The chapter presents a review of a highly sensitive technique for time-resolved imaging and measurement of the 2D intensity profiles of millimeter waves (MMW) based on the use of visible continuum radiation (VCR) from the positive column (PC) of a medium pressure Cs-Xe DC discharge (VCRD technique). The review focuses on the operating principles, fundamentals, and applications of this new technique. The design of a discharge tube and an experimental setup which were used to create a wide homogeneous PC plasma slab are described. The MMW effects on the plasma slab are studied. The mechanism of microwave-induced variations in the VCR intensity and the causes of violation of the local relation between the visible continuum emissivity and the MMW intensity are discussed. The main characteristics, e.g., spatial and temporal resolution, and sensitivity of the VCRD technique have been evaluated. Experiments on imaging of the field patterns of horn antennas and quasioptical beams demonstrated that the VCRD technique can be used for a good-quality imaging of the MMW beams in the entire MM-wavelength band. The VCRD technique was applied for imaging of output field patterns of the MMW electron tubes and determination of some of their characteristics, as well as for active real-time imaging and nondestructive testing using MM waves.
- Electric discharges
Millimeter waves (MMWs) are electromagnetic (EM) waves with wavelengths ranging from 1 to 10 mm in free space. Millimeter waves are widely used in radar, navigation, telecommunications, remote sensing, plasma heating and diagnostics, material processing, spectroscopy, etc. Imaging and nondestructive testing (NDT) with millimeter waves is also of great interest for scientific, industrial, security, and biomedical applications [1–10]. In many MMW applications, as well as for engineering of MMW devices and systems, it is necessary to measure the spatial profiles of MMW radiation in real time. Electronic, electro-optic (EO), and thermographic techniques are commonly used for measuring and imaging the MMW field profiles. The electronic techniques employ receivers with semiconductor [4–9], superconducting , and glow discharge [11–13] MMW detectors. Electro-optic techniques use EO sensors for MM waves [14, 15]. Mechanically scanned receiver systems are widespread. However, a mechanically scanned receiver cannot be applied for a time-resolved imaging of MMW field profiles. Time-resolved images of MMW beams can be obtained with two-dimensional (2D) antenna arrays with MMW detectors [4–8, 12, 13]. The images of MMW beams obtained using 2D antenna arrays are of rather poor quality, because of the element-to-element gain and sensitivity variations, large element-to-element spacing, and small number of sensor elements. Because of the strong scattering and reflection of millimeter waves from antenna arrays, they can hardly be used for near-field imaging. Moreover, 2D antenna arrays are expensive and sophisticated systems. A live electro-optic camera has recently been used for imaging of traveling millimeter waves at video frame rates . However, a live 2D electro-optic imaging system is a very complex system as well. Small aperture of the modern live EO sensor is another disadvantage of this technique. In thermographic techniques of measuring of the MMW beam profiles, thermo-sensitive phosphor or liquid crystal films, thermal paper, and dielectric sheets are used as screens, which are irradiated with millimeter waves. Thermographic techniques, which use thermo-sensitive phosphor [16, 17] or liquid crystal films , provide images of MMW intensity profiles in the visible region. A very simple way of obtaining MMW beam images in the visible region is based on the utilization of thermal papers. However, only rough time-integrated images of the field profiles of high-energy MMW beams can be obtained by using thermal paper . In another variant of the thermographic technique, a flat sheet of dielectric material (e.g., paper, polyvinylchloride) is used as an absorbing screen for MMWs [20–23]. A spatial distribution of the microwave-induced variation in the screen temperature is measured by an infrared (IR) camera. This technique has proven itself well in installation, adjustment, and evaluation of the characteristics of the MMW transmission lines and sources of CW and long-pulse high-power millimeter waves. The main drawbacks of all thermographic methods of the MMW imaging are their low temporal resolution, which can be 10 ms at best, and low energy flux sensitivity, which is no better than 1 mJ/cm2. Moreover, distortions, which are caused by heat conduction, can significantly impair the quality of thermographic images of MMW beams. These distortions increase with increasing MMW pulse duration or camera exposure time.
Light emission from microwave-induced gas breakdowns in space and in gas-filled tubes (luminescent lamps, neon indicator lamps, etc.), as well as breakdowns near a dielectric surface coated with a thin layer of metal powder, have been exploited to analyze the field profiles of millimeter waves [24, 25]. However, the microwave-induced breakdown yields rough distorted images of the field pattern of high-power pulsed MM waves. This technique operates only for narrow ranges of MMW intensities and pulse durations. It is impossible to obtain good-quality images by using this technique because of the properties both of the microwave-breakdown plasma and the light emission from such a plasma. No plasma glow is observed when the intensity of millimeter waves is below the breakdown threshold, or the MMW pulse duration is shorter than the time to breakdown. When the breakdown threshold is exceeded, a filamentary array with subwavelength spacing is formed in space if a gas pressure is higher than a few Torr . The electron density in the filaments is higher than the critical plasma density; therefore, millimeter waves are reflected and scattered by the filaments. The boundary of the region occupied by the breakdown plasma propagates towards the MMW beam. The main contribution to the light emission from the breakdown plasma is given by a bound-bound transition between electronic levels of atoms and molecules. The dependences of the intensity of the atomic and molecular emission lines on the MMW intensity are sophisticated and nonlinear. Moreover, the dependences are different for different spectral lines.
