A method for diagnosing parameters of inhomogeneous plasma based on local microwave penetration effect

Abstract

This invention provides a method for diagnosing parameters of non-uniform plasmas based on the local microwave penetration effect. This method relates to the fields of electromagnetics and plasma diagnostics, and includes a combined diagnosis of the electron density distribution and collision frequency of a plasma profile. The method models the plasma to the left of the peak layer by layer and iteratively optimizes the distribution results. The method also uses the maximum reflection coefficient amplitude slope to derive the plasma electron density peak. For the plasma to the right of the peak, the method models multiple distribution models, determining the model using the attenuation coefficient. Furthermore, the method uses the maximum reflection coefficient amplitude to diagnose the collision frequency. This method addresses the problem of diagnosing parameters of non-uniform plasma profiles.

Description

Technical Field

[0001] The present invention belongs to the technical fields of electromagnetics and plasma diagnosis, and in particular relates to a method for diagnosing parameters of non-uniform plasmas based on the local penetration effect of microwaves. Background Art

[0002] When a spacecraft flies at hypersonic speeds between 20 and 100 kilometers above the ground, its nose surface rubs violently against the air, forming a plasma sheath. This attenuates and phase-shifts electromagnetic waves, severely impacting communication quality and even causing radio outages, a phenomenon known as "blackout." To predict, assess, and even mitigate this "blackout" phenomenon, it's necessary to diagnose plasma sheath parameters, typically including electron density and collision frequency.

[0003] Microwave diagnostics is one of the main methods currently used for plasma diagnosis, and they can be categorized as both invasive and non-invasive. Invasive microwave diagnostics primarily utilize probes, including microwave resonance probes, plasma impedance probes, and plasma absorption probes. Non-invasive microwave diagnostics can be further categorized as microwave reflectometry and microwave transmission. Microwave reflectometry uses the amplitude and phase of electromagnetic waves reflected from the plasma interface to diagnose plasma parameters, while microwave transmission utilizes the attenuation of electromagnetic waves through the plasma to infer electron density and collision frequency.

[0004] Existing plasma diagnostic technology has the following disadvantages:

[0005] Electrostatic probes and microwave probes are invasive diagnostic methods that can interfere with the plasma flow field, such as changing the flow pattern and forming space charge sheaths, and are generally unable to diagnose collision frequencies.

[0006] Although the microwave transmission method does not interfere with the plasma being measured, it requires multiple transmitting and receiving channels and generally has low spatial resolution, making it impossible to accurately diagnose the distribution of plasma electron density.

[0007] Traditional microwave reflectometry diagnoses the profile by inferring electron density from the incident frequency based on the total reflection of electromagnetic waves at different locations in the plasma. This method ignores the influence of the plasma layer near the reflecting surface on the reflection amplitude and phase, resulting in insufficient diagnostic accuracy. Summary of the Invention

[0008] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for diagnosing parameters of non-uniform plasmas based on the local penetration effect of microwaves, which solves the problem of diagnosing parameters of non-uniform plasma profiles.

[0009] In order to achieve the above objectives, the technical solution adopted by the present invention is: a method for diagnosing parameters of non-uniform plasma based on the local penetration effect of microwaves, comprising the following steps:

[0010] S1. Obtaining an amplitude and phase curve of a plasma reflection coefficient, wherein the phase curve of the plasma reflection coefficient is used to query an actual reflection coefficient phase according to an incident frequency;

[0011] S2, searching for the maximum value of the slope of the amplitude decrease of the swept plasma reflection coefficient to determine the peak electron density, wherein the frequency of the maximum value is the cutoff frequency fc corresponding to the peak electron density;

[0012] S3. Divide the plasma to be diagnosed with a thickness of d into N spatial resolution units according to non-uniformity, and introduce an additional layer 0 before layer L = 1, wherein the thickness of each spatial resolution unit is divided according to the cutoff frequency fc corresponding to the peak electron density and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength;

[0013] S4, setting the initial value of the collision frequency inversion to a number close to 0;

[0014] S5. Iteratively invert the plasma density rising edge profile based on the local penetration effect and non-uniform partitioning results;

[0015] S6. At the initial inversion frequency f1, gradually increase the collision frequency until the reflection coefficient amplitude of the rising edge inversion profile at this frequency point is close to the reflection coefficient amplitude of the measured curve. This value is the collision frequency inversion value, and the collision frequency diagnosis is completed. The collision frequency value is the collision frequency that makes the reflection coefficient amplitude of the rising edge inversion profile close to the reflection coefficient amplitude of the measured curve.

