CN108872267B - Plasma complex dielectric constant transient microwave reflection measurement method and device - Google Patents
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Abstract
The invention belongs to the technical field of plasma diagnosis, relates to a microwave measurement technology, and particularly provides a method and a device for measuring the transient microwave reflection of a plasma complex dielectric constant, wherein the measuring device is based on a shock wave tube experimental platform, the measuring method processes received reflection signals through a calibration and cancellation technology to obtain the real reflection coefficient of the wall surface of the shock wave tube, and the influence of the self reflection signals of a test system is removed; then, the obtained reflection coefficient of the surface of the wall of the shock tube is utilized to reversely push the change of the complex dielectric constant of the plasma in the shock tube; meanwhile, aiming at the problem of multivalueness of the function of the complex dielectric constant of the plasma reversely deduced by the reflection coefficient of the shock wave pipe wall, the invention solves the problem by utilizing the approximation of the linear change of the complex dielectric constant of the plasma in a short time, thereby effectively realizing the transient measurement of the complex dielectric constant of the plasma.
Description
Technical Field
The invention belongs to the technical field of plasma diagnosis, relates to a microwave measurement technology, and particularly provides a method and a device for measuring the transient microwave reflection of a plasma complex dielectric constant based on a shock tube experimental platform.
Background
The plasma, which is a fourth state of matter different from solid, liquid and gas, is mainly composed of charged ions and free electrons, and it exhibits a highly excited unstable state and thus hardly persists in the natural environment. There are many ways to artificially generate plasma, and as a device for generating high-density plasma applied to experimental research, plasma can only be generated in the device and only lasts for hundreds of microseconds, although the langmuir probe diagnosis method has been applied to measure the electron density and the collision frequency of plasma, the microwave diagnosis method has better application prospect in non-contact measurement of the electron density and the collision frequency of plasma due to the fact that the density distribution of plasma in a tube is influenced by the characteristics of the intervention method to cause test errors. The microwave diagnosis method can be divided into a transmission method and a reflection method, the transmission method utilizes the change of the amplitude phase of the electromagnetic wave through the plasma to reversely deduce the electron density and the collision frequency of the plasma, and the plasma density test range of the transmission method has high requirements on the dynamic test range of the received signals of the system hardware because the high-density plasma has great attenuation to the electromagnetic wave and even generates a signal cutoff phenomenon; in contrast, the reflection method analyzes the change of the electron density and the collision frequency of the plasma by using the reflected wave generated by the interaction of the electromagnetic wave and the plasma, and has lower requirement on the dynamic test range of the received signal of the system hardware and stronger applicability because the signal cutoff phenomenon does not exist and the influence of the plasma on the amplitude change of the reflected signal is relatively small. The invention provides a method and a device for measuring transient microwave reflection of a plasma complex dielectric constant based on a shock tube experimental platform on the basis that the electron density and the collision frequency of the plasma have a one-to-one corresponding equivalence relation with the equivalent complex dielectric constant of the plasma.
Disclosure of Invention
The invention aims to provide a method and a device for measuring the transient microwave reflection of a plasma complex dielectric constant based on a shock tube experimental platform, wherein the method and the device are used for processing received reflection signals through a calibration and cancellation technology to obtain the real reflection coefficient of the wall surface of the shock tube and removing the influence of the self reflection signals of a test system; then, the obtained reflection coefficient of the surface of the wall of the shock tube is utilized to reversely push the change of the complex dielectric constant of the plasma in the shock tube; meanwhile, aiming at the problem of multivalueness of the function of the complex dielectric constant of the plasma reversely deduced by the reflection coefficient of the shock tube wall, the invention utilizes the approximation of the linear change of the complex dielectric constant of the plasma in a short time to solve the problem, thereby realizing the test method which comprises the complete hardware test operation and the complete software calculation processing.