The above-specified drawbacks of the conventional techniques for imaging and measurement of the MMW field profiles require their further improvement, as well as the development of alternative techniques. Recently, a technique for imaging of MMWs based on visible continuum (VC) radiation from a slab of the positive column (PC) of a medium-pressure DC discharge in a mixture of cesium vapor and xenon (a Cs-Xe DC discharge) was proposed and developed [27–35]. The idea behind this MMW imaging technique is to use the effect of the increase in intensity of the VC radiation from the PC of a Cs-Xe discharge due to MMW electron heating. By means of this technique, MMW beam profiles are converted into visible images, thus allowing a conventional digital camera with an optical filter to acquire the images. This review is focused on the operating principles, fundamentals, and applications of this new technique for imaging of MMWs. The chapter is organized as follows. Section 2 provides methods for a plasma slab generation using a Cs-Xe DC discharge and its diagnostics. Section 3 focuses on the experimental evaluation of some important characteristics of the technique for MMW imaging, which is based on using visible continuum radiation from the discharge (VCRD) in a mixture of Cs-Xe. We shall call this technique for imaging of MMWs a VCRD technique. In Section 3, experiments on imaging of the field profiles at the output of MMW horn antennas and quasioptical MMW beams are also discussed. The subjects of Section 4 are the fundamentals of the VCRD technique for imaging of MMWs. In particular, it discusses the nature of the visible continuum radiation (VCR) from the PC of a Cs-Xe discharge, the mechanism of microwave-induced variations in the VCR intensity, and the causes of violation of the local relation between the VC emissivity and the MMW intensity. Section 5 reviews applications of the VCRD technique for imaging of output field patterns of short-wavelength MMW vacuum electron tubes and determination of some characteristics of these tubes. Applications of the VCRD technique for real-time imaging and nondestructive testing using MMWs are also the subject of Section 5.
2. Plasma slab generation using a Cs-Xe DC discharge and experimental study of its characteristics
A sealed discharge tube (DT) was used to generate a slab of the positive column of a Cs-Xe DC discharge in the experiments on imaging of MM waves . Figures 1(a) and 1(b) show side and top views of the discharge tube. A hollow rectangular parallelepiped was located at the center of the tube. It was glued from fused quartz plates. Two square quartz windows with 10 × 10 cm2 apertures and 0.65 cm thick were set at a distance of 2 cm from each other. They were used to form the plasma slab and input the MMW beam into the discharge tube. Two plane anodes and two heated cathodes were sealed in glass cylinders 10 cm in diameter. The glass cylinders were glued to the quartz cell. The distance between the anodes and cathodes was 30 cm. Each pair of electrodes was powered by a separate power supply. Two pairs of thin quartz plates with a size of 5 × 9 cm2 were installed inside the cylinders parallel to each other at a distance of 2 cm. These two pairs of quartz plates restricted the region in the cylinders occupied by the positive column and increased the length of a homogeneous part of the PC plasma. The longitudinal electric field
The characteristics of the positive column of a Cs-Xe discharge and the spectrum of the light from the PC plasma were studied when there were no incident MM waves [27, 28]. The discharge current
The decrease in the cesium density with decreasing DT temperature was the main reason for the deconstriction of the PC of a Cs-Xe discharge and the transition from the first to the second PC mode. The electron temperature in the first and second PC modes is too low for a considerable ionization of xenon, and the main ion species in these PC modes are cesium atomic ions Cs+ [27, 28, 35]. The ionization degree of cesium in the Cs-Xe discharge plasma is high and the number density of positive cesium ions is more than 80% of cesium . Therefore, a decrease in the cesium density with decreasing tube temperature results in an almost proportional decrease in the density of cesium atomic ions. Owing to the plasma quasineutrality, the electron density in the PC is equal to the density of cesium atomic ions; hence, a decrease in the tube temperature also leads to a decrease in the electron density in the PC of the Cs-Xe discharge. For a fixed value of the discharge current, a decrease in the electron number density in the PC plasma leads to an increase in the transverse dimension of the current flow region, i.e., deconstriction of the PC. The positive column ceased to become wider with decreasing tube temperature only when the PC plasma filled entirely the internal cross section of the quartz cell.
Gray thin line in Figure 2(b) shows emission spectrum of the homogeneous positive column (second PC mode) in the visible region for the discharge current density
The wide homogeneous plasma slab, i.e., the second PC mode, was used as an imager for MM waves. In the experiments on imaging of MMWs, the discharge current was 1.5 A, and the DT temperature was about 90oС. When there were no incident MMWs, the DC electric field in the PC was equal to , the electron temperature was = 0.47 ± 0.03 eV, and the electron density was = (2.7 ± 0.3)∙1012 cm–3. The electron density in the homogeneous PC of a Cs-Xe discharge was much less than the critical density for MMW frequency band, so reflection of the MM waves from the plasma was weak (less than 1%) . The absorption coefficients of the PC plasma for Ka and D band MM waves were equal to 0.3 cm–1 and 0.01 cm–1, respectively [27, 29].
3. Evaluation of the performance of the VCRD technique
The MMW effects on a slab of the PC of a Cs-Xe discharge have been experimentally studied to develop the VCRD technique for imaging of MMWs and determine its basic characteristics. The model experiments In the model experiments, the MMW field profiles have been known from calculations or measurements by conventional techniques.
In the model experiments, the MMW field profiles have been known from calculations or measurements by conventional techniques.
To evaluate the microwave-induced variation in the VCR energy flux , the background VCR energy flux was subtracted from the VCR energy flux . The VCR energy flux was obtained using the CCD camera frame simultaneous with the MMW pulse, and the background VCR energy flux was obtained using the CCD camera frame preceding the MMW pulse. When the VC emissivity is time-independent during the camera exposure time , the VCR energy flux is equal to , where is the intensity of the visible continuum radiation, and the relative variation in the VCR intensity is equal to the relative variation in the VCR energy flux where ; here is the background VCR intensity.
