WO2020240665A1 - Dielectric constant measurement device, dielectric constant measurement system, plasma parameter measurement device, and plasma parameter measurement system - Google Patents

Abstract

A dielectric constant measurement device (11) that is for use in a measurement system that includes a transmitter (20) that radiates electromagnetic waves from a transmission antenna (TX) toward a measurement space (SF), a reception antenna (RX) that receives, from the measurement space (SF), scattered waves that correspond to the radiated electromagnetic waves, and a receiver (30) that generates a reception signal (RS) on the basis of an output signal from the reception antenna (RX). The dielectric constant measurement device (11) comprises a scattering characteristics measurement unit (41) that calculates a scattering characteristics measurement (MS) from the reception signal (RS), a scattering characteristics estimation unit (42) that uses a mathematical model to calculate a scattering characteristics estimate (ES), and an updating unit (43) that updates a dielectric constant distribution estimate such that the magnitude of the difference between the measurement (MS) and the estimate (ES) decreases.

Description

Permittivity measuring device, permittivity measuring system, plasma parameter measuring device and plasma parameter measuring system

The present invention relates to a technique for measuring the spatial distribution of characteristic values such as the dielectric constant of a space to be measured using electromagnetic waves.

Techniques for measuring the characteristics of a medium that transmits or scatters electromagnetic waves using electromagnetic waves are widely used in various technical fields. For example, the smoke emitted from a rocket engine is called a plume, and it is known that this type of plume is composed of plasma. The plasma behaves as a dielectric having a complex dielectric constant (complex permittivity) with respect to the electromagnetic wave, and scatters the electromagnetic wave. The complex permittivity of plasma is determined by the distribution of plasma parameters. Here, the plasma parameters include electron density, collision frequency, and plasma frequency. The electron density is a quantity representing the density of electrons constituting the plasma, and the collision frequency is a quantity representing the frequency with which electrons collide with other particles. The plasma frequency can be determined based on the electron density.

One of the methods for measuring plasma parameters is to insert a metal probe electrode into the plasma space where the plasma exists, measure the change in the current value that occurs in the probe electrode when scanning the plasma space, and use that measured value. This is a method of calculating plasma parameters based on the above. However, this measurement method has a problem that a measurement error occurs because the distribution of plasma is disturbed by inserting the probe electrode into the plasma space. Therefore, in the measurement method disclosed in Non-Patent Document 1 below, transmission measurement of electromagnetic waves is performed in a plurality of paths in the plasma space. Then, the electron density distribution is measured by obtaining the difference in transmission phase depending on the path.

The measurement method disclosed in Non-Patent Document 1 has a problem that the frequency band used is limited because it is necessary to know the frequency band through which electromagnetic waves pass through the plasma space in advance.

In view of the above, an object of the present invention is to provide a dielectric constant measuring device and a dielectric constant measuring system capable of measuring the spatial distribution of the dielectric constant of the measured space without being limited by the frequency band used by the electromagnetic wave. Another object of the present invention is to provide a plasma parameter measuring device and a plasma parameter measuring system capable of measuring the spatial distribution of plasma parameters in a space to be measured without being limited by the frequency band used by electromagnetic waves.

The dielectric constant measuring device according to one aspect of the present invention corresponds to a transmitting antenna arranged to face the measured space, a transmitter that emits an electromagnetic wave from the transmitting antenna toward the measured space, and the emitted electromagnetic wave. A dielectric constant measuring device used in a measuring system including at least one receiving antenna that receives scattered waves from the measured space and a receiver that generates a receiving signal based on the output signal of the at least one receiving antenna. The dielectric constant distribution and the scattering characteristic are obtained by using the scattering characteristic measuring unit that calculates the measured amount of the scattering characteristic of the measured space from the received signal and the estimated amount of the dielectric constant distribution in the measured space. The dielectric constant distribution so as to reduce the magnitude of the error between the measured amount and the estimated amount and the scattering characteristic estimation unit that calculates the estimated amount of the scattering characteristic based on the mathematical model showing the relationship between the two. It is characterized by including an update unit that updates the estimated amount of.

The plasma parameter measuring device according to another aspect of the present invention includes a transmitting antenna arranged so as to face the measured space containing a substance in a plasma state, a transmitter that emits an electromagnetic wave from the transmitting antenna toward the measured space, and a transmitter. In a measurement system including at least one receiving antenna that receives a scattered wave corresponding to the emitted electromagnetic wave from the measured space and a receiver that generates a receiving signal based on the output signal of the at least one receiving antenna. The plasma parameter measuring device used is the scattering characteristic measuring unit that calculates the measured amount of the scattering characteristic of the measured space from the received signal, and the estimated amount of the plasma parameter distribution in the measured space. The magnitude of the error between the measured amount and the estimated amount is reduced between the scattering characteristic estimation unit that calculates the estimated amount of the scattering characteristic based on the mathematical model showing the relationship between the parameter distribution and the scattering characteristic. It is characterized by including an update unit that updates the estimated amount of the plasma parameter distribution so as to be performed.

According to one aspect of the present invention, the dielectric constant distribution can be measured without being limited by the frequency band used by electromagnetic waves. Further, according to another aspect of the present invention, the plasma parameter distribution can be measured without being limited by the frequency band used by electromagnetic waves.

It is a figure which shows the schematic structure of the dielectric constant measurement system of Embodiment 1 which concerns on this invention. It is a block diagram which shows schematic the hardware structure example of the dielectric constant measuring apparatus of Embodiment 1. FIG. It is a figure which shows an example of the dielectric model used for the mathematical model which concerns on Embodiment 1. FIG. It is a figure which shows the matrix used for the mathematical model which concerns on Embodiment 1. It is a flowchart which shows typically an example of the operation procedure of the dielectric constant measuring apparatus of Embodiment 1. FIG. It is a figure which shows the schematic structure of the dielectric constant measurement system of Embodiment 2 which concerns on this invention. It is a flowchart which shows typically an example of the operation procedure of the dielectric constant measuring apparatus of Embodiment 2. It is a figure which shows the schematic structure of the dielectric constant measurement system of Embodiment 3 which concerns on this invention. It is a graph which shows the angular characteristic of scattering obtained by executing the simulation calculation. It is a graph which shows the electron density distribution obtained by executing the simulation calculation. It is a graph which shows the spatial distribution of the real part of the relative permittivity obtained by executing the simulation calculation. It is a graph showing the spatial distribution of the imaginary part of the relative permittivity obtained by executing the simulation calculation. It is a figure which shows the schematic structure of the dielectric constant measurement system of Embodiment 4 which concerns on this invention. It is a flowchart which shows typically an example of the operation procedure of the dielectric constant measuring apparatus of Embodiment 4. It is a figure which shows the schematic structure of the dielectric constant measurement system of Embodiment 5 which concerns on this invention. It is the schematic which shows the positional relationship between a space under measurement and a plurality of receiving antennas. It is a figure which shows the schematic structure of the plasma parameter measurement system of Embodiment 6 which concerns on this invention. It is a flowchart which shows typically an example of the operation procedure of the plasma parameter measurement apparatus of Embodiment 6. It is a figure which shows the schematic structure of the plasma parameter measurement system of Embodiment 7 which concerns on this invention. It is a flowchart which shows typically an example of the operation procedure of the plasma parameter measuring apparatus of Embodiment 7.

Hereinafter, various embodiments according to the present invention will be described in detail with reference to the drawings. In addition, the components having the same reference numerals in the entire drawing shall have the same configuration and the same function.