In order to achieve the purpose, the invention adopts the technical scheme that:
a plasma complex dielectric constant transient microwave reflection measuring device comprises a signal source, a pair of cancellation branch machines, a receiver, an industrial personal computer, a lens, a horn antenna, a shock tube and two microwave darkrooms; the plasma generation device is characterized in that the horn antenna and the lens are arranged in a first microwave darkroom, the signal source output signal excites the horn antenna to emit microwaves through the cancellation branch machine, and the microwaves act on plasma in the shock tube through the lens; the plasma is partially transmitted and partially reflected, and the transmitted wave enters a second microwave dark room and is absorbed; the reflected wave returns along the original path to be received by the horn antenna and reaches the receiver after passing through the canceling and distributing machine, and the industrial personal computer measures and processes data of signals of the receiver and outputs the complex dielectric constant of the plasma.
The method for measuring the plasma complex dielectric constant transient microwave reflection is characterized by comprising the following steps of:
step 1: opening a signal source, shielding a window of a first microwave darkroom by adopting a wave-absorbing material, adjusting an attenuator phase shifter of a cancellation branch machine to enable a received signal of a receiver to tend to noise, measuring and recording the received signal at the moment, and marking as E1;
step 2: keeping the state of a signal source and a cancellation extension unchanged, removing wave-absorbing materials, carrying out a plasma transient experiment and recording a receiving signal of a receiver to obtain a discrete receiving signal data:
data＝[data(1),data(2),data(3),...,data(T)]
wherein, T is the total number of sampling points: t is M multiplied by N, N is the number of sampling points in a preset single processing time period, and M is the number of the single processing time periods;
and step 3: calibrating the discrete receiving signal to obtain the reflection coefficient gamma of the shock wave tube wall1(n)：
And 4, step 4: reflection coefficient gamma based on shock tube wall1(n), calculating the complex dielectric constant of the plasma:
according to the reflection coefficient gamma of the wall of the shock tube1(n) constructing an objective function:
m＝1,2,3,...,M
wherein a is an initial value of the dielectric constant of the plasma, c is an initial value of the loss, b is a rate of change of the dielectric constant of the plasma, e is a rate of change of the loss, Delta epsilonr' is a dimension of a predetermined rate of change of dielectric constant, Δ εrIs a dimension of a preset loss change rate;
Zin4＝η0，
wherein eta is0Representing the characteristic impedance, η, of airTRepresenting the characteristic impedance, eta, of the wall of the shock tubepRepresenting the characteristic impedance of the plasma:
k0is the wave number, epsilon, of the electromagnetic wave in free spaceTIs the dielectric constant of the wall of the shock tube, epsilonrIs the complex dielectric constant of the plasma, d1Thickness of the shock tube wall, d2Is the plasma thickness;
initializing an initial value a of the dielectric constant of the plasma 11, initial loss value c1When the target function F is equal to 0, the target function F is minimum, and the change rate b of the dielectric constant of the plasma is solved1And rate of change of loss e1(ii) a According to the update formula:
am＝am-1+bm-1Δε′r，cm＝cm-1+em-1Δε″r
updating the initial value of the dielectric constant and the initial value of the loss of the plasma, taking the target function F as the minimum value, solving the change rate and the change rate of the dielectric constant of the plasma until the initial value a of the dielectric constant of the plasma in the Mth section of the single processing time period is obtainedMInitial loss value cMRate of change of dielectric constant of plasma bMAnd rate of change of loss eMThe complex dielectric constant of the plasma is obtained.
The invention has the beneficial effects that:
the invention provides a method and a device for measuring the transient microwave reflection of a plasma complex dielectric constant based on a shock tube experimental platform, wherein the method and the device are used for processing received reflection signals through a calibration and cancellation technology to obtain the real reflection coefficient of the wall surface of a shock tube, and removing the influence of the self reflection signals of a test system; then, the obtained reflection coefficient of the surface of the wall of the shock tube is utilized to reversely push the change of the complex dielectric constant of the plasma in the shock tube; meanwhile, the invention effectively realizes the transient measurement of the complex dielectric constant of the plasma by utilizing the approximate treatment of the linear change of the complex dielectric constant of the plasma in a short time.