[0016] S7. Based on the collision frequency diagnosis results, multiple distribution models are modeled, the attenuation coefficient is determined by the amplitude of the plasma reflection coefficient, and the reflection coefficient amplitude curve is obtained by sweeping the attenuation coefficient;

[0017] S8. Compare the reflection coefficient amplitude curve with the standard amplitude curve to determine whether the second inflection point of the reflection coefficient amplitude curve is closest to the standard amplitude curve. If so, complete the falling edge distribution diagnosis; otherwise, return to step S7.

[0018] The present invention has the following beneficial effects: It proposes a plasma electron density distribution diagnosis method based on the local penetration characteristics of plasma, including a combined diagnosis of plasma profile electron density distribution and collision frequency. The present invention layer-by-layer modeling is performed on the plasma to the left of the peak, and the distribution results are iteratively optimized. The present invention uses the maximum reflection coefficient amplitude slope to derive the plasma electron density peak. The present invention models multiple distribution models for the plasma to the right of the peak, determining the model using the attenuation coefficient. Furthermore, the present invention uses the maximum reflection coefficient amplitude to diagnose the collision frequency. This invention solves the problem of diagnosing parameters in non-uniform plasma profiles.

[0019] Furthermore, the expression of the electron density is as follows:

[0020]

[0021] Among them, ne p represents the electron density of the plasma, f represents the plasma cutoff frequency, m e represents the mass of the electron, ε0 represents the dielectric constant of vacuum, and e represents the charge of the electron.

[0022] Furthermore, step S5 includes the following steps:

[0023] S501, according to the actual test obtained by the sweep reflection coefficient phase, by determining the initial reflection phase Get the initial inversion frequency f1 and the corresponding electron density ne1, where Indicates the maximum value of the reflected phase;

[0024] S502, start i=1 round of iteration, invert the plasma electron density of layer L=1, when the plasma passes through the thickness d0 of the 0th layer, total reflection occurs, and the thickness d0 corresponding to the density of the 0th layer is inverted according to the initial phase of the reflection;

[0025] S503, divide the thickness d0 into and Two floors, and An infinite metal boundary is placed behind, where Δd represents the diagnostic spatial resolution, which is divided into two layers according to the peak electron density corresponding to the cutoff frequency fc and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength;

[0026] S504: Based on the setting result of step S503, the reflection coefficient phase is calculated using the equivalent transmission line model. And repeatedly adjust The position of the reflection coefficient phase Close to the actual reflection coefficient phase, determine the first layer of plasma position;

[0027] S505, continue i=1 rounds of iteration, invert the plasma electron density of L=2 layers, and calculate the reflection coefficient phase using the equivalent transmission line model And repeatedly adjust The position of the reflection coefficient phase Close to the actual reflection coefficient phase, repeat step S505 until the peak electron density is reached, and the position of the second layer of plasma is determined; wherein, this round of inversion is three layers of plasma plus a metal boundary, the three layers of plasma density are ne0, ne1 and ne2 respectively, the first layer of plasma and the second layer of plasma correspond to the cutoff frequencies f1 and f2 respectively, and the positions are and

[0028] S506, determine whether the completion of arrive If yes, then go to step S6, otherwise, add 1 to the value of i and return to step S502 to iteratively invert the plasma density rising edge profile. In each round, a layer of local penetrable thickness is added. That is, in the i-th round, when determining the thickness of the l-th layer of electron density, a metal plate is placed after the l+i-1 layer. arrive The value remains unchanged from the previous inversion result. The value of the reflection coefficient phase Closest to the actual reflection coefficient phase, complete the arrive Iterative update of , where Indicates the position of the 0th layer in the i-th round, represents the first layer position in round i, Indicates the second-level position in round i, Indicates the position of the N-i+1th layer in the i-th round, and They represent the l+1th layer position and the l+i-1th layer position in the i-th round respectively.