Embodiment 1.
FIG. 1 is a diagram showing a schematic configuration of a permittivity measurement system 1 according to a first embodiment of the present invention. As shown in FIG. 1, the dielectric constant measuring system 1 has a transmitting antenna TX arranged to face the measured space SF containing a substance in a plasma state (for example, a plume), and a transmitting antenna TX toward the measured space SF. The transmitter 20 that radiates the transmitted electromagnetic wave Tw, the receiving antenna RX that is arranged opposite to the measured space SF and receives the scattered wave Sw from the measured space SF, and the digital reception signal RS based on the output signal of the receiving antenna RX. It is configured to include a receiver 30 to be generated and a dielectric constant measuring device 11 for measuring a spatial distribution of complex dielectric constants (hereinafter referred to as “dielectric constant distribution”) in the space SF to be measured based on a digital reception signal RS. ing. The measurement target in the first embodiment and the second to fifth embodiments described later is a substance in a plasma state, but the measurement target is not limited to this. Not limited to the substance in the plasma state, any substance that scatters the transmitted electromagnetic wave Tw can be the measurement target.

The transmitter 20 operates according to the transmission control signal Tc supplied from the dielectric constant measuring device 11, generates a transmission signal in a high frequency band such as a microwave band, and supplies the transmission signal to the transmission antenna TX to transmit the transmission antenna. The transmitted electromagnetic wave Tw can be radiated from the TX toward the measured space SF. The transmitted electromagnetic wave Tw is scattered by a substance in the space SF to be measured. The receiving antenna RX receives the scattered wave Sw generated by the scattering of the transmitted electromagnetic wave Tw.

The receiver 30 has a frequency conversion function that converts the output signal of the receiving antenna RX into an analog signal having a frequency lower than the frequency of the output signal, and a phase detection that phase-detects the analog signal to generate an analog received signal. It has a function and an A / D conversion function that converts the analog received signal into a digital received signal RS (hereinafter, simply referred to as "received signal RS"). The received signal RS is a complex signal composed of an in-phase signal component and an orthogonal signal component.

As shown in FIG. 1, the permittivity measuring device 11 calculates the estimator MS of the scattering characteristic of the space SF to be measured from the control unit 40 that supplies the transmission control signal Tc to the transmitter 20 and the received signal RS. To reduce the magnitude of the error Δ between the measuring unit 41, the scattering characteristic estimation unit 42 that calculates the estimated amount ES of the scattering characteristics based on the mathematical model prepared in advance, and the measured amount MS and the estimated amount ES. Is provided with an update unit 43 for updating the estimated amount Pd of the dielectric constant distribution.

All or part of the functions of such a dielectric constant measuring device 11 are, for example, a semiconductor having a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), or an FPGA (Field-Programmable Gate Array). Or it can be realized by multiple processors. Alternatively, all or part of the functions of the dielectric constant measuring device 11 may be a single or multiple processors including an arithmetic unit such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit) that executes software or firmware program code. It may be realized by. Alternatively, all or part of the functions of the dielectric constant measuring device 11 can be realized by a single or a plurality of processors including a combination of a semiconductor integrated circuit such as a DSP, ASIC or FPGA and an arithmetic unit such as a CPU or GPU. Is.

FIG. 2 is a functional block diagram showing a schematic configuration of a signal processing device 70, which is an example of a hardware configuration of the permittivity measuring device 11 of the first embodiment. The signal processing device 70 shown in FIG. 2 includes a processor 71, a memory 72, a storage device 73, an input / output interface circuit 74, and a signal path 75. The signal path 75 is a bus for connecting the processor 71, the input / output interface circuit 74, the memory 72, and the storage device 73 to each other. The input / output interface circuit 74 has a function of transferring a signal input from the outside to the processor 71 and a function of outputting a signal transferred from the processor 71 to the outside.

The memory 72 includes a work memory used when the processor 71 executes digital signal processing, and a temporary storage memory in which data used in the digital signal processing is expanded. For example, the memory 72 may be composed of a flash memory and a semiconductor memory such as SDRAM (Synchronous Dynamic Random Access Memory). Further, when the processor 71 includes an arithmetic unit such as a CPU or GPU, the storage device 73 can be used as a storage area for storing a program code of software or firmware to be executed by the arithmetic unit. For example, the storage device 73 may be composed of a flash memory or a non-volatile semiconductor memory such as a ROM (Read Only Memory).

In the example of FIG. 2, the number of processors 71 is one, but the number is not limited to this. The hardware configuration of the permittivity measuring device 11 may be realized by using a plurality of processors that operate in cooperation with each other.

With reference to FIG. 1, the scattering characteristic measuring unit 41 analyzes the received signal RS to obtain the intensity of the scattered wave Sw, the phase of the scattered wave Sw, the frequency characteristic related to the intensity, and the frequency characteristic related to the phase. The measured amount MS of the scattering characteristic can be calculated.

On the other hand, the scattering characteristic estimation unit 42 uses the estimation amount Pd of the permittivity distribution in the space SF to be measured, and estimates the scattering characteristic ES based on a mathematical model showing the relationship between the dielectric constant distribution and the scattering characteristic. Can be calculated. By using a mathematical model, it is possible to calculate the estimated amount ES of scattering characteristics at high speed with a low calculation load.

FIG. 3 is a diagram showing an example of a dielectric model of the space SF to be measured used in the mathematical model. This dielectric model is a multilayer dielectric model in which a plurality of dielectric layers are symmetrically distributed with respect to an axis orthogonal to both the X-axis and the Z-axis (the axis in the direction perpendicular to the paper surface). Therefore, the dielectric model of FIG. 3 has axial symmetry. The dielectric model of Figure 3, the first layer L1 having a dielectric constant epsilon _1, a second layer L2 having a dielectric constant epsilon _2, and the third layer L3 having a dielectric constant epsilon _3, the dielectric constant epsilon ₄ It is composed of a fourth layer L4 having a dielectric constant of ε ₀ , and is surrounded by a peripheral region L ₀ having a dielectric constant ε ₀ . In the example of FIG. 3, the number of layers of the dielectric layer is four, but the number of layers is not limited to this, and the number of layers may be determined according to the desired resolution of the dielectric constant distribution. Spatial distribution of the permittivity ε of the dielectric model, where r is the distance (radius) from the central axis, that is, the axis of symmetry, and θ is the angle from the X axis in the XZ plane including the X and Z axes. Can be expressed by a function related to the distance r and the angle θ. The dielectric model of FIG. 3 is suitable for the analysis of such plumes because the plumes injected from the rocket engine form a nearly axisymmetric flow.

The following equation (1) is a mathematical expression representing an example of a mathematical model based on a multilayer dielectric model.

In equation (1), S (f, θ) is the scattering characteristic, f is the frequency of the transmitted electromagnetic wave Tw, θ is the angle around the axis of symmetry, j is a complex unit, k ₀ is the wave number in vacuum, and r _r is the receiving point. position from the axis of symmetry of the r _t position from the axis of symmetry of the transmission ^{_{point, H n (2) (x}} ) is the second kind Hankel function, J n _(x) is a Bessel function.

_{A 0n} in the formula (1), as shown in the following equation (2) is an element of the first row and first column of the inverse matrix _{A n} ^-1 for the matrix _{A n} shown in FIG.

In matrix A _n shown in FIG. 4, k _i is the i-th layer of the multilayer dielectric model (i is a positive integer) wave number, radius of r ₀ is axisymmetric scatterers, r _i, of the i-th layer The radius. Further, H _n ⁽²⁾ '(x) is the first derivative of the Type 2 Hankel function, and J _n '(x) is the first derivative of the Bessel function. Further, the wave number _{k i} is given by the following equation (3).

Here, ε _i is the permittivity of the i-th layer, and μ is the magnetic permeability.

Given the value of the frequency f of the transmitted electromagnetic wave Tw and the value of the angle θ, and given the estimated values of the permittivity ε ₁ to ε ₄ as the estimator Pd of the permittivity distribution, the scattering characteristic estimation unit 42 uses the equation ( The estimator ES of the scattering characteristic S (f, θ) can be calculated based on 1).