Study of the millimeter wave effect on the homogeneous positive column of a Cs-Xe discharge was performed using conical horn antennas (see Figure 3) excited by the mode of a circular waveguide . A 35.4-GHz magnetron was used as a source of MM waves. The magnetron supplied coherent radiation with an output power of up to 20 W in the long-pulse mode. The MMW pulse length was up to 100 ms, and the pulse leading edge was less than 0.1 µs. Mode converters were used to transform the mode of a rectangular waveguide into the mode of a circular waveguide [43, 44]. The conical horns had aperture radii from 10 to 30 mm. The MMW electric field polarization in the vicinity of the beam axis was directed along the
When the MMW intensity exceeded the breakdown threshold , a microwave-induced breakdown of the PC slab occurred, and bright thin filaments were observed in the plasma area affected by a MMW beam. The filaments were elongated in the direction of the MMW electric field. Figure 4(a) shows the spatial distribution of the VCR energy flux variation when there was a microwave-induced breakdown of the plasma slab. The threshold value of the microwave breakdown for the Ka-band was equal to about 4 W/cm2 for 1.1 V/cm. It decreased to approximately 2 W/cm2 for 1.5 V/cm. When , MMW heating increases the electron temperature so that excitation and ionization of xenon become significant. Ionization of xenon is the major cause of ionization instability of the homogeneous PC and the appearance of filaments with a high electron density, i.e., a microwave breakdown of the plasma slab .
Figure 4(b) shows a 2D distribution of the VCR energy flux variation at the output of a conical horn antenna, The coordinates are denoted
The coordinates are denoted
The data of the experiment on the imaging MMW intensity profile at the output of the conical horn antenna with an aperture radius of 22.5 mm excited by the mode (see Figure 4(b)) were compared with the calculated spatial distribution of the EM wave intensity for the mode of a circular waveguide of the same radius. For
The experiments on imaging of the MMW field profiles at the output of the conical horn antennas excited by the axially symmetric mode of a circular waveguide were carried out in ref. . The same 35.4 GHz long-pulse magnetron was used in these experiments. The mode of a rectangular waveguide was transformed into the mode of a circular waveguide by a Marier transducer (see Figure 3). Figure 6(a) shows a 2D distribution of the MM wave-induced variation of the VCR intensity at the output of a conical horn with a taper angle of 6o and output aperture radius 28 mm. The MMW intensity at the field maximum was 1 W/cm2. The CCD camera exposure time was 100 μs. The obtained pattern of the VC glow corresponds to the mode with a small admixture of other modes An experiment showed that the dependence of the VCR intensity on the azimuthal coordinate (see Figure 6(a)) is caused by the admixture of other waveguide modes excited in a conical horn, but not the spurious plasma effect. In this experiment, a rectangular waveguide, which was twisted through an angle of approximately 90°, was installed before the Marier transducer. The image of the spatial distribution of the MMW intensity was also rotated through an angle 90° in the same direction.
An experiment showed that the dependence of the VCR intensity on the azimuthal coordinate (see Figure 6(a)) is caused by the admixture of other waveguide modes excited in a conical horn, but not the spurious plasma effect. In this experiment, a rectangular waveguide, which was twisted through an angle of approximately 90°, was installed before the Marier transducer. The image of the spatial distribution of the MMW intensity was also rotated through an angle 90° in the same direction.
An experiment on imaging of the Ka-band quasioptical millimeter-wave beam using the VCRD technique is described in ref. . The quasi-Gaussian MMW beam was focused by a double-convex Teflon lens 20 cm in diameter and a focal length of 32 cm at the center of the plasma slab. The width of the MMW beam (FWHM) in the focus was approximately 2.5 cm. The distribution of the VCR intensity variations in the focal plane of the lens was compared with the MMW field profile. The MMW intensity profile was measured by a mechanically scanned receiver with calibrated MMW detector. The patterns measured by the two techniques coincided within the limits of the random experimental error. Thus, model experiments on imaging of the field profiles of horn antennas and quasioptical beams have demonstrated that the VCRD technique can be used for good-quality imaging of Ka-band MMW beams.
The response time of the VCR intensity to the variation in the MMW intensity was measured using a photomultiplier tube (PMT) . In these experiments, the photomultiplier tube was set in place of the CCD camera (see Figure 3). The optical filter set rejecting atomic emission lines and transmitting the VC radiation from the PC of a Cs-Xe discharge was mounted before the PMT input window. The temporal resolution of the setup used for recording of the VCR intensity time history was less than 50 ns. After the MMW radiation was switched on, the measured waveform of VCR intensity fit well with the exponential time dependence:
where is the VCR intensity variation, is the time point at which the MMW pulse was switched on, and is the characteristic time of VCR intensity variation. The VCR response time was about μs. This time is approximately equal to the time of the electron temperature variation in the PC plasma (see Section 4.2 and refs. [27, 35]). Thus, it was shown that the VCRD technique for MMW imaging is very rapid and its temporal resolution was less than 1 μs.
In the experiments on imaging of Ka-band MM waves using the VCRD technique, a single-shot signal to noise ratio (SNR) was about one when the MMW intensity was 1 W/cm2 and the CCD camera exposure time was set at 10 μs . Thus, in the Ka-band, a single-shot threshold energy flux sensitivity (SNR = 1) of about 10 μJ/cm2 was achieved. In the performed experiments, the energy flux sensitivity was restricted by the noise performance of the CCD camera. The actual sensitivity of the VCRD technique is determined by fluctuations of the parameters of the PC of a Cs-Xe discharge, primarily, by the fluctuations of the electron temperature in the plasma . Estimated sensitivity of the VCRD technique is higher by at least an order than the sensitivity achieved in the experiments. Further study is required for more accurate determination of the VCRD technique sensitivity.