[0029] The beneficial effect of the above further solution is that the position of each layer of plasma is continuously corrected through multiple rounds of iterative inversion, making the inversion result more accurate.

[0030] Furthermore, the thickness d0 is expressed as follows:

[0031]

[0032] Here, k0 represents the free space wave number.

[0033] The beneficial effect of the above further solution is: through the above formula, the thickness of the 0th layer is determined for plasma inversion, and on this basis, the 0th layer is divided to form the 1st layer, laying the foundation for plasma inversion.

[0034] Furthermore, the expression of the equivalent transmission line model is as follows:

[0035]

[0036] Among them, R l and R l+1 They represent the reflection coefficients of the lth layer and the l+1th layer inside the equivalent transmission line model, respectively. l and k l+1 denote the wave vectors along the incident direction in the lth layer and the l+1th layer, j denotes the imaginary unit, μ l and μ l+1 Represent the magnetic permeability of the lth layer and the magnetic permeability of the l+1th layer, R l(l+1) and P l(l+1) Both represent two intermediate parameters, R0 represents the final reflection coefficient of the equivalent transmission line model to the outside, represents the reflection coefficient phase, d l Represents the position coordinates of the lth layer.

[0037] The beneficial effects of the above further solution are: providing theoretical support for the calculation of the reflection coefficient and providing a basis for the subsequent calculation of the plasma layer position. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flow chart of the method of the present invention.

[0039] Figure 2 Schematic diagram of the original reflection coefficient amplitude curve.

[0040] Figure 3 Schematic diagram of the original reflection coefficient phase curve.

[0041] Figure 4 This is the plasma inversion result on the left side of the peak.

[0042] Figure 5 Schematic diagram of the amplitude curve when the attenuation coefficient a=1400.

[0043] Figure 6 Schematic diagram of the plasma electron density distribution inversion results. DETAILED DESCRIPTION

[0044] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0045] Example

[0046] Based on the above, the present invention provides a method for inverting the electron density distribution of the plasma profile and diagnosing the collision frequency at the same time, which is specifically divided into the diagnosis of the electron density peak, the diagnosis of the distribution on the left side of the peak, the diagnosis of the distribution on the right side of the peak, and the diagnosis of the collision frequency. Figure 1 As shown, a method for diagnosing parameters of non-uniform plasma based on the local penetration effect of microwaves is implemented as follows:

[0047] S1. Obtaining an amplitude and phase curve of a plasma reflection coefficient, wherein the phase curve of the plasma reflection coefficient is used to query an actual reflection coefficient phase according to an incident frequency;

[0048] S2, searching for the maximum value of the slope of the amplitude decrease of the swept plasma reflection coefficient to determine the peak electron density, wherein the frequency of the maximum value is the cutoff frequency fc corresponding to the peak electron density;

[0049] In this embodiment, the peak electron density is determined by searching for the maximum value of the slope of the sweep reflection coefficient amplitude. The frequency of this point is the cutoff frequency corresponding to the peak electron density. The electron density can be converted by formula (1) according to the cutoff frequency. Then, within this order of magnitude, the electron density is divided into

[0050]

[0051] Among them, ne p represents the electron density of the plasma, f represents the plasma cutoff frequency, m e represents the mass of the electron, ε0 represents the dielectric constant of vacuum, and e represents the charge of the electron.

[0052] S3. Divide the plasma to be diagnosed with a thickness of d into N spatial resolution units according to non-uniformity, and introduce an additional layer 0 before layer L = 1, wherein the thickness of each spatial resolution unit is divided according to the cutoff frequency fc corresponding to the peak electron density and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength;

[0053] In this embodiment, the plasma with a thickness of d to be diagnosed is divided into 1, 2, ..., N spatial resolution units based on their inhomogeneity. For iterative inversion, an additional layer 0 is introduced before layer L = 1. Specifically, the thickness of each spatial resolution unit can be determined based on the peak electron density corresponding to the cutoff frequency fc and the maximum incident frequency finc corresponding to 1 / 3 of the wavelength.