Next, referring to FIG. 1, the update unit 43 includes a comparison unit 44 and a dielectric constant distribution estimation unit 45. The comparison unit 44 calculates the error Δ between the measured amount MS of the scattering characteristic and the estimated amount ES calculated based on the mathematical model. The permittivity distribution estimation unit 45 corrects the current estimator of the permittivity distribution so that the magnitude of the error Δ becomes small according to the update formula of the adaptive algorithm such as the steepest descent method (Stepest Descent Algorithm). The updated estimator Pd of the permittivity distribution can be calculated. The updated estimator Pd is supplied to the scattering characteristic estimation unit 42. The scattering characteristic estimation unit 42 can calculate the estimated amount ES of the scattering characteristic based on the updated estimated amount Pd. The scattering characteristic estimation unit 42 and the update unit 43 can converge the estimation amount Pd of the dielectric constant distribution by executing an iterative operation based on the adaptive algorithm.

Next, the operation of the permittivity measuring device 11 will be described with reference to FIG. FIG. 5 is a flowchart schematically showing an example of the operation procedure of the permittivity measuring device 11.

First, the permittivity measuring device 11 radiates an electromagnetic wave from the transmitting antenna TX toward the space SF to be measured to obtain the received signal RS (step ST31). Specifically, the control unit 40 supplies the transmission control signal Tc to the transmitter 20. The transmitter 20 radiates the transmission electromagnetic wave Tw from the transmission antenna TX by supplying the transmission signal in the frequency band corresponding to the transmission control signal Tc to the transmission antenna TX. The receiving antenna RX receives the scattered wave Sw generated by the scattering of the transmitted electromagnetic wave Tw. The receiver 30 generates a received signal RS based on the output signal of the receiving antenna RX, and supplies the received signal RS to the scattering characteristic measuring unit 41.

After that, the scattering characteristic measuring unit 41 calculates the measured amount MS of the scattering characteristic of the space SF to be measured from the received signal RS (step ST32). On the other hand, the scattering characteristic estimation unit 42 and the update unit 43 initialize the estimation distribution of the dielectric constant by setting the estimation amount Pd of the dielectric constant distribution as the initial estimation amount (step ST33). For example, a uniform distribution of permittivity may be set as the initial estimator of the permittivity distribution. After that, the scattering characteristic estimation unit 42 and the update unit 43 update the estimated amount Pd of the dielectric constant distribution by executing an iterative operation based on a predetermined adaptive algorithm (steps ST34 to ST36).

That is, as described above, the scattering characteristic estimation unit 42 calculates the estimated amount ES of the scattering characteristic based on the mathematical model showing the relationship between the dielectric constant distribution and the scattering characteristic in the space SF to be measured (step ST34). The update unit 43 updates the estimator Pd of the permittivity distribution so as to reduce the magnitude of the error Δ between the estimator MS and the estimator ES of the scattering characteristics (step ST35). Specifically, after the comparison unit 44 calculates the error Δ, the permittivity distribution estimation unit 45 calculates the updated estimator Pd of the permittivity distribution according to an update formula of a predetermined adaptive algorithm such as the steepest descent method. Then, the updated estimator Pd is supplied to the scattering characteristic estimation unit 42.

After step ST35, the permittivity distribution estimation unit 45 determines whether or not to end the iterative calculation based on the adaptive algorithm (step ST36). For example, when the number of iterative operations reaches the upper limit value, or when the magnitude of the error Δ satisfies a predetermined convergence condition, the permittivity distribution estimation unit 45 can determine that the iterative operation is completed ( YES in step ST36). For example, as a predetermined convergence condition, there is a condition that the magnitude of the error Δ is continuously equal to or less than a certain value a predetermined number of times.

When it is determined that the iterative calculation is not completed (NO in step ST36), the scattering characteristic estimation unit 42, the comparison unit 44, and the dielectric constant distribution estimation unit 45 are performed in steps ST34 and ST35 based on the updated estimator Pd. Is executed again. When it is finally determined that the iterative calculation is completed (YES in step ST36), the permittivity measuring device 12 outputs the last updated estimated amount CPd of the permittivity distribution (step ST38).

As described above, in the permittivity measuring device 11 of the first embodiment, the receiving antenna RX receives the scattered wave Sw generated by the scattering of the transmitted electromagnetic wave Tw in the space SF to be measured, and the receiver 30 receives the receiving antenna RX. The received signal RS is generated based on the output signal of. The scattering characteristic measuring unit 41 calculates the measured amount MS of the scattering characteristic of the space SF to be measured, and the scattering characteristic estimation unit 42 calculates the estimated amount ES of the scattering characteristic based on the mathematical model. The update unit 43 can estimate the permittivity distribution by updating the estimator Pd of the permittivity distribution so as to reduce the magnitude of the error Δ between the measured quantity MS and the estimated quantity ES. As described above, as compared with the prior art, it is possible to estimate the dielectric constant distribution without being limited by the frequency band used by the transmitted electromagnetic wave Tw. In the present embodiment, since the probe electrode is not inserted into the measurement space SF, the distribution of the measurement target is not disturbed. Therefore, it is possible to measure the dielectric constant distribution without being restricted by the measurement target. In addition, there is an advantage that not only the characteristics of forward scattering (transmission) but also the characteristics of backscattering can be estimated using a mathematical model.

Further, since the scattering characteristic estimation unit 42 and the update unit 43 converge the estimated amount Pd of the permittivity distribution by executing an iterative operation based on a predetermined adaptive algorithm, the permittivity distribution can be estimated with high accuracy. Is.

Embodiment 2.
Next, the second embodiment according to the present invention will be described. In the present embodiment, the spatial distribution of plasma parameters (hereinafter referred to as “plasma parameter distribution”) is calculated using the estimation result of the dielectric constant distribution. FIG. 6 is a diagram showing a schematic configuration of a permittivity measurement system 2 according to a second embodiment of the present invention.

As shown in FIG. 6, the permittivity measuring system 2 includes a transmitting antenna TX, a transmitter 20, a receiving antenna RX, and a receiver 30, and measures the permittivity distribution of the space SF to be measured based on the received signal RS. It is configured to include a dielectric constant measuring device 12. The configuration of the permittivity measuring device 12 of the present embodiment is the same as the configuration of the permittivity measuring device 11 of the first embodiment except that the parameter distribution calculation unit 46 is provided.

As described above, the update unit 43 can calculate the estimated amount CPd of the dielectric constant distribution. Assuming that this estimated quantity CPd is expressed by the relative permittivity ε, the parameter distribution calculation unit 46 uses the relative permittivity ε and based on the following equations (4) to (6), the electron density of the space SF to be measured spatial distribution of n _e (hereinafter referred to as "electron density distribution."), spatial distribution of the plasma collision frequency [nu (hereinafter referred to as "collision frequency distribution".) and the spatial distribution of the plasma frequency omega _p (hereinafter referred to as "plasma frequency distribution" ) Can be calculated as the plasma parameter distribution.

In equation (4), ε ₀ is the permittivity in vacuum, and ω is the angular frequency of the transmitted electromagnetic wave Tw. Further, in the equation (6), _me is the mass of an electron and e is an elementary charge. Since the real part and the imaginary part of the complex permittivity ε on the left side of the equation (4) are given by the estimated amount CPd of the permittivity distribution, the equation determined by the real part on the left side and the right side of the equation (4) and the equation ( The collision frequency ν and the plasma frequency ω _p can be calculated from the equation determined by the imaginary parts on the left and right sides of 4). Using equation (6), it is possible to calculate the electron density n _e of the plasma frequency omega _p.

Next, the operation of the permittivity measuring device 12 will be described with reference to FIG. 7. FIG. 7 is a flowchart schematically showing an example of the operation procedure of the permittivity measuring device 12. Steps ST31 to ST36 in FIG. 7 are the same as steps ST31 to ST36 in FIG.