The VCRD technique can be used to image the intensity patterns of the EM waves in a wide band from short-wavelength centimeter to submillimeter waves. When the MMW frequency increases, the plasma becomes more transparent for MMWs due to a decrease in the MMW absorption coefficient, and the MMW effect on the plasma parameters decreases [27, 29]. At the xenon pressure of tens of Torr, the electron-Xe atom collision frequency for the momentum transfer was much less than the angular frequency of MM waves [27, 29]. In this case, the scaling law for the efficiency of electron heating under the MMW effect is , where is the electron temperature variation. Therefore, on passing from long-wavelength to short-wavelength millimeter waves, the sensitivity of the technique decreases if the identical systems are used for VC radiation recording. The threshold of the microwave breakdown of a plasma slab is significantly increased in a short MMW band. For example, on passing from Ka-band to D-band the threshold of the microwave breakdown of a plasma slab increases to the value of the order of 100 W/cm2, but the energy sensitivity of the VCRD technique deteriorates to the level of hundreds of μJ/cm2.
The ability to image the intensity profiles of short-wavelength MM waves using the VCRD technique was demonstrated in refs. [29, 30]. Thus, the wide frequency band of the technique has been confirmed. In paper , the intensity profile of the D-band MMW beam was measured at the output of a corrugated conical horn antenna. The arrangement of this model experiment was similar to the arrangement of the experiment on imaging of Ka-band MMWs at the output of conical horn antennas (see Figure 3). A pulsed F- and D-band orotron OR-180 was used as a source of MM waves (see Section 5.1 and ref. ). In this experiment, the orotron radiation frequency was 140 GHz. The maximum orotron power was about 0.6 W. The MMW pulse length was 3 ms, and the pulse repetition rate was 10 Hz. The corrugated conical horn was fed by the orotron through an E-band rectangular waveguide and a down taper. The output diameter of the corrugated horn was 16 mm, and its length was about 90 mm. The discharge tube window was attached to the output of the horn. The corrugated horn forms a high-quality axially symmetric Gaussian beam . The width (FWHM) of the Gaussian MMW beam in the middle plane of the plasma slab was equal to 7.8 mm. The MMW electric field vector at the output of the horn was directed along the When a section of the D-band rectangular waveguide twisted by an angle of 90° was installed before the corrugated conical horn, the horn rotated around its axis by 90°, and the MMW polarization in the Gaussian beam also changed from direction along the
When a section of the D-band rectangular waveguide twisted by an angle of 90° was installed before the corrugated conical horn, the horn rotated around its axis by 90°, and the MMW polarization in the Gaussian beam also changed from direction along the
4. Fundamentals of the VCRD technique
This section discusses the nature of the visible continuum radiation from the PC of a Cs–Xe discharge and the mechanism responsible for the VCR intensity variation under the MMW effect. The relationship of the spatial distributions of the VC emissivity variation and intensity of MMW radiation incident on the plasma slab is also studied. The factors determining the spatial and temporal resolution of the VCRD technique are discussed.
4.1. Mechanism of the MMW effect on the intensity of the VC radiation from the PC of a Cs-Xe discharge
The nature of the visible continuum radiation from the positive column of a Cs-Xe discharge for plasma parameters that are typical for the MMW imaging experiments was studied in refs. [27, 28]. It was shown that the electron-Xe atom bremsstrahlung continuum (e-Xe BC) and the cesium recombination continuum (RC) give the main contributions to the visible continuum radiation from the PC of a Cs-Xe discharge. The VC emission coefficient is equal to the sum of emission coefficients for the electron-Xe atom bremsstrahlung continuum [39–41, 48–50] and the cesium recombination continuum [39, 51]:
Visible RC radiation originates from recombination of the electrons and Cs+ ions into 6
The intensity of the visible continuum from the PC of a Cs-Xe discharge rises when the millimeter waves incident on the plasma slab or the DC electric field in the PC plasma increases. It follows from Eqs. (3) and (4) that the rise in the VCR intensity can be caused by an increase in the electron number density or by EEDF variation. The electron-density variation induced by the MMW or DC electric field cannot explain the observed increase in the VCR intensity. Firstly, due to a high ionization degree of cesium in the homogeneous positive column, the microwave-induced variation in the electron density is relatively small () , whereas the effect of watt-scale Ka-band MMWs on the PC plasma increases the VCR intensity significantly () (see Figure 5). Secondly, the characteristic time of the electron density variation [35, 36] is several orders of magnitude longer than the VCR response time (see Section 3). Thirdly, when the discharge tube temperature was decreased, the electron number density in the homogeneous PC also decreased, whereas the VCR intensity and the DC electric field increased . Hence, the VCR intensity variation is caused by the EEDF variation resulting from the MMW or DC electron heating. Using Eqs. (2)–(4), the VC emission coefficient were calculated for different electron temperatures in the homogeneous PC plasma. The electron density was assumed constant. Solid lines in Figure 8 show the continuum emission coefficient in the visible region calculated for 45 Torr xenon, 2.5∙1012 cm–3 and the EEDF with the effective electron temperatures 0.45, 0.5, 0.55, and 0.6 eV. Dashed lines in Figure 8 show the e-Xe BC emission coefficient calculated for the same plasma parameters. In the visible region, the wavelength-integrated emission coefficient for the e-Xe BC radiation exceeds the wavelength-integrated emission coefficient for the cesium recombination continuum by about one order of magnitude. Figure 8 demonstrates that the increase in the VC emissivity is caused by the e-Xe BC emissivity increase due to an additional electron heating and is not caused by an increase in the cesium recombination continuum emissivity as was believed earlier . As the electron temperature rises from 0.45 to 0.6 eV, the intensity of the e-Xe BC in the visible region increases more than fourfold.