Drawings
FIG. 1 is a schematic diagram of a plasma complex dielectric constant transient microwave reflection measurement apparatus according to the present invention.
FIG. 2 is a schematic diagram illustrating the calibration and cancellation process of the present invention.
FIG. 3 shows an electromagnetic model of a shock tube according to the present invention.
FIG. 4 is a graph of complex permittivity test results of a high density state plasma in an embodiment of the invention.
FIG. 5 is a graph of complex permittivity test results for a medium density state plasma in an embodiment of the present invention.
FIG. 6 is a graph of complex permittivity test results of low density state plasma in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following drawings and examples.
The invention provides a plasma complex dielectric constant transient microwave reflection measuring device, the structure of which is shown in figure 1; the system comprises a signal source, a cancellation branch machine, a receiver, an industrial personal computer, a lens, a horn antenna, a shock tube and two microwave darkrooms; the horn antenna and the lens are arranged in a first microwave darkroom, the signal source output signal excites the horn antenna to emit microwaves through the cancellation machine, and the microwaves act on plasma in the shock tube through the lens; the plasma is partially transmitted and partially reflected, and the transmitted wave enters a second microwave dark room and is absorbed; the reflected wave returns along the original path to be received by the horn antenna and reaches the receiver after passing through the canceling and distributing machine, and the industrial personal computer measures and processes data of signals of the receiver and outputs the complex dielectric constant of the plasma. The measuring method based on the measuring device is divided into two parts, wherein the first part is to obtain the change of the reflection coefficient of the surface of the shock tube by utilizing the calibration and cancellation technology; the second part is to optimize and reversely deduce the change of the complex dielectric constant of the plasma in the shock tube through a set objective function according to the measured reflection coefficient of the surface of the shock tube.
The calibration and cancellation principle is shown in fig. 2; the test of the invention comprises the calibration of the results of three different states, which is described in detail as follows:
1. test condition one
As shown in fig. 2(a), the lens, the horn antenna, the waveguide coaxial converter and the rf cable are regarded as a whole, that is, the window of the first microwave dark room is shielded by the wave-absorbing material in step 1; the electromagnetic characteristic of the cable is characterized by using a two-port scattering matrix, wherein a port 1 is a feed incident port of a radio frequency cable, a port 2 is an emergent surface of a lens, and the specific expression of the scattering matrix is as follows:
wherein S is11Is the reflection coefficient of 1 port, S12Is the transmission coefficient from 1 port to 2 port, S21Is the transmission coefficient from 2 port to 1 port, S22Reflection coefficient of 2 ports;
in the case where the cancellation operation is not performed, the reflected wave E1 obtained by the test can be expressed as follows:
E1＝E0(S12S21Γ+S11)
since the background is a wave-absorbing material in this state, Γ can be regarded as 0, i.e. there is no reflection of the background, and the above formula can be rewritten as:
E1＝E0S11
the cancellation operation is divided into two steps of hardware cancellation and software cancellation, wherein the hardware cancellation utilizes a directional coupler to couple part of the transmitted signals to a receiving signal branch, and the coupled signals and the reflected signals E1 in the state are in equal amplitude and opposite phase through an attenuator and a phase shifter, so that the received signals in the state are as small as possible; however, since hardware cancellation is limited by that it is difficult to achieve an ideal cancellation effect by human operation, software cancellation is required, the received signal of the system in this state is measured and the amplitude phase of the received signal is determined, and then the received signal at this time is changed from E1 to a known quantity E1, and the specific expression is as follows:
E1*＝E0S11-E0*
wherein E0 is a coupling signal introduced by hardware cancellation;
the aim of the cancellation operation is to remove the influence of the reflected signals generated by the horn antenna, the lens and the waveguide coaxial converter on the emission coefficient of the surface of the wall of the test shock wave tube;
2. test state two
As shown in fig. 2(b), when no plasma is generated in the shock tube, the visible interior is filled with air and is in a stable state, the transmission signal remains unchanged, cancellation operation is performed before the transient test experiment, and then the reflected signal E2 received by the receiver during the transient test experiment can be represented as:
E2＝E0S12S21Γ0+E1*
Γ0the reflection coefficient of the plane wave vertically incident to the wall of the shock tube when the shock tube is filled with air;
3. test State three
As shown in fig. 2(c), when plasma is generated in the shock tube, the visible interior is filled with plasma and has uniform distribution, the transmission signal remains unchanged, cancellation operation is performed before the transient test experiment, and then the state that the receiver receives the reflected signal E3 during the transient test experiment can be represented as:
E3＝E0S12S21Γ1+E1*
Γ1the reflection coefficient of the plane wave vertically incident to the shock tube wall when the shock tube is filled with plasma.