[0054] S4. Set the initial value of the collision frequency inversion to a number close to 0, for example, it can be set to 1e-30;

[0055] S5. Based on the local penetration effect and the non-uniform partitioning results, iteratively invert the plasma density rising edge profile. The implementation method is as follows:

[0056] S501, according to the actual test obtained by the sweep reflection coefficient phase, by determining the initial reflection phase Get the initial inversion frequency f1 and the corresponding electron density ne1, where Indicates the maximum value of the reflected phase;

[0057] In this embodiment, the initial reflection phase is determined based on the sweep reflection coefficient phase obtained in actual testing. The initial inversion frequency f1 is determined by this, The closer to 180 degrees, the lower the initial inversion frequency, and the smaller the plasma density at the starting position of the corresponding plasma profile. The actual electron density corresponding to the cutoff frequency f1 can also be obtained by formula (1), recorded as ne1, and the position corresponding to the density is inverted

[0058] S502, start i=1 round of iteration, invert the plasma electron density of layer L=1, when the plasma passes through the thickness d0 of the 0th layer, total reflection occurs, and the thickness d0 corresponding to the density of the 0th layer is inverted according to the initial phase of the reflection;

[0059] S503, divide the thickness d0 into and Two floors, and An infinite metal boundary is placed behind, where Δd represents the diagnostic spatial resolution, which is divided into two layers according to the peak electron density corresponding to the cutoff frequency fc and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength;

[0060] S504: Based on the setting result of step S503, the reflection coefficient phase is calculated using the equivalent transmission line model. And repeatedly adjust The position of the reflection coefficient phase Close to the actual reflection coefficient phase, determine the first layer of plasma position;

[0061] In this embodiment, the iteration starts with round i = 1. First, the plasma electron density of layer L = 1 is inverted. Specifically, assuming that the electron density of layer 0 is ne0 = 0, the plasma undergoes total reflection after passing through the layer thickness d0. The thickness corresponding to the density of layer 0 is inverted based on the initial phase of the reflection, which can be converted according to the following formula:

[0062]

[0063] Where k0 represents the free space wave number. Divide d0 into two layers, denoted as Δd is the diagnostic spatial resolution, which can be divided according to the peak electron density corresponding to the cutoff frequency fc and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength. An infinite metal boundary is placed behind it. The local penetration effect of plasma is defined as the plasma reflection phase is no longer affected by the electron density behind it after passing through a few resolution units of the plasma cutoff frequency. Therefore, placing a metal boundary will not affect the reflection phase. At this time, the inversion model is the reflection of two layers of plasma and the metal boundary under the irradiation of the incident wave of frequency f1. The reflection coefficient phase of this model can be obtained using the equivalent transmission line model The equivalent transmission line model formula is as follows:

[0064]

[0065]

[0066]

[0067]

[0068] Among them, R l and R l+1 They represent the reflection coefficients of the lth layer and the l+1th layer inside the equivalent transmission line model, respectively. l and k l+1 denote the wave vectors along the incident direction in the lth layer and the l+1th layer, j denotes the imaginary unit, μ l and μ l+1 Represent the magnetic permeability of the lth layer and the magnetic permeability of the l+1th layer, R l(l+1) and P l(l+1) Both represent two intermediate parameters, R0 represents the final reflection coefficient of the equivalent transmission line model to the outside, represents the reflection coefficient phase, d l Represents the position coordinates of the first layer. The value of R0 can be obtained by reverse deduction based on the reflection coefficient of the last layer using formula (2).

[0069] Repeated adjustments Position until Approximate the reflection coefficient phase of the real inhomogeneous plasma at this frequency. At this time, the position corresponding to the electron density ne1 is Determine the position of the first plasma layer. In particular, if If it deviates far from d0, the resolution unit size needs to be readjusted.