Explanation of the phenomenon of the increase in the e-Xe BC radiation intensity in the visible region induced by the electron heating is quite obvious. Bremsstrahlung photons with wavelength can be emitted only by electrons with kinetic energies greater than the energy of a light quantum, i.e., . The visible light wavelengths ranging from 620 nm to 410 nm correspond to photon energies from 2 to 3 eV. The bremsstrahlung photons with such an energy can be emitted by the electrons from the tail of the EEDF ( > 2–3 eV) because the electron temperature in the homogeneous PC of a Cs-Xe discharge is from 0.4 to 0.8 eV. Thus, the increase in the e-Xe bremsstrahlung radiation intensity in the visible region is caused primarily by an increase in the fast electron number density, which results from the additional electron heating induced by the MMW or DC electric field. The bremsstrahlung cross section for electron-atom collisions increases with increasing electron energy (see Eq. (4) and refs. [40, 50]). This is another cause of the increase in the VC brightness due to DC- or microwave-induced electron heating.
Verification of the previously discussed mechanism of the electromagnetic field effect on the brightness of the visible continuum radiation from the PC of a Cs-Xe discharge was carried out in ref. , where the effects of the DC electric field strength and electron density on the intensity of VC radiation were studied experimentally. There was no MMW radiation incident on the plasma. The electron density was varied by changing the discharge current. The DC electric field strength was varied by changing the tube temperature for a fixed value of the discharge current. Experimental data are in a good agreement with the results of calculations done using the above model . In ref. , the dependence of the relative intensity variation of the VC radiation from the PC of a Cs-Xe discharge, , on the electron temperature was calculated. The best agreement between the results of calculations and the experimental data is achieved when it is assumed that the microwave breakdown of the plasma slab occurs at an electron temperature equal to 0.7 eV. Dashed line in Figure 5 shows the calculated dependence for 0.7 eV.
4.2. Relation between spatial profiles of the VC emissivity and the MMW intensity. Spatial and temporal resolution of the VCRD technique
The causes of violation of the local relation between the visible continuum emissivity and the MMW intensity, as well as the main factors which limit the spatial resolution of the VCRD technique, were explored in ref. . The emissivity of the e-Xe bremsstrahlung continuum depends locally on the effective electron temperature and electron density in the PC of a Cs-Xe discharge (see Eqs. (2)–(4)). The electron density variation is relatively small in the PC plasma, and its effect on the brightness of VC radiation is not significant. The main cause of the increase in the VC intensity is the microwave-induced increase in (see Section 4.1). The value of is directly proportional to the local value of the electron temperature variation when 0.1 eV. Spatial profiles of the microwave-induced perturbations in the electron temperature and density in the slab of the PC of a Cs-Xe DC discharge were analytically modeled . The model considers the effects of the electron heating by the DC and MMW electric field, the electron energy loss due to electron-atom collisions, electron heat conduction, diffusion, and thermal diffusion of the charged particles. The perturbations of the electron temperature induced by MMW beams which had different shapes were described by the electron-energy balance equation. Perturbation technique was used to find the solutions for this equation. It was sufficient to calculate the first- and second-order terms for the electron temperature perturbation to explain the results of the experiments. For a one-dimensional (1D) MMW beam having a width much smaller than the size of the operating aperture of a plasma slab, the spatial distribution of the electron temperature perturbation of the first order is given by the convolution of the MMW intensity and the line spread function (LSF) for the VCRD technique :
In Eq. (5), the coordinate is a linear function of
here , where is the electron heat conduction coefficient divided by the electron density. For a xenon pressure of 45 Torr and an electron temperature of 0.5 eV, is equal to about 1.5 mm, so the width of the line spread function (FWHM) equals to approximately 2 mm. When the plasma slab is affected by a two-dimensional beam, whose width is significantly smaller than the aperture sizes of the discharge tube, the electron temperature perturbation of the first order is given by a 2D convolution of with a modified Bessel function of the second kind of order zero ,
where . It follows from Eqs. (5) to (7) that the value of spatial broadening of the MMW beam image is determined by a parameter , which depends on the electron heat conduction coefficient and the time of electron energy relaxation due to electron-atom collisions. Therefore, at a first-order approximation, the nonlocality of the microwave-induced variation in the intensity of the VC radiation is caused by the electron heat conduction effect. The electron heat conduction restricts the spatial resolution of the VCRD technique. Using Eq. (7), one can find that the plasma imager with aperture dimensions of about 10 cm has an equivalent number of effective sensor elements of the order of one thousand.
The calculations of the microwave-induced electron temperature perturbation based on the above-described model were compared with the data of the experiments on imaging of 34.5GHz MMW field profiles at the output of conical horn antennas with different aperture radii, which were excited by the mode (see Section 3). The dashed line in Figure 6(d) shows the calculated dependence of the first-order perturbation of the electron temperature on transverse coordinate
When a smooth and wide (i.e., wider than 2 cm) MMW beam affects the plasma slab, the influence of the electron heat conduction and other manifestations of nonlocality can be neglected in a first-order approximation. In this case, the perturbation in the electron temperature induced by a long pulse of MMW radiation with a sharp leading edge is given by 
The time history of the electron temperature perturbation, calculated using Eq. (8), coincides well with the measured time history of the VCR intensity variation. Therefore, the response time of the VC radiation is approximately equal to the characteristic time of electron temperature variations due to the electron energy loss in electron-atom collisions.