In this embodiment, the measurement process of the plasma complex dielectric constant transient microwave reflection is as follows:
the method comprises the following steps: according to the figure 1, the connection system is provided with an experimental platform;
step two: opening a signal source, setting a first test state (a window of a first microwave darkroom is shielded by adopting a wave-absorbing material) as shown in fig. 2(a), adjusting an attenuator phase shifter of a cancellation extension set to enable a received signal of a receiver to tend to noise, and measuring and recording the received signal at the moment, wherein the received signal is marked as E1;
step three: keeping the states of the signal source and the cancellation branch machine unchanged, and removing the wave-absorbing material to keep the device in a preparation experiment state; then, performing a plasma transient experiment and recording a receiver receiving signal to obtain a discrete receiving signal data:
data＝[data(1),data(2),data(3),...,data(T)]
wherein, T is the total number of sampling points: t is M multiplied by N, N is the number of sampling points in a preset single processing time period, and M is the number of the single processing time periods; it should be noted that: data (1) is the data for no plasma generation (i.e., test state two E2), and the remaining data are considered as the values for test state three E3;
step four: calibrating the discrete receiving signal to obtain the reflection coefficient gamma of the shock wave tube wall1(n)：
Step five: reflection coefficient gamma based on shock tube wall1And (n) calculating the complex dielectric constant of the plasma.
In the invention, the shock tube surface reflection coefficient calculation model is shown in figure 3, and only one reflection, eta, is considered in each region of the shock tube0Representing the characteristic impedance, η, of airTRepresenting the characteristic impedance, η, of TeflonpRepresents the characteristic impedance of the plasma and,
k0is the wave number, epsilon, of the electromagnetic wave in free spaceTIs the dielectric constant of Teflon ∈rIs the complex dielectric constant of the plasma; gamma-shaped2、Γ3、Γ4Respectively, Z represents the reflection coefficient of the interfaces T2, T3 and T4in、Zin2、Zin3、Zin4The input impedances of interfaces T1, T2, T3 and T4 are represented respectively, and specific expressions are shown as follows:
Zin4＝η0
and the shock tube surface reflection coefficient Γ can be expressed as:
in shock tube experiments, the dielectric constant and loss of the plasma are continuously varied with time, e.g. by varyingrViewed as a function of time, the reflection coefficient expression may be expressed as f ═ f (epsilon)r) Within a very short time, we can consider that the dielectric constant and the loss vary linearly with time, i.e. can assume epsilon'r(t)＝a+bt、ε″r(t) ═ c + et, a and c represent initial values of dielectric constant and loss in a single processing period, and b and e represent rates of change, so that the measurement data are divided into M single processing periods each including N sampling points in the calculation process of the present invention;
further to facilitate analysis, time is normalized for a single processing time period, and to facilitate optimization, a dimension of the rate of change is set, and the above equation is then changed to
The unknowns at this time are only b and e, and the dielectric constant of the plasma changesSmaller change, dimension Δ ε 'of dielectric constant change rate in this example'rLet us assume a dimension Δ ε ″, a loss change rate of 0.0001rSet to 0.0001; the reflection coefficient expression at this time can be expressed as:
the measurement of dielectric constant and loss becomes an optimal calculation problem, and the function of the test value is gamma1The optimization objective function can be expressed as:
where M ═ 1,2, 3.., M, denotes the mth single treatment session.
