar plasma

However, the presence of the radioactive material indicates that the statistical delay time always has the same distribution formula due to the free electrons generated by the radioactive material. Due to the presence of the radioactive material, the S term must be permanently stable to fit. The location of the focusing mirror is 60 cm from the gyrotron center, shown in Figure 3-2.

Second, we also calculate the transmittance and reflectance for the appropriate window size [24]. This measurement is performed by means of a standard W-band wave with a bend for the direction of the electric field. From this motion of the plasma image, the plasma velocity was calculated as 16.75 km/s.

The combined data was simplified from the minimum delay time to 50% of the total sample amount. As the distance increases from 20 cm to 120 cm, the spread of the delay time also spreads further. The reason for the reduction is due to the decrease in the average number of free electrons [28].

This electric field amplitude was measured in compressed Ar gas and atmospheric air.

Experimental Setup for Radioactive Material Detection

Components for plasma breakdown measurement

• Focusing mirror
• Chamber window
• Detectors for incident RF wave and fluorescent light
• Radioactive material; 0.64 mCi of 60 Co

An electric field integral equation code 'Surf3d' is used for the design of a focusing mirror [22]. Based on the characteristic of the output beam from the gyrotron window and calculation using quasi-optical equation, the curvature of Rx and Ry is determined by 19 cm and 37 cm, respectively. The incident ray from the window is reflected and focused 18.5 cm away from the center of the focusing mirror.

When we determine a window material for the vacuum chamber, the most important parameters are the transmission and the absorption. A fused silica (SiO2) was chosen as the window material which was the same as the gyrotron's window. To calculate the thickness and opening size, we first derive the equation for a minimum thickness of the window needed to withstand an external pressure [23].

The fused silica is used for the material of the window the same material of the gyrotron's window. Here, xmn is the Bessel zero of the mode, and D is the diameter of the window. We also prepare one fixed 20 dB attenuator and one variable attenuator with detector by Millitech Incorporated, model DET-10 to modulate the incoming signal from the output power of the gyrotron.

In our experiment, a kind of disc of radioactive material is adopted and positioned in the center of the hole of the bullet chamber (see Fig. 3.

Figure 3-1: Normalized power of the microwave output beam at 95 GHz

Schematic design for plasma breakdown experiment

With an analysis of the relationship between the presence of the radioactive material and the required electric field, the different pressure conditions are required to study for statistics. The t2 is determined that RF wave signal rapidly decreases after the creation of the plasma discharge. The plasma breakdown with a beam of light was performed up to 250 Torr without external source, and the data were plotted with and without casing.

This is an important limitation to ensure the distance of the detection range. Although most of the delay time spread region was overlapped at 120 cm, we could still distinguish the delay time spread due to the presence of radioactive material. As estimated, the probability of breakdown discharge decreased as the amount of free electrons decreased.

The failure phenomenon was observed only in the case of a radioactive source, and the weakened RF signal disappeared after the radioactivity was removed. Under these conditions, R varies from 50 m to 1 km, depending on the strength of the turbulent parameter. Therefore, it is advantageous for the wavelength to be longer, since R depends on the size of the focused incident EM beam.

The theoretical delay time composed of the formative delay time and statistical delay time was derived to compare the experimental data.

Figure 3-10: Experimental setup for the measurement of plasma discharge delay time with radioactive material

Results of Plasma Breakdown for Radioactive Material

Experimental results for Ar plasma breakdown

• Plasma breakdown image
• Plasma velocity
• Spectroscopy

At 300 Torr, the incident power was close to the 100% no-occurrence threshold value for the initiation of plasma breakdown to prevent the propagation of plasma formation. The observed filament array was called a "fishbone" structure and was about 1.04 mm that had a small discrepancy of the known parameter, λ/4 (=0.79 mm) due to plasma diffusion and camera resolution. However, the plasma propagates in the opposite k' direction of the incident wave because the plasma performed as a conductor and the beam intensity was high along the opposite direction as the plasma occurs at the focal point.

Plasma velocity measurement was performed in the threshold electric field of 100 Torr with Ar gas using an intensified charge coupled device (ICCD), Andor iStar 320T Gen3 model 18F-63. The second image was taken after 0.4 μs of plasma build-up and the peak plasma intensity shifted 0.66 cm. Fluorescent light was collected for 1 s of signal integration, and a background signal was eliminated as reference data.

Figure 4-1: Plasma image measurement for the measurement of plasma discharge delay time

Experimental results for breakdown threshold electric field

These considered plasma densities did not reach the critical density, which was defined that the angular frequency was the same as the plasma frequency for the plasma avalanche ionization to occur.

Figure 4-4: Theoretical Paschen curve and experimental measurement of threshold electric field for breakdown in Ar and air

Experimental results for delay time

• Delay time in Ar condition
• Delay time in air condition

In other words, the minimum delay time over 200 samples in normal mode is 2.88 μs, and the total data is listed in ascending order. Due to the existence of radioactive sources, both formative delay time and statistical delay time were reduced in total pressure. The delay time distribution without source (blue circles) is much wider than with mode (red squares).

The operation of the gyrotron oscillator was at 19 kW and 250 Torr, the same as previous experiment. The increased delay time as the distance grows has a close affinity with the average number of free electrons. 4-10(a), the distribution of delay time in both 30 kW and 32 kW is narrow, and the starting point of the formative delay time for 32 kW is shorter than 30 kW.

Same trend with light emission of plasma breakdown, the higher output power of the microwave beam reduces the delay time at fixed pressure. It is almost impossible to distinguish the amplitude of different output powers at 30 Torr in Ar because the sufficient power gives the narrow width of the delay time spread. At 760 Torr in the Ar case, the delay time becomes shorter as the power increases from 29 kW to 32 kW.

As the pressure increased from 60 to 760 Torr, the lag time increased similar to the Ar experiment (see Fig.

Figure 4-6: Survival rate for an incident RF wave during pulse duration. The experimental data are shown without radioactive material (blue circles) and with radioactive material (red crosses)

Analysis of delay time measurement

• Sensitivity of delay time
• Reduction of required electric field with radioactive material
• Possible detection ranges and limitation

The effective ionization frequency, eff ,i, is a function of the RF field amplitude, E0, therefore, can be expressed for the ionization rate as. Therefore, if the incident RF field is the same as the threshold field, and the ratio of the threshold field to the critical field is given by. Furthermore, E0 depends on the logarithm of the ratio of the critical plasma density to the initial seed electron number density.

Given the correct size of the antenna and the wavelength of the millimeter unit, the detection distance is determined. The potential distance is expressed as R(m) = 2D2/λ, where D and λ are the correct size of the antenna diameter and the wavelength of the EM source. In addition, the underdense plasma density model was chosen to calculate for the transmittance and reflectance of the attenuated RF wave signal.

A fundamental study on Ar plasma breakdown, such as the herringbone structure of the plasma filament array, the plasma velocity opposing the RF wave, and spectroscopy in Ar plasma, has been carried out. In addition, another reason was that the definition of plasma volume decay was 100% occurrence of it during more than 200 bursts of 1 Hz repetition pulses. The sensitivity based on the delay time measurement was 4800 times higher than that predicted by theoretical approaches in terms of detection mass using the plasma on/off phenomenon; this was achieved by precisely measuring the delay time of the plasma avalanche.

The plasma on/off method requires high frequency THz output beam to create a small decay-prone volume with no free electron in the normal state, so that the free electron created by the decay of the radioactive material inside.

Figure 4-12: Production rate of electrons for 0.64 mCi of 60 Co located 20 cm away from center of the RF beam

Conclusion