5. Applications of the VCRD technique
The study of the performance and fundamentals of the VCRD technique, which was reviewed above, shows that this technique has some advantages over conventional techniques for MM imaging. In contrast to the imaging techniques, which use the receiving antenna arrays, a continuous medium with a small MMW reflection coefficient is exploited in the VCRD technique as an imager. Hence, it is possible to perform imaging of MMW beam profiles in the near-field region via the VCRD technique. The advantages of the VCRD technique over the thermographic techniques include a much higher energy sensitivity and a microsecond temporal resolution. These and some other advantages of the VCRD technique give hope for its applications for determination of the characteristics of output radiation from moderate-power MMW sources as well as for imaging and nondestructive testing with MM waves. At the same time, the VCRD technique has some peculiarities; therefore, experimental verification of the possibility of its use for solving applied problems is required. In this regard, Section 5 is focused on demonstration of two application capabilities of the VCRD technique. Subsection 5.1 discusses the experiments, where this technique is successfully used to measure the parameters of MM waves at the output of new-designed electron tubes. These studies are very relevant because short-wavelength millimeter waves are supposed to be widely used in new advanced radar, communication, diagnostic, and spectroscopy systems. However, in these frequency bands, the power of most types of modern CW and pulsed sources of EM waves is insufficient for use of thermographic imaging techniques. Due to its higher sensitivity, the VCRD technique can be successfully used for measuring the output characteristics of such MM wave sources. Subsection 5.2 provides an overview of experiments on the use of the VCRD technique for real-time imaging and nondestructive testing in the millimeter-wave band. Time-resolved imaging and NDT using MM waves are required for many applications [1–9]. Millimeter waves can penetrate through many opaque dielectric materials, such as paper, wood, fabric, ceramics, polymers, semiconductors, and others. This fact gives MMW imaging and NDT systems some advantage over optical and infrared systems, even though the spatial resolution of MMW systems is much worse than that of optical and IR systems. MMW imaging also has some advantages over THz imaging: first, atmospheric absorption and scattering is lower in the millimeter-wave region, and second, many types of conventional MMW sources and components are widely available. In contrast to EM radiation of the centimeter-wave band, which is also used for imaging and nondestructive testing, millimeter waves have a better spatial resolution. X-ray imaging also has some disadvantages compared to MMW imaging: first, the X-ray is ionizing and requires the implementation of stringent safety rules, and second, some materials, e.g., water, produce only low-contrast images in the X-ray region.
5.1. Imaging of the beam profiles at the output of a D-band orotron and a W-band gyrotron
Orotrons are vacuum electron sources of coherent EM radiation of the short-wavelength band of the MMW range. They are used in the microwave and NMR spectroscopy, for MMW frequency standards. A pulsed orotron OR-180 has been designed and manufactured by a collaboration of Russian organizations . The orotron frequency was tuned electromechanically in the F and D bands. Output coupling of MMW radiation from the orotron cavity occurred through an oversized E-band rectangular waveguide. The design of the orotron assumes that the mode of a rectangular waveguide will be excited predominantly in its output waveguide. Verification of this assumption and determination of the field profiles at the output of the orotron when it was tuned to the different frequencies were important steps towards the comprehension of the operating principle of this device and the improvement of its performance. For the solution of these problems, the VCRD technique for imaging of MM waves has been successfully used . The scheme of this experiment is similar to that shown in Figure 3. Millimeter waves were generated by the orotron OR-180. The orotron pulse duration was 3 ms. A pyramidal horn antenna with aperture dimensions 14 × 14 mm2 and 21 cm long was installed at the output of the E-band waveguide. The MMW electric field vector at the output of the horn was directed along the
The VCRD technique was applied for imaging of the field profiles at the output of a 110 GHz kilowatt-scale gyrotron with a pulsed magnetic field . These experiments are of interest for the improvement of this type of gyrotrons and for their successful exploitation in various applications. The scheme of this experiment is similar to that shown in Figure 3. The millimeter waves were output from the gyrotron cavity without mode conversion via a circular hollow metal waveguide 16 mm in diameter and about 200 mm long. A circular hollow metal waveguide 16 mm in diameter and 640 mm long was attached to the gyrotron waveguide. A conical horn antenna 140 mm long and having an aperture diameter of 40 mm was set at the output of the circular waveguide. The gyrotron power can be varied by changing the electron beam voltage and current. The pulse duration of the gyrotron was 60 μs. The CCD camera exposure time was 64 μs. The gyrotron was in the stage of debugging and improvements at the time of the experiments on imaging of its output field profiles. In accordance with the gyrotron design, its operating mode was the rotating mode of a circular waveguide. In the first series of experiments, the length of the gyrotron cavity was by 1.5 times longer than optimal for its high-efficiency operation. The maximum output power of the gyrotron with that long cavity was about 3 kW. Figure 10(a) shows a 2D distribution of CVR intensity variation under the MMW effect, which was measured at the output of a conical horn for a gyrotron output power P = 1 kW. For such a power, the MMW intensity in the field maxima did not exceed the microwave breakdown threshold of the PC of a Cs-Xe discharge. The VCR image corresponds to the mode pattern. The standing- wave pattern in the azimuthal direction occurred due to the presence of an admixture of the counter-rotating mode. Figure 10(b) shows the image of VCR intensity variation recorded at the output of a horn antenna for the gyrotron power
Thus, the VCRD technique has been successfully applied for determining of the fundamental waveguide modes of moderate-power MMW electron tubes and evaluating the relative power of some spurious modes.