[0070] S505, continue i=1 rounds of iteration, invert the plasma electron density of L=2 layers, and calculate the reflection coefficient phase using the equivalent transmission line model And repeatedly adjust The position of the reflection coefficient phase Close to the actual reflection coefficient phase, repeat step S505 until the peak electron density is reached, and the position of the second layer of plasma is determined; wherein, this round of inversion is three layers of plasma plus a metal boundary, the three layers of plasma density are ne0, ne1 and ne2 respectively, the first layer of plasma and the second layer of plasma correspond to the cutoff frequencies f1 and f2 respectively, and the positions are and

[0071] In this embodiment, the second layer electron density position is determined according to the above steps. The inversion is continued for i=1 iterations, and the inversion of L=2 layers of electron density. At this time, the inversion model is a three-layer plasma plus a metal boundary. The three-layer plasma density is known, namely ne0, ne1 and ne2. The cutoff frequencies of the first and second layers of plasma are f1 and f2, respectively, and their positions are and Among them, only The position that needs to be inverted is unknown, and the reflection coefficient phase of the model can be obtained by using the equivalent transmission line model Repeated adjustments Position until Approximate the reflection coefficient phase of a real inhomogeneous plasma at this frequency. Repeat this step until the peak electron density is reached, completing the first iteration.

[0072] S506, determine whether the completion of arrive If yes, then go to step S6, otherwise, add 1 to the value of i and return to step S502 to iteratively invert the plasma density rising edge profile. In each round, a layer of local penetrable thickness is added. That is, in the i-th round, when determining the thickness of the l-th layer of electron density, a metal plate is placed after the l+i-1 layer. arrive The value remains unchanged from the previous inversion result. The value of the reflection coefficient phase Closest to the actual reflection coefficient phase, complete the arrive Iterative update of , where Indicates the position of the 0th layer in the i-th round, represents the first layer position in round i, Indicates the second-level position in round i, Indicates the position of the N-i+1th layer in the i-th round, and They represent the l+1th layer position and the l+i-1th layer position in the i-th round respectively.

[0073] In this embodiment, steps S502 to S504 are repeated to start the subsequent rounds of iterative inversion. In each round, a layer of local penetrable thickness is added. That is, in the i-th round, when determining the thickness of the l-th layer of electron density, a metal plate is placed after the l+i-1 layer. arrive The value of remains unchanged from the previous inversion result. The value of Closest to the actual reflection coefficient phase, complete the arrive Iterative updates.

[0074] In this embodiment, the subsequent rounds of iterative inversion are started, and each round adds a layer of local penetrable thickness. Taking the first layer as an example, in order to invert Instead of placing a metal border directly behind this layer, place the first round After the corresponding electron density, the metal boundary is placed. At this time, adjust and The positions of the two layers make it possible to re-satisfy the consistency between the inversion phase and the real phase of the electron density below the cutoff frequency of the layer; similarly, in order to invert Instead of putting a metal border directly behind this layer, put a round After the layer corresponds to the electron density, place the metal boundary, and at this time, adjust The positions of the two layers are such that the inversion phase of the electron density below the cutoff frequency of the layer is consistent with the true phase.

[0075] In this embodiment, the inversion of the plasma electron density rising edge profile is based on the plasma local penetration effect. That is, after crossing a few resolution cells of the plasma cutoff frequency, the plasma reflection phase is no longer affected by the subsequent electron density. Therefore, the addition of a metal boundary does not affect the reflection phase.

[0076] In this embodiment, multiple iterations are performed on the inversion of the plasma electron density rising edge profile, taking into account the influence of the subsequent plasma layer on the reflection phase of the current inverted layer.

[0077] S6. At the initial inversion frequency f1, gradually increase the collision frequency until the reflection coefficient amplitude of the rising edge inversion profile at this frequency point is close to the reflection coefficient amplitude of the measured curve. This value is the collision frequency inversion value, and the collision frequency diagnosis is completed. The collision frequency value is the collision frequency that makes the reflection coefficient amplitude of the rising edge inversion profile close to the reflection coefficient amplitude of the measured curve.