Referring to FIG. 7, when it is determined in step ST36 that the iterative calculation is completed (YES in step ST36), the parameter distribution calculation unit 46 uses the last updated estimator CPd of the dielectric constant distribution to be used. The plasma parameter distribution is calculated (step ST37). Then, the permittivity measuring device 12 outputs the data Ep showing the plasma parameter distribution and the estimated amount CPd of the permittivity distribution (step ST39).

As described above, the permittivity measuring device 12 of the second embodiment can accurately estimate the plasma parameter distribution based on the estimated amount CPd of the permittivity distribution.

Embodiment 3.
Next, the third embodiment according to the present invention will be described. FIG. 8 is a diagram showing a schematic configuration of a permittivity measurement system 3 according to a third embodiment of the present invention. As shown in FIG. 8, the dielectric constant measuring system 3 includes a transmitting antenna TX, a transmitter 20, a receiving antenna RX, and a receiver 30, and measures the dielectric constant distribution of the space SF to be measured based on the received signal RS. It is configured to include a dielectric constant measuring device 13. The configuration of the permittivity measuring device 13 is the same as the configuration of the permittivity measuring device 12 of the second embodiment except that the control unit 40C is provided instead of the control unit 40 of the second embodiment.

The permittivity measurement system 3 is provided with a moving mechanism 50. The moving mechanism 50 is a mechanism that operates according to the position control signal Pc supplied from the control unit 40C and positions the receiving antenna RX by moving it relative to the transmitting antenna TX. As a result, the permittivity measurement system 3 can receive the scattered wave Sw at a plurality of reception positions and can estimate the permittivity distribution for the plurality of reception positions, so that the estimation accuracy can be improved. .. For example, as shown in FIG. 8, the moving mechanism 50 may be configured to move the receiving antenna RX along the arcuate line RM surrounding the measured space SF on a plane intersecting the measured space SF. It is possible. As a result, the permittivity measuring device 13 can estimate the permittivity distribution using the angular characteristics of scattering.

The moving mechanism 50 of the present embodiment is configured to mechanically move the receiving antenna RX. Instead, the configuration of the moving mechanism 50 may be modified so that the transmitting antenna TX is mechanically moved, or both the transmitting antenna TX and the receiving antenna RX are mechanically moved.

9 to 12 are graphs showing the results obtained by executing the simulation calculation using the configuration of the permittivity measurement system 3 and the mathematical model according to the first embodiment. A uniform distribution was used as the initial permittivity distribution (initial estimator). FIG. 9 shows the angular characteristics of scattering. In the graph of FIG. 9, the horizontal axis represents the angle θ, and the vertical axis represents the logarithm of the absolute value of the scattering characteristic S (f, θ). Figure 10 is a graph showing the spatial distribution of the electron density n _e of the first to fourth layers in the multilayer dielectric model. In the graph of FIG. 10, the horizontal axis represents the radius r (unit: m), and the vertical axis indicates the electron density n _e. FIG. 11 is a graph showing the spatial distribution of the real part of the relative permittivity ε _r (= ε / ε ₀ ), and FIG. 12 is a graph showing the spatial distribution of the imaginary part of the relative permittivity ε _r . In the graphs of FIGS. 11 and 12, the horizontal axis indicates the radius r (unit: m). In the graphs of FIGS. 9 to 12, the estimation result obtained by the simulation calculation is displayed by a solid line, and the target calculation result obtained from the dielectric constant distribution of the correct answer is displayed by a broken line. The estimation result and the target calculation result are almost the same, and it can be seen that the permittivity distribution and the plasma parameter distribution are estimated accurately.

Embodiment 4.
Next, the fourth embodiment according to the present invention will be described. FIG. 13 is a diagram showing a schematic configuration of the permittivity measurement system 4 according to the fourth embodiment of the present invention. In the first to third embodiments, one receiving antenna RX is used. On the other hand, in the present embodiment, M receiving antennas RX ₁ to RX _M (M is an integer of 2 or more) are used. The receiving antennas RX ₁ to RX _M are held by an annular holding member 51 surrounding the space SF to be measured.

As shown in FIG. 13, the dielectric constant measuring system 4 includes a transmitting antenna TX, a transmitter 20, M receiving antennas RX ₁ to RX _M arranged so as to surround the space SF to be measured, and a receiving antenna. The dielectric constant distribution of the receiver 30D that generates the digital reception signals RS ₁ to RS _M of the M channel based on the output signals of RX ₁ to RX _M and the measured space SF based on the digital reception signals RS ₁ to RS _M. It is configured to include a dielectric constant measuring device 14 for measuring.

The receiver 30D has a frequency conversion function for converting the output signals of the receiving antennas RX ₁ to RX _M into analog signals of M channels (M receiving channels) having a frequency lower than the frequency of the output signals, and the analog. A phase detection function that phase-detects a signal to generate an analog reception signal of M channel, and the analog reception signal is referred to as an M channel digital reception signal RS ₁ to RS _M (hereinafter, simply referred to as "reception signal RS ₁ to RS _M "). It has an A / D conversion function that converts to.). Each of the received signals RS ₁ to RS _M is a complex signal composed of an in-phase signal component and an orthogonal signal component.

As shown in FIG. 13, the permittivity measuring device 14 is an estimator of the scattering characteristics of the space SF to be measured from the control unit 40 that supplies the transmission control signal Tc to the transmitter 20 and the received signals RS ₁ to RS _M MS _1. -Measurement with the scattering characteristic measuring unit 41D that calculates MS _M, and the scattering characteristic estimation unit 42 that calculates the estimated amount ES ₁ to ES _M of the scattering characteristics corresponding to each M channel based on the mathematical model prepared in advance. configured to include an update unit 43D for updating the estimated amount of Pd permittivity distribution so as to reduce the magnitude of the error Δ ₁ ~ Δ _M between the amount _MS 1 ~ MS _M and estimator _ES 1 ~ ES _M Has been done.

Scattering characteristic measuring section 41D, by analyzing each of the received signals RS 1 _~ RS _M, the intensity of the scattered wave Sw and scattered waves Sw phase, as well as the frequency characteristics relating to its strength, and, like the frequency characteristics related to the phase Measurements of scattering characteristics MS ₁ to MS _M can be calculated.

The scattering characteristic estimation unit 42D uses the estimation amount Pd of the dielectric constant distribution of the space SF to be measured, and estimates the scattering characteristics ES ₁ to ES _M based on the same mathematical model as the mathematical model according to the first embodiment. Can be calculated. By using a mathematical model similar to the mathematical model of the first embodiment, it is possible to calculate the estimated scattering characteristics ES ₁ to ES _M at high speed with a low calculation load.

The update unit 43D includes a comparison unit 44D and a dielectric constant distribution estimation unit 45D. Comparing unit 44D calculates an error Δ ₁ ~ Δ _M between the measured quantity _MS 1 ~ MS _M and estimator _ES 1 ~ ES _M calculated on the basis of the mathematical model of the scattering characteristics. Permittivity distribution estimation unit 45D in accordance with update equation of the adaptive algorithm such as the steepest descent method, by modifying the current estimate of permittivity distribution such that the magnitude of the error Δ _{1 ~} Δ _M is reduced, the dielectric The updated estimator Pd of the rate distribution can be calculated. For example, the magnitude of the error Δ _{1 ~} Δ _M, mean squared error need be calculated. The updated estimator Pd is supplied to the scattering characteristic estimation unit 42D. The scattering characteristic estimation unit 42D can calculate the scattering characteristic estimators ES ₁ to ES _M based on the updated estimator Pd. The scattering characteristic estimation unit 42D and the update unit 43D can converge the estimation amount Pd of the dielectric constant distribution by executing an iterative operation based on the adaptive algorithm.

Next, the operation of the permittivity measuring device 14 will be described with reference to FIG. FIG. 14 is a flowchart schematically showing an example of the operation procedure of the permittivity measuring device 14.