5.2. Applications of the VCRD technique for imaging and nondestructive testing with MM waves
The VCRD technique has been used for active near-field MMW imaging and NDT via shadow projection method [33, 34]. In active-mode MMW imaging and NDT systems MM wave sources are used for object illumination [1–8]. A slab of the positive column of a Cs-Xe DC discharge has been used as a rapid imager for millimeter waves. In the near-field shadow projection method of MMW imaging, the objects are located close to the plasma imager. This is a drawback of the method in comparison with the quasioptical camera-mode method of MMW imaging, in which the object is located far away from the receiver [4, 6, 8, 13]. Realization of the active camera-mode method of imaging based on the VCRD technique is also feasible with using short-wavelength MM waves for object illumination. However, in the camera-mode method distortions of the images occur due to the diffraction and aberrations by lenses and mirrors. Diffraction and aberration effects are very significant when long-wavelength MM waves are used for object illumination. In this case, the use of the shadow projection method may provide a better image quality.
Figure 11 shows schematic of the experimental setup (top view), which was used for active near-field shadow projection MMW imaging using the VCRD technique . A 35.4 GHz magnetron was used as a MMW source. The parameters of the magnetron were specified in Section 3. The MMW pulse length was about 10 ms. The repetition rate of MMW pulses was 12.5 Hz, i.e., half of the frame rate of the CCD camera. Camera frames, which were simultaneous with the MMW pulses, alternated with frames with the background VC radiation from the plasma slab. The CCD camera exposure time was 1 ms. The MMW beam was radiated by a pyramidal horn antenna with a length of 50 cm and aperture dimensions 6 × 8 cm2. A plane-convex Teflon lens collimated the MMW beam. The polarization of the MMW beam was directed along the The VCRD technique is well suited for inspection and MMW imaging of the inanimate objects. The time-averaged MMW intensity of 3mW/cm2 is several times larger than the maximum MMW dose, which is permitted for general public use in the case of uniform MMW irradiation the whole human body . However, this value is an order of magnitude less than the maximum permitted dose for local MMW irradiation of a part of the human body. Therefore, the VCRD technique cannot be used for entire-body personnel screening, but its applications for security screening and medical imaging with irradiation of a part of human body may be feasible.
The VCRD technique is well suited for inspection and MMW imaging of the inanimate objects. The time-averaged MMW intensity of 3mW/cm2 is several times larger than the maximum MMW dose, which is permitted for general public use in the case of uniform MMW irradiation the whole human body . However, this value is an order of magnitude less than the maximum permitted dose for local MMW irradiation of a part of the human body. Therefore, the VCRD technique cannot be used for entire-body personnel screening, but its applications for security screening and medical imaging with irradiation of a part of human body may be feasible.
The near-field MMW images of the amplitude objects, which are made of materials that are opaque for MMWs, and the phase objects, which are transparent to the MMW radiation, have been obtained using the VCRD technique. At first, static amplitude and phase objects were imaged. The letters and numbers from IRMMW-THZ 08, an acronym for the name of the International conference, were used as the amplitude test objects. They were cut in the aluminum foil. The foils were glued on cardboard sheets. The letters and numbers were 50 mm high. The width of the rectangular strips transparent for MMWs was 12 mm. The images of the VCR intensity variation under the effect of the MM waves transmitted through the slit objects are shown in Figure 12. The single-shot signal-to-noise ratio for the images was about 20:1. The noise level of the images was given by the noise performance of the CCD camera. The obtained images were distorted by the diffraction because the plasma slab was located in the Fresnel region. Nevertheless, all of the letters and numbers can easily be recognized. Figure 13(a) shows the image of letter E cut out of aluminum foil and glued on a cardboard sheet. The letter was 50 mm high and 45 mm wide. The width of the foil strips was 10 mm. The shape of this object, which is opaque for MM waves, can be easily determined from the image.
Due to the peculiarities of the electromagnetic wave diffraction at the edge of transparent and opaque objects, the images of phase objects can have a higher quality as compared to the images of amplitude objects. The EM wave transmitted through a transparent dielectric slab with the thickness acquires an additional phase shift , where is the permittivity of the material from which the object is made, is the wavelength of the MMW radiation. If the additional phase shift of the EM wave transmitted through the object differs from the multiple of 2π, then the diffraction gives rise to a narrow minimum of the EM wave intensity in the near-field region behind the edge [53, 54]. The minimum is located between two maxima of intensity, i.e., an edge contrast enhancement occurs in the image of a phase object. Exploiting the VCRD technique, a shadow projection MMW image of a rectangular parallelepiped from Teflon ( 2) was obtained. The length, width, and thickness of the parallelepiped were 180, 28, and 6.8 mm, respectively. In the experiment, the long edges of the parallelepiped were directed parallel to the
The VCRD technique was used for time-resolved record of the MMW images of moving objects and registration of transient processes . In particular, real-time shadow projection images of damped pendulum oscillation were obtained. The pendulum was a Teflon ring suspended by a thread about 15 cm long. The outer and inner ring diameters were 25 mm and 13 mm, respectively, and the ring was 8 mm thick. The ring affected the MMW beam as a three-zone phase filter which focused the MMW beam in the near field in a focal spot about 7 mm in diameter. The decay time of the pendulum oscillation was about 4 s, and the oscillation period was approximately 0.8 s. Figures 16(a) –16(e) show a sequence of MMW images of the pendulum motion, which was recorded at equal time intervals during half of the first period of pendulum oscillations. The process, by which a cylindrical glass tube filled with water became empty, was also imaged (see Figures 16(f) –16(j)). The inner and outer tube diameters were 6 and 8 mm, respectively. The tube filled with water was opaque for MMWs (see Figure 16(f)). After opening a valve which was located at the foot of the glass tube (outside the aperture), the water began to flow out of the tube. Figures 16(g) –16(i) show how the glass tube becomes transparent for MMWs as it is emptied. The water poured out of the tube for about 1 s. The MMW transmission image of the empty tube is shown in Figure 16(j). The tube wall is well defined in Figure 16(j) because of the considerable difference in the refractive indices of glass and air.