[0078] S7. Based on the collision frequency diagnosis results, multiple distribution models are modeled, the attenuation coefficient is determined by the amplitude of the plasma reflection coefficient, and the reflection coefficient amplitude curve is obtained by sweeping the attenuation coefficient;

[0079] S8. Compare the reflection coefficient amplitude curve with the standard amplitude curve to determine whether the second inflection point of the reflection coefficient amplitude curve is closest to the standard amplitude curve. If so, complete the falling edge distribution diagnosis; otherwise, return to step S7.

[0080] In this embodiment, the collision frequency is a parameter that needs to be diagnosed. Based on the result of the collision frequency, the plasma falling edge is modeled to complete the diagnosis of the falling edge profile distribution.

[0081] In this embodiment, the falling edge plasma profile is inverted. For distribution models such as double Gaussian, parabolic, and exponential decay, the attenuation coefficient is adjusted. A frequency sweep is applied to the fitted falling edge model and the obtained rising edge distribution model. The resulting reflection coefficient amplitude curve is compared with a standard amplitude curve to find the attenuation coefficient that most closely matches the standard curve at the second inflection point, thereby determining the falling edge distribution.

[0082] Double Gaussian distribution model formula:

[0083]

[0084] Parabolic distribution model formula:

[0085] ne i =-a(x i -thick p ) 2 +ne p (8)

[0086] Exponential decay distribution model formula:

[0087]

[0088] Among them, x i Indicates the location of the plasma layer i, nei represents the electron density of the i-th layer of plasma, thick p Indicates the location of the peak electron density of plasma, ne p represents the plasma peak electron density, and a represents the model's attenuation coefficient. For each distribution model, adjust the attenuation coefficient a and perform a frequency sweep for the distribution model to the right of the peak and the inverted distribution model to the left of the equal peak. Compare the obtained reflection coefficient amplitude curve with the standard amplitude curve to see if the second inflection point of the curve is closest to the standard curve. If so, the distribution model at that point is determined to be the original plasma peak right distribution. Otherwise, change the value of a, adjust the model, and repeat this step until the diagnosis of the plasma peak right distribution is complete.

[0089] In this embodiment, multiple modeling assumptions are made for the falling edge profile, and the attenuation coefficient is determined by the second inflection point of the reflection coefficient amplitude curve being closest to the standard curve.

[0090] Diagnostic Examples:

[0091] Establish a multi-layer plasma model and set the plasma model parameters as follows: peak electron density ne p 1*10 18 cm 3 The electron density distribution conforms to the double Gaussian distribution, the attenuation coefficient a on the right side of the peak is 1500, and the collision frequency v e 1.2*10 8 Hz, the total thickness of the plasma is 0.1m. The reflection coefficient amplitude and phase are obtained by sweeping the frequency from 4 to 18 GHz for the plasma. Figure 2 、 Figure 3 shown.

[0092] According to the plasma electron density distribution diagnosis method provided by the present invention, firstly, Figure 2 The peak electron density ne of the plasma is obtained at the maximum slope of the amplitude curve p 1.0048*10 18 cm 3 Then, according to this method, the layered model is built on the left side of the peak, and after three iterative inversions, the plasma electron density distribution on the left side of the peak and the diagnostic results after interpolation processing are obtained, as shown in the figure. Figure 4 As shown; then, the plasma collision frequency v is obtained by comparing the reflection coefficient amplitude curve with the original amplitude curve. e 1.25*10 8 Hz, the attenuation coefficient a distributed on the right side of the peak is 1400. The reflection coefficient amplitude curve and the plasma electron density distribution inversion results at this time are as follows: Figure 5 、 Figure 6After calculation, the electron density distribution obtained by the layer-by-layer inversion of electron density distribution and collision frequency diagnosis method based on the local penetration characteristics of plasma is very close to the original distribution, and the relative error of collision frequency diagnosis is 4.2%.