First, the permittivity measuring device 11 radiates an electromagnetic wave from the transmitting antenna TX toward the space SF to be measured to obtain reception signals RS ₁ to RS _M of a plurality of channels (step ST41). After that, the scattering characteristic measuring unit 41D calculates the measured quantities MS ₁ to MS _M of the scattering characteristic of the space SF to be measured from the received signals RS ₁ to RS _M (step ST42). On the other hand, the scattering characteristic estimation unit 42D and the update unit 43D initialize the estimation distribution of the permittivity by setting the estimation amount Pd of the dielectric constant distribution of the space SF to be measured as the initial estimation amount (step ST43). For example, a uniform distribution of permittivity may be set as the initial estimator of the permittivity distribution. After that, the scattering characteristic estimation unit 42D and the update unit 43D update the estimated amount Pd of the dielectric constant distribution by executing an iterative operation based on a predetermined adaptive algorithm (steps ST44 to ST46).

That is, as described above, the scattering characteristic estimation unit 42D uses the estimator Pd of the permittivity distribution in the space SF to be measured, and the scattering characteristics are based on a mathematical model showing the relationship between the permittivity distribution and the scattering characteristics. Estimators ES ₁ to ES _M are calculated (step ST44). Updating unit 43 updates the estimated amount of Pd permittivity distribution so as to reduce the magnitude of the error Δ ₁ ~ Δ _M between the measured quantity _MS 1 ~ MS _M scattering properties and the estimated amounts _ES 1 ~ ES _M (Step ST45). Specifically, after the comparing unit 44D has calculated error Δ _{1 ~} Δ _M, permittivity distribution estimation unit 45D in accordance with update equation of predetermined adaptive algorithm such as the steepest descent method, updated estimate of the permittivity distribution The quantity Pd is calculated, and the updated estimated quantity Pd is supplied to the scattering characteristic estimation unit 42D.

After step ST45, the permittivity distribution estimation unit 45D determines whether or not to end the iterative calculation based on the adaptive algorithm (step ST46). For example, if the number of iterative operations has reached the upper limit value, or when the magnitude of the error Δ _{1 ~} Δ _M is a predetermined convergence condition is satisfied, it is determined that the permittivity distribution estimation unit 45D terminates the iterative operation Can be done (YES in step ST46). For example, the predetermined convergence condition, the condition that the magnitude of the error Δ _{1 ~} Δ _M is equal to or less than a predetermined value continuously for a predetermined number of times and the like.

When it is determined that the iterative calculation is not completed (NO in step ST46), the scattering characteristic estimation unit 42D, the comparison unit 44D, and the dielectric constant distribution estimation unit 45D are performed in steps ST44 and ST45 based on the updated estimator Pd. Is executed again. When it is finally determined that the iterative calculation is completed (YES in step ST46), the parameter distribution calculation unit 46 uses the last updated estimator CPd of the dielectric constant distribution to use the above equation (4). The plasma parameter distribution is calculated based on (6) (step ST47). Then, the permittivity measuring device 12 outputs the data Ep showing the plasma parameter distribution and the estimated amount CPd of the permittivity distribution (step ST49).

As described above, the permittivity measurement system 1 of the fourth embodiment can instantly obtain an angular distribution of scattering characteristics by using a plurality of receiving antennas RX ₁ to RX _M surrounding the space SF to be measured. Therefore, the permittivity distribution can be estimated accurately even for the space SF to be measured having a scatterer that fluctuates in a short time.

Embodiment 5.
Next, the fifth embodiment according to the present invention will be described. FIG. 15 is a diagram showing a schematic configuration of a permittivity measuring system 5 according to a fifth embodiment of the present invention. As shown in FIG. 15, the permittivity measuring system 5 includes a transmitting antenna TX, a transmitter 20, M receiving antennas RX ₁ to RX _M, and a receiver 30D, and receives signals RS ₁ to RS _{M of the} M channel. The permittivity measuring device 15 for measuring the permittivity distribution of the space SF to be measured is provided based on the above. The configuration of the permittivity measuring device 15 is the same as the configuration of the permittivity measuring device 14 of the fourth embodiment except that the control unit 40E is provided instead of the control unit 40 of the fourth embodiment.

Further, the permittivity measuring system 5 includes a moving mechanism 52. The control unit 40E supplies the transmission control signal Tc to the transmitter 20 and supplies the position control signal Pc to the moving mechanism 52. The moving mechanism 52 operates according to the position control signal Pc supplied from the control unit 40E, and positions the transmitting antenna TX and the receiving antennas RX ₁ to RX _{M as a} whole by moving them relative to the space SF to be measured. is there.

FIG. 16 is a schematic view showing the positional relationship between the space SF to be measured and the receiving antennas RX ₁ to RX _M. The space SF to be measured has an axisymmetric distribution with respect to the central axis Y. The receiving antennas RX ₁ to RX _M are arranged so as to surround the space SF to be measured on the plane CS orthogonal to the central axis Y. By moving the holding member 51 along the central axis Y, the moving mechanism 52 can move the receiving antennas RX ₁ to RX _M surrounding the space to be measured SF along the central axis Y.

By having the above-mentioned configuration, the permittivity measurement system 5 can obtain a three-dimensional distribution of the permittivity in the space SF to be measured.

Embodiment 6.
Next, a sixth embodiment of the present invention will be described. In the above embodiments 2 to 5, the plasma parameter distribution is calculated based on the estimation result of the dielectric constant distribution. In the sixth embodiment and the seventh embodiment described later, the plasma parameter distribution is estimated without estimating the dielectric constant distribution.

FIG. 17 is a diagram showing a schematic configuration of the plasma parameter measurement system 6 of the sixth embodiment according to the present invention. As shown in FIG. 17, the plasma parameter measurement system 6 has a transmitting antenna TX arranged to face the measured space SF containing a substance in a plasma state (for example, a plume), and a transmitting antenna TX toward the measured space SF. The transmitter 20 that radiates the transmitted electromagnetic wave Tw, the receiving antenna RX that is arranged opposite to the measured space SF and receives the scattered wave Sw from the measured space SF, and the digital reception signal RS based on the output signal of the receiving antenna RX. The receiver 30 to be generated, the moving mechanism 50 to move and position the receiving antenna RX relative to the transmitting antenna TX, and the plasma parameter distribution (electron density distribution, electron density distribution) in the measured space SF based on the digital received signal RS. It is configured to include a plasma parameter measuring device 16 for measuring the plasma frequency distribution and the collision frequency distribution).

The configuration of the transmitter 20, the transmitting antenna TX, the receiving antenna RX, the receiver 30, and the moving mechanism 50 in the present embodiment includes the transmitter 20, the transmitting antenna TX, the receiving antenna RX, the receiver 30, and the moving mechanism 50 in the third embodiment. The configuration is the same as that of the mechanism 50.

The plasma parameter measuring device 16 supplies the transmission control signal Tc to the transmitter 20 and the position control signal Pc to the moving mechanism 50, and the estimator MS of the scattering characteristic of the space SF to be measured from the received signal RS. The magnitude of the error Δ between the measured amount MS and the estimated amount ES, the scattering characteristic measuring unit 41 to be calculated, the scattering characteristic estimation unit 42E that calculates the estimated amount ES of the scattering characteristic based on the mathematical model prepared in advance, and the measured amount MS. It is configured to include an update unit 43E that updates the estimator Ed of the plasma parameter distribution so as to reduce the value, and a dielectric constant distribution calculation unit 47 that calculates the dielectric constant distribution of the space SF to be measured from the updated estimator Ed. ing. The configuration of the scattering characteristic measuring unit 41 and the control unit 40C in the present embodiment is the same as the configuration of the scattering characteristic measuring unit 41 and the control unit 40C in the third embodiment.

The scattering characteristic estimation unit 42E uses the estimated amount Ed of the plasma parameter distribution in the space SF to be measured, and calculates the estimated amount ES of the scattering characteristic based on a mathematical model showing the relationship between the plasma parameter distribution and the scattering characteristic. be able to. By using a mathematical model, it is possible to calculate the estimated amount ES of scattering characteristics at high speed with a low computational load.