In the embodiment, the plasma in the high, medium and low density states is measured, the signal source frequency adopts 10GHz, hardware cancellation and software cancellation are respectively performed before an experiment, the measurement is performed according to the technical scheme of the invention, the specific result is shown in fig. 4, 5 and 6, and the result shows that the plasma in different density states can be completely distinguished, so that the feasibility and effectiveness of the invention are proved.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.
Claims (1)
1. A plasma complex dielectric constant transient microwave reflection measuring device comprises a signal source, a pair of cancellation branch machines, a receiver, an industrial personal computer, a lens, a horn antenna, a shock tube and two microwave darkrooms; the plasma generation device is characterized in that the horn antenna and the lens are arranged in a first microwave darkroom, the signal source output signal excites the horn antenna to emit microwaves through the cancellation branch machine, and the microwaves act on plasma in the shock tube through the lens; the plasma is partially transmitted and partially reflected, and the transmitted wave enters a second microwave dark room and is absorbed; the reflected wave returns along the original path, is received by the horn antenna and reaches the receiver after passing through the canceling and distributing machine, and the industrial personal computer measures and processes data of a signal of the receiver and outputs a plasma complex dielectric constant;
the measuring method of the measuring device comprises the following steps:
step 1: opening a signal source, shielding a window of a first microwave darkroom by adopting a wave-absorbing material, adjusting an attenuator phase shifter of a cancellation branch machine to enable a received signal of a receiver to tend to noise, measuring and recording the received signal at the moment, and marking as E1;
step 2: keeping the state of a signal source and a cancellation extension unchanged, removing wave-absorbing materials, carrying out a plasma transient experiment and recording a receiving signal of a receiver to obtain a discrete receiving signal data:
data＝[data(1),data(2),data(3),...,data(T)]
wherein, T is the total number of sampling points: t is M multiplied by N, N is the number of sampling points in a preset single processing time period, and M is the number of the single processing time periods;
and step 3: calibrating the discrete receiving signal to obtain the reflection coefficient gamma of the shock wave tube wall1(n)：
And 4, step 4: reflection coefficient gamma based on shock tube wall1(n), calculating the complex dielectric constant of the plasma:
according to the reflection coefficient gamma of the wall of the shock tube1(n) constructing an objective function:
wherein a is the initial value of the dielectric constant of the plasma, c isInitial loss value, b is the rate of change of the plasma dielectric constant, e is the rate of change of the loss,. DELTA.. epsilon.'rFor a predetermined dimension of the rate of change of the dielectric constant, Δ ε ″)rIs a dimension of a preset loss change rate;
Zin4＝η0，
wherein eta is0Representing the characteristic impedance, η, of airTRepresenting the characteristic impedance, eta, of the wall of the shock tubepRepresenting the characteristic impedance of the plasma:
k0is the wave number, epsilon, of the electromagnetic wave in free spaceTIs the dielectric constant of the wall of the shock tube, epsilonrIs the complex dielectric constant of the plasma, d1Thickness of the shock tube wall, d2Is the plasma thickness;
initializing an initial value a of the dielectric constant of the plasma11, initial loss value c1When the target function F is equal to 0, the target function F is minimum, and the change rate b of the dielectric constant of the plasma is solved1And rate of change of loss e1(ii) a According to the update formula:
am＝am-1+bm-1Δε′r，cm＝cm-1+em-1Δε″r
updating the initial value of the dielectric constant and the initial value of the loss of the plasma, taking the target function F as the minimum value, solving the change rate and the change rate of the dielectric constant of the plasma until the initial value a of the dielectric constant of the plasma in the Mth section of the single processing time period is obtainedMInitial loss value cMRate of change of dielectric constant of plasma bMAnd rate of change of loss eMThe complex dielectric constant of the plasma is obtained.
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