The chapter presents a review of the VCRD technique for imaging and measurement of the 2D spatial profiles of MMW intensity based on the use of visible continuum radiation from the positive column of a Cs-Xe DC discharge. The design of the discharge tube and the experimental setup that were used to create a CW homogeneous slab of thermal nonequilibrium discharge in a mixture of medium pressure xenon and cesium vapor were described. Results of the study of the basic parameters of the positive column of a Cs-Xe discharge were presented. Three modes of the positive column of a Cs-Xe discharge were observed depending on the tube temperature for a fixed value of the discharge current: a constricted PC, a spatially homogeneous PC, and a PC with a filament. For imaging of MM waves, a wide homogeneous PC plasma slab was used. The MMW effects on the plasma slab have been experimentally studied. It was shown that brightness of the VC radiation from the PC plasma increases by several times when the MMW intensity changes from zero to the threshold of the microwave-induced plasma breakdown. The model experiments on imaging of the field patterns of horn antennas and quasioptical beams have been performed using the VCRD technique. These experiments demonstrate that the VCRD technique can be used for a good-quality time-resolved imaging of MMW beams with a width of about 10 mm or more. The temporal resolution of the technique is about 0.8 μs. It was shown that the VCRD technique is wideband and can be used for imaging of the intensity profiles of the EM waves in the entire MMW band. Energy flux sensitivities of about 10 μJ/cm2 in the Ka band and about 200 μJ/cm2 in the D band have been demonstrated.
The fundamentals of the VCRD technique for imaging of MMWs have been discussed. The studies of the nature of the visible continuum radiation from the PC of a Cs-Xe discharge and mechanism of microwave-induced variations in the VCR intensity were reviewed. It is shown that the electron-xenon atom bremsstrahlung is the dominant component of the visible continuum emitted by the homogeneous PC of a Cs-Xe discharge. The increase in the e-Xe bremsstrahlung intensity in the visible region is caused by an increase in the number density of electrons with the energy more than 2 eV, which is a result of the additional electron heating induced by the MM waves. The profiles of the microwave-induced variation in the intensity of the VC radiation from the plasma slab were analytically modeled. It was proved that the nonlocality of the microwave-induced variations in the VC radiation intensity, as well as the spatial resolution of the VCRD technique of MMW imaging, are primarily determined by the influence of the electron heat conduction. The line spread function for the VCRD technique has been calculated. It was found that its width is about 2 mm. It was shown that the main cause of the axial asymmetry of images of the axisymmetric MMW beams is the MM wave-induced spatial inhomogeneity of the electron heating by a DC electric field.
The final part of the paper reviews some applications of the CVRD technique for MMW imaging. The experiments on imaging of the output field pattern of a D-band watt-scale orotron and a W-band kilowatt-scale gyrotron were described. Operating modes for these vacuum tubes were identified and the power of spurious modes were determined. Applications of the VCRD technique for real-time imaging and nondestructive testing using MM waves are also the subject of the final part of the review. Near-field shadow projection images of the objects which are opaque and transparent for MM waves have been obtained using pulsed watt-scale MM waves for object illumination. Near video frame rate millimeter-wave shadowgraphy has been demonstrated. It was shown that this technique can be used for a single-shot security screening, including the screening of drugs hidden in envelopes, and for a real-time imaging of the transient processes.
The author acknowledges A. E. Fedotov, M. Yu. Glyavin, V. V. Golovanov, A. G. Luchinin, A. G. Spivakov, S. E. Stukachev, A. I. Tsvetkov, and V. V. Zelenogorsky for their contributions to this work. The author is also grateful to N. A. Bogatov, I. L. Epstein, Yu. A. Lebedev, V. I. Malygin, and V. E. Semenov for helpful discussions.
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- In the model experiments, the MMW field profiles have been known from calculations or measurements by conventional techniques.
- The coordinates are denoted x and y in the reference frame, whose origin coincides with the center of the DT window, and the coordinates are denoted x' and y' in the reference frame, whose origin coincides with the MMW beam center.
- An experiment showed that the dependence of the VCR intensity on the azimuthal coordinate (see Figure 6(a)) is caused by the admixture of other waveguide modes excited in a conical horn, but not the spurious plasma effect. In this experiment, a rectangular waveguide, which was twisted through an angle of approximately 90°, was installed before the Marier transducer. The image of the spatial distribution of the MMW intensity was also rotated through an angle 90° in the same direction.
- In the D band, a single-shot energy flux sensitivity of about 200 μJ/cm was demonstrated [29, 30].
- When a section of the D-band rectangular waveguide twisted by an angle of 90° was installed before the corrugated conical horn, the horn rotated around its axis by 90°, and the MMW polarization in the Gaussian beam also changed from direction along the y-axis to direction along the x-axis. However, this rotation does not change the shape of the image of the MMW beam.
- The VCRD technique is well suited for inspection and MMW imaging of the inanimate objects. The time-averaged MMW intensity of 3mW/cm is several times larger than the maximum MMW dose, which is permitted for general public use in the case of uniform MMW irradiation the whole human body . However, this value is an order of magnitude less than the maximum permitted dose for local MMW irradiation of a part of the human body. Therefore, the VCRD technique cannot be used for entire-body personnel screening, but its applications for security screening and medical imaging with irradiation of a part of human body may be feasible.