As the mathematical model, the above equation (1) based on the multilayer dielectric model can be used. In consideration of the above equation (4), the complex permittivity ε _i of the i-th layer in the equation (1) is the electron density _ne ⁽ⁱ⁾ and the plasma of the i-layer as shown in the following equation (7). It is expressed using the frequency ω _p ⁽ⁱ⁾ (where ω = 2πf).

Therefore, the value of the frequency f of the transmitted electromagnetic wave Tw and the value of the angle θ are given, and the electron densities _ne ⁽¹⁾ to _ne ⁽⁴⁾ and the plasma frequencies ω _p ⁽¹⁾ to are used as the estimators Ed of the plasma parameter distribution. Given the estimated value of ω _p ⁽⁴⁾ , the scattering characteristic estimation unit 42E can calculate the estimator ES of the scattering characteristic S (f, θ) based on the equation (1).

Further, in consideration of the above equation (6), the complex permittivity ε _i of the i-th layer has the electron density _ne ⁽ⁱ⁾ and the collision frequency ν ^{(i ) of} the i-layer as shown in the following equation (8). ⁾ Is used.

Therefore, the value of the frequency f of the transmitted electromagnetic wave Tw and the value of the angle θ are given, and the electron densities _ne ⁽¹⁾ to _ne ⁽⁴⁾ and the collision frequencies ν ⁽¹⁾ to ν are used as the estimators Ed of the plasma parameter distribution. Given the estimated value of ⁽⁴⁾ , the scattering characteristic estimation unit 42E can calculate the estimator ES of the scattering characteristic S (f, θ) based on the equation (1).

The update unit 43E includes a comparison unit 44 and a parameter distribution estimation unit 45E. The comparison unit 44 calculates the error Δ between the measured amount MS of the scattering characteristic and the estimated amount ES calculated based on the mathematical model. The parameter distribution estimation unit 45E corrects the current estimator of the plasma parameter distribution so that the magnitude of the error Δ becomes small according to the update formula of the adaptive algorithm such as the steepest descent method (Stepest Descent Algorithm). The updated estimator Ed of the parameter distribution can be calculated. The updated estimator Ed is supplied to the scattering characteristic estimation unit 42E. The scattering characteristic estimation unit 42E can calculate the estimated amount ES of the scattering characteristic based on the updated estimated amount Ed. The scattering characteristic estimation unit 42E and the update unit 43E can converge the estimated amount Ed of the plasma parameter distribution by executing an iterative operation based on the adaptive algorithm.

Next, the operation of the plasma parameter measuring device 16 will be described with reference to FIG. FIG. 18 is a flowchart schematically showing an example of the operation procedure of the plasma parameter measuring device 16.

First, as in the case of the first embodiment, the plasma parameter measuring device 16 radiates an electromagnetic wave from the transmitting antenna TX toward the measured space SF to obtain the received signal RS (step ST31). Subsequently, the scattering characteristic measuring unit 41 calculates the measured amount MS of the scattering characteristic of the space SF to be measured from the received signal RS (step ST32).

After that, the scattering characteristic estimation unit 42E and the update unit 43E set the estimated amount Ed of the plasma parameter distribution to the initial estimated amount and initialize the estimated distribution of the plasma parameters (step ST53). For example, as the initial estimator of the plasma parameter distribution, an amount corresponding to a uniform distribution of the dielectric constant may be set. After that, the scattering characteristic estimation unit 42E and the update unit 43E update the estimated amount Ed of the plasma parameter distribution by executing an iterative operation based on a predetermined adaptation algorithm (steps ST54 to ST56).

That is, as described above, the scattering characteristic estimation unit 42E calculates the estimated amount ES of the scattering characteristics based on the mathematical model showing the relationship between the plasma parameter distribution and the scattering characteristics in the space SF to be measured (step ST54). The update unit 43E updates the estimator Ed of the plasma parameter distribution so as to reduce the magnitude of the error Δ between the estimator MS and the estimator ES of the scattering characteristics (step ST55). Specifically, after the comparison unit 44E calculates the error Δ, the parameter distribution estimation unit 45E calculates the updated estimator Ed of the plasma parameter distribution according to an update formula of a predetermined adaptive algorithm such as the steepest descent method. , The updated estimator Ed is supplied to the scattering characteristic estimation unit 42E.

After step ST55, the parameter distribution estimation unit 45E determines whether or not to end the iterative calculation based on the adaptive algorithm (step ST56). For example, when the number of iterative operations reaches the upper limit value, or when the magnitude of the error Δ satisfies a predetermined convergence condition, the parameter distribution estimation unit 45E can determine that the iterative operation is completed (step). YES of ST56). For example, as a predetermined convergence condition, there is a condition that the magnitude of the error Δ is continuously equal to or less than a certain value a predetermined number of times.

When it is determined that the iterative calculation is not completed (NO in step ST56), the scattering characteristic estimation unit 42E, the comparison unit 44, and the parameter distribution estimation unit 45E perform steps ST54 and ST55 based on the updated estimator Ed. Try again. When it is finally determined that the iterative calculation is completed (YES in step ST56), the permittivity distribution calculation unit 47 uses the estimator CEd of the last updated plasma parameter distribution and uses a predetermined calculation formula (for example, YES). , Equations (7) and (8)) to calculate the permittivity distribution (step ST57). Then, the plasma parameter measuring device 16 outputs the data Pp showing the dielectric constant distribution and the estimated amount CEd of the plasma parameter distribution (step ST59).

As described above, in the plasma parameter measuring device 16 of the sixth embodiment, the receiving antenna RX receives the scattered wave Sw generated by the scattering of the transmitted electromagnetic wave Tw in the measured space SF, and the receiver 30 receives the receiving antenna RX. The received signal RS is generated based on the output signal of. The scattering characteristic measuring unit 41 calculates the measured amount MS of the scattering characteristic of the space SF to be measured, and the scattering characteristic estimating unit 42E calculates the estimated amount ES of the scattering characteristic based on the mathematical model. The update unit 43E can estimate the plasma parameter distribution by updating the estimated amount Ed of the plasma parameter distribution so as to reduce the magnitude of the error Δ between the measured amount MS and the estimated amount ES. As described above, as compared with the prior art, it is possible to estimate the plasma parameter distribution without being limited by the frequency band used by the transmitted electromagnetic wave Tw. In the present embodiment, since the probe electrode is not inserted into the measurement space SF, the distribution of the measurement target is not disturbed. Therefore, it is possible to measure the plasma parameter distribution without being restricted by the measurement target. In addition, there is an advantage that not only the characteristics of forward scattering (transmission) but also the characteristics of backscattering can be estimated using a mathematical model.

Further, since the scattering characteristic estimation unit 42E and the update unit 43E converge the estimated amount Ed of the plasma parameter distribution by executing an iterative operation based on a predetermined adaptive algorithm, the plasma parameter distribution can be estimated with high accuracy. Is.

Further, the plasma parameter measurement system 6 is provided with a moving mechanism 50. As a result, the plasma parameter measurement system 6 can receive the scattered wave Sw at a plurality of reception positions, and can estimate the plasma parameter distribution for the plurality of reception positions, so that the estimation accuracy can be improved. ..

Embodiment 7.
Next, the seventh embodiment according to the present invention will be described. FIG. 19 is a diagram showing a schematic configuration of the plasma parameter measurement system 7 according to the seventh embodiment of the present invention. In the sixth embodiment, one receiving antenna RX is used. On the other hand, in the present embodiment, as in the fourth and fifth embodiments, M receiving antennas RX ₁ to RX _M are used. The receiving antennas RX ₁ to RX _M are held by an annular holding member 51 surrounding the space SF to be measured.

As shown in FIG. 19, the plasma parameter measurement system 7 includes M transmission antennas TX, a transmitter 20, and M units facing each other so as to surround a space SF to be measured including a substance in a plasma state (for example, a plume). To the receivers 30D that generate the digital reception signals RS ₁ to RS _M of the M channel based on the output signals of the reception antennas RX ₁ to RX _M and the reception antennas RX ₁ to RX _M , and the digital reception signals RS ₁ to RS _M. A plasma parameter measuring device 17 that measures the plasma parameter distribution (electron density distribution, plasma frequency distribution, and collision frequency distribution) of the space SF to be measured based on the measurement space SF, and a transmitting antenna TX and receiving antennas RX ₁ to RX for the space SF to be measured. It is configured to include a moving mechanism 52 that relatively moves and positions the entire _M.

Transmitter 20 in the present embodiment, the configuration of the transmission antenna TX, the receiving antennas _RX 1 ~ RX _M, receiver 30D and the moving mechanism 52, transmitter 20, transmit antennas TX in the fifth embodiment, the receiving antennas _RX 1 ~ The configuration is the same as that of the RX _M , the receiver 30D, and the moving mechanism 52.

Plasma parameter measurement device 17 includes a control unit 40E supplied to the moving mechanism 52 of the position control signal Pc supplied to the transmission control signal Tc to the transmitter 20, from the received signal _RS 1 ~ RS _M scattering characteristic of the measurement space SF The scattering characteristic measurement unit 41F that calculates the measured quantities MS ₁ to MS _M , respectively, and the scattering characteristic estimation unit that calculates the estimated amount ES ₁ to ES _M of the scattering characteristics corresponding to the M channels based on the mathematical model prepared in advance. and 42F, and the update unit 43F for updating the measurand _MS 1 ~ MS _M and the estimated amount Ed plasma parameter distribution to reduce the magnitude of the error Δ ₁ ~ Δ _M between the estimator _ES 1 ~ ES _M , The dielectric constant distribution calculation unit 47 that calculates the dielectric constant distribution of the space SF to be measured from the updated estimator Ed is provided. The configuration of the scattering characteristic measuring unit 41D and the control unit 40E in the present embodiment is the same as the configuration of the scattering characteristic measuring unit 41D and the control unit 40E in the fifth embodiment.

The scattering characteristic estimation unit 42F uses the estimated amount Ed of the plasma parameter distribution in the space SF to be measured, and the estimated amount ES ₁ to ES of the scattering characteristics based on the mathematical model showing the relationship between the plasma parameter distribution and the scattering characteristics. _M can be calculated. By using a mathematical model similar to the mathematical model of the sixth embodiment, it is possible to calculate the estimated scattering characteristics ES ₁ to ES _M at high speed with a low calculation load.

The update unit 43F includes a comparison unit 44D and a parameter distribution estimation unit 45F. Comparing unit 44D calculates an error Δ ₁ ~ Δ _M between the measured quantity _MS 1 ~ MS _M and estimator _ES 1 ~ ES _M calculated on the basis of the mathematical model of the scattering characteristics. Parameter distribution estimating unit 45F in accordance with update equation of the adaptive algorithm such as the steepest descent method, by modifying the current estimate of the plasma parameter distribution such that the magnitude of the error Δ _{1 ~} Δ _M is reduced, plasma parameters The updated estimator Ed of the distribution can be calculated. For example, the magnitude of the error Δ _{1 ~} Δ _M, mean squared error need be calculated. The updated estimator Ed is supplied to the scattering characteristic estimation unit 42F. The scattering characteristic estimation unit 42F can calculate the scattering characteristic estimators ES ₁ to ES _M based on the updated estimator Ed. The scattering characteristic estimation unit 42F and the update unit 43F can converge the estimated amount Ed of the plasma parameter distribution by executing an iterative operation based on the adaptive algorithm.

Next, the operation of the plasma parameter measuring device 17 will be described with reference to FIG. FIG. 20 is a flowchart schematically showing an example of the operation procedure of the plasma parameter measuring device 17.

First, as in the case of the fifth embodiment, the plasma parameter measuring device 17 radiates an electromagnetic wave from the transmitting antenna TX toward the space SF to be measured to obtain the received signals RS ₁ to RS _M of a plurality of channels (step). ST41). Subsequently, the scattering characteristic measuring unit 41D calculates the measured quantities MS ₁ to MS _M of the scattering characteristic of the space SF to be measured from the received signals RS ₁ to RS _M (step ST42).

After that, the scattering characteristic estimation unit 42F and the update unit 43F initialize the estimated distribution of plasma parameters by setting the estimated amount Ed of the plasma parameter distribution of the space SF to be measured as the initial estimated amount (step ST63). For example, as the initial estimator of the plasma parameter distribution, an amount corresponding to a uniform distribution of the dielectric constant may be set. After that, the scattering characteristic estimation unit 42F and the update unit 43F update the estimated amount Ed of the plasma parameter distribution by executing an iterative operation based on a predetermined adaptation algorithm (steps ST64 to ST66).

That is, the scattering characteristic estimation unit 42F calculates the estimated scattering characteristics ES ₁ to ES _M based on the mathematical model showing the relationship between the plasma parameter distribution and the scattering characteristics in the space SF to be measured (step ST64). Update unit 43F is updated estimate Ed of the plasma parameter distribution to reduce the magnitude of the error Δ ₁ ~ Δ _M between the measured quantity _MS 1 ~ MS _M scattering properties and the estimated amounts _ES 1 ~ ES _M (Step ST65). Specifically, after the comparing unit 44D has calculated error Δ _{1 ~} Δ _M, the parameter distribution estimating unit 45F in accordance with update equation of predetermined adaptive algorithm such as the steepest descent method, updated estimates of the plasma parameter distribution Ed is calculated, and the updated estimator Ed is supplied to the scattering characteristic estimation unit 42F.

After step ST65, the parameter distribution estimation unit 45F determines whether or not to end the iterative operation based on the adaptive algorithm (step ST66). For example, if the number of iterative operations has reached the upper limit value or, if the magnitude of the error Δ _{1 ~} Δ _M is a predetermined convergence condition is satisfied, determining a parameter distribution estimating unit 45F finishes the iterative operation Can be done (YES in step ST66). For example, the predetermined convergence condition, the condition that the magnitude of the error Δ _{1 ~} Δ _M is equal to or less than a predetermined value continuously for a predetermined number of times and the like.

When it is determined that the iterative calculation is not completed (NO in step ST66), the scattering characteristic estimation unit 42F, the comparison unit 44D, and the parameter distribution estimation unit 45F perform steps ST64 and ST65 based on the updated estimator Ed. Try again. When it is finally determined that the iterative calculation is completed (YES in step ST66), the permittivity distribution calculation unit 47 uses the estimator CEd of the last updated plasma parameter distribution and uses a predetermined calculation formula (for example, YES). , Equations (7) and (8)) to calculate the permittivity distribution (step ST67). Then, the plasma parameter measuring device 16 outputs the data Pp showing the dielectric constant distribution and the estimated amount CEd of the plasma parameter distribution (step ST69).

As described above, the plasma parameter measurement system 7 of the seventh embodiment can instantly obtain an angular distribution of scattering characteristics by using a plurality of receiving antennas RX ₁ to RX _M surrounding the space SF to be measured. Therefore, it is possible to accurately estimate the plasma parameter distribution even for the measured space SF having a scatterer that fluctuates in a short time.

Although the embodiments 1 to 7 according to the present invention have been described above with reference to the drawings, the embodiments 1 to 7 are examples of the present invention, and various embodiments other than the embodiments 1 to 7 are used. It can also be adopted. Within the scope of the present invention, any combination of embodiments 1 to 7, modification of any component of each embodiment, or omission of any component of each embodiment is possible.

For example, as in the case of the first embodiment, all or a part of the functions of the permittivity measuring devices 11 to 15 and the plasma parameter measuring devices 16 and 17 of the second to seventh embodiments may be, for example, DSP. It can be realized by one or more processors having semiconductor integrated circuits such as ASIC or FPGA. Alternatively, all or part of the functionality of each device may be implemented by one or more processors, including arithmetic units such as CPUs or GPUs, that execute software or firmware program code. Alternatively, it is also possible to realize all or part of the functions of each device by a single or a plurality of processors including a combination of a semiconductor integrated circuit such as a DSP, ASIC or FPGA and a computing device such as a CPU or GPU. The hardware configuration of each device may be realized by the signal processing device 70 shown in FIG.

The permittivity measuring device, the permittivity measuring system, the plasma parameter measuring device, and the plasma parameter measuring system according to the present invention can estimate the spatial distribution of characteristic values such as the permittivity in the space under test with high accuracy. , Suitable for use in rocket engine plume analysis.

1 to 5 plasma parameter measurement system, 2,6 dielectric constant measurement system, 11 to 15 dielectric constant measurement device, 16,17 plasma parameter measurement device, 20 transmitters, 30, 30D receiver, 40, 40C, 40E control unit, 41,41D scattering characteristic measurement unit, 42,42D, 42E, 42F scattering characteristic estimation unit, 43,43D, 43E, 43F update unit, 44,44D comparison unit, 45,45D dielectric constant distribution estimation unit, 45E, 45F parameter distribution Estimating unit, 46 parameter distribution calculation unit, 47 dielectric constant distribution calculation unit, 50, 52 moving mechanism, 51 holding member, TX transmitting antenna, RX, RX ₁ to RX _M receiving antenna, SF measured space.

Claims (19)

1. A transmitting antenna arranged to face the measured space, a transmitter that radiates an electromagnetic wave from the transmitting antenna toward the measured space, and at least a scattered wave corresponding to the radiated electromagnetic wave is received from the measured space. A dielectric constant measuring device used in a measuring system including one receiving antenna and a receiver that generates a receiving signal based on the output signal of the at least one receiving antenna.
   A scattering characteristic measuring unit that calculates a measured amount of scattering characteristics in the space to be measured from the received signal,
   A scattering characteristic estimation unit that calculates an estimated amount of the scattering characteristics based on a mathematical model showing the relationship between the dielectric constant distribution and the scattering characteristics using the estimated amount of the dielectric constant distribution in the space to be measured.
   A permittivity measuring device comprising an updating unit that updates the estimated amount of the dielectric constant distribution so as to reduce the magnitude of an error between the measured amount and the estimated amount.
2. The permittivity measuring device according to claim 1, wherein the scattering characteristic estimation unit and the update unit converge the estimated amount of the permittivity distribution by executing an iterative operation based on a predetermined adaptive algorithm. A featured permittivity measuring device.
3. The permittivity measuring device according to claim 1 or 2, wherein at least one of the electron density distribution, the collision frequency distribution, and the plasma frequency is calculated as a plasma parameter distribution using the estimated amount of the permittivity distribution. A permittivity measuring device, further comprising a parameter distribution calculation unit.
4. The permittivity measuring device according to any one of claims 1 to 3, wherein the space to be measured is a plasma space in which a plume exists.
5. The permittivity measuring device according to any one of claims 1 to 4, wherein the frequency band of the electromagnetic wave is a microwave band.
6. The dielectric constant measuring device according to any one of claims 1 to 5.
   The at least one receiving antenna includes a plurality of receiving antennas arranged to face each other so as to surround the space to be measured.
   The receiver generates a plurality of channels of received signals based on the output signals of the plurality of receiving antennas.
   The scattering characteristic measuring unit calculates a plurality of measured quantities of the scattering characteristic from the received signals of the plurality of channels, respectively.
   The scattering characteristic estimation unit calculates a plurality of estimated amounts of the scattering characteristics corresponding to the plurality of channels based on the mathematical model.
   The updater updates the estimate of the permittivity distribution so as to reduce the magnitude of the error between the plurality of measurements and the plurality of estimates.
   A permittivity measuring device characterized by this.
7. The dielectric constant measuring device according to any one of claims 1 to 5, the transmitting antenna, the transmitter, at least one receiving antenna, and the receiver are provided. Dielectric constant measurement system.
8. The dielectric constant measuring system according to claim 7, further comprising a moving mechanism for moving at least one receiving antenna relative to the transmitting antenna.
9. The permittivity measuring system according to claim 6, further comprising the permittivity measuring device, the transmitting antenna, the transmitter, the plurality of receiving antennas, and the receiver.
10. The dielectric constant measuring system according to claim 9, further comprising a moving mechanism for moving the transmitting antenna and the plurality of receiving antennas relative to the space to be measured. ..
11. The dielectric constant measuring system according to claim 10.
    The plurality of receiving antennas are arranged in an annular shape around the axis of symmetry of the space to be measured.
    The moving mechanism is configured to relatively move the transmitting antenna and the plurality of receiving antennas along the axis of symmetry.
    A permittivity measurement system characterized by this.
12. A transmitting antenna arranged to face the measured space containing a substance in a plasma state, a transmitter that radiates an electromagnetic wave from the transmitting antenna toward the measured space, and a scattered wave corresponding to the radiated electromagnetic wave are subjected to the subject. A plasma parameter measuring device used in a measuring system including at least one receiving antenna receiving from a measurement space and a receiver that generates a receiving signal based on the output signal of the at least one receiving antenna.
    A scattering characteristic measuring unit that calculates a measured amount of scattering characteristics in the space to be measured from the received signal,
    A scattering characteristic estimation unit that calculates an estimated amount of the scattering characteristics based on a mathematical model showing the relationship between the plasma parameter distribution and the scattering characteristics using the estimated amount of the plasma parameter distribution in the space to be measured.
    A plasma parameter measuring apparatus including an update unit that updates the estimated amount of the plasma parameter distribution so as to reduce the magnitude of an error between the measured amount and the estimated amount.
13. The plasma parameter measuring device according to claim 12, wherein the scattering characteristic estimation unit and the updating unit converge the estimated amount of the plasma parameter distribution by executing an iterative calculation based on a predetermined adaptive algorithm. A featured plasma parameter measuring device.
14. The plasma parameter measuring apparatus according to claim 12 or 13.
    The at least one receiving antenna includes a plurality of receiving antennas arranged to face each other so as to surround the space to be measured.
    The receiver generates a plurality of channels of received signals based on the output signals of the plurality of receiving antennas.
    The scattering characteristic measuring unit calculates a plurality of measured quantities of the scattering characteristic from the received signals of the plurality of channels, respectively.
    The scattering characteristic estimation unit calculates a plurality of estimated amounts of the scattering characteristics corresponding to the plurality of channels based on the mathematical model.
    The updating unit updates the estimated amount of the plasma parameter distribution so as to reduce the magnitude of the error between the plurality of measured quantities and the plurality of estimated quantities.
    A plasma parameter measuring device characterized in that.
15. A plasma parameter measurement system comprising the plasma parameter measuring device according to claim 12 or 13, the transmitting antenna, the transmitter, at least one receiving antenna, and the receiver.
16. The plasma parameter measurement system according to claim 15, further comprising a moving mechanism for moving at least one receiving antenna relative to the transmitting antenna.
17. A plasma parameter measurement system comprising the plasma parameter measuring device according to claim 14, the transmitting antenna, the transmitter, the plurality of receiving antennas, and the receiver.
18. The plasma parameter measurement system according to claim 17, further comprising a moving mechanism for moving the transmitting antenna and the plurality of receiving antennas relative to the space to be measured. ..
19. The plasma parameter measurement system according to claim 18.
    The plurality of receiving antennas are arranged in an annular shape around the axis of symmetry of the space to be measured.
    The moving mechanism is configured to relatively move the transmitting antenna and the plurality of receiving antennas along the axis of symmetry.
    A plasma parameter measurement system characterized by this.

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