[0093] In summary, the present invention takes into account the local penetration characteristics of electromagnetic waves in plasma when inverting the plasma electron density distribution, resulting in more accurate diagnostic results. The present invention is applicable to the diagnosis of plasma model parameters with a variety of different distributions, including double Gaussian, parabolic, and exponential distributions. The plasma parameter diagnosis method of the present invention can simultaneously diagnose the electron density distribution and collision frequency, making the diagnosis more efficient.

Claims

1. A method for diagnosing parameters of non-uniform plasma based on the local penetration effect of microwaves, characterized in that: The following steps are involved: S1. Obtaining an amplitude and phase curve of a plasma reflection coefficient, wherein the phase curve of the plasma reflection coefficient is used to query an actual reflection coefficient phase according to an incident frequency; S2, searching for the maximum value of the slope of the amplitude decrease of the swept plasma reflection coefficient to determine the peak electron density, wherein the frequency of the maximum value is the cutoff frequency fc corresponding to the peak electron density; S3. Divide the plasma to be diagnosed with a thickness of d into N spatial resolution units according to non-uniformity, and introduce an additional layer 0 before layer L = 1, wherein the thickness of each spatial resolution unit is divided according to the cutoff frequency fc corresponding to the peak electron density and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength; S4, setting the initial value of the collision frequency inversion to a number close to 0; S5. Iteratively invert the plasma density rising edge profile based on the local penetration effect and non-uniform partitioning results; S6. At the initial inversion frequency f1, gradually increase the collision frequency until the reflection coefficient amplitude of the rising edge inversion profile at this frequency point is close to the reflection coefficient amplitude of the measured curve. This value is the collision frequency inversion value, and the collision frequency diagnosis is completed. The collision frequency value is the collision frequency that makes the reflection coefficient amplitude of the rising edge inversion profile close to the reflection coefficient amplitude of the measured curve. S7. Based on the collision frequency diagnosis results, multiple distribution models are performed, the attenuation coefficient is determined by the amplitude of the plasma reflection coefficient, and the reflection coefficient amplitude curve is obtained by sweeping the attenuation coefficient; S8. Compare the reflection coefficient amplitude curve with the standard amplitude curve to determine whether the second inflection point of the reflection coefficient amplitude curve is closest to the standard amplitude curve. If so, complete the falling edge distribution diagnosis; otherwise, return to step S7.

2. The method for diagnosing parameters of non-uniform plasmas based on the microwave local penetration effect according to claim 1, characterized in that: The expression of the electron density is as follows: Among them, ne p represents the electron density of the plasma, f represents the plasma cutoff frequency, m e represents the mass of the electron, ε0 represents the dielectric constant of vacuum, and e represents the charge of the electron.

3. The method for diagnosing inhomogeneous plasma parameters based on microwave local penetration effect according to claim 1, characterized in that: The step S5 comprises the following steps: S501, according to the actual test obtained by the sweep reflection coefficient phase, by determining the initial reflection phase Get the initial inversion frequency f1 and the corresponding electron density ne1, where Indicates the maximum value of the reflected phase; S502, start i=1 round of iteration, invert the plasma electron density of layer L=1, when the plasma passes through the thickness d0 of the 0th layer, total reflection occurs, and the thickness d0 corresponding to the density of the 0th layer is inverted according to the initial phase of the reflection; S503, divide the thickness d0 into and Two floors, and An infinite metal boundary is placed behind, where Δd represents the diagnostic spatial resolution, which is divided into two layers according to the peak electron density corresponding to the cutoff frequency fc and the maximum value of the incident frequency finc corresponding to 1 / 3 of the wavelength; S504: Based on the setting result of step S503, the reflection coefficient phase is calculated using the equivalent transmission line model. And repeatedly adjust The position until the reflection coefficient phase Close to the actual reflection coefficient phase, determine the first layer of plasma position; S505, continue i=1 rounds of iteration, invert the plasma electron density of L=2 layers, and calculate the reflection coefficient phase using the equivalent transmission line model And repeatedly adjust The position until the reflection coefficient phase Close to the actual reflection coefficient phase, repeat step S505 until the peak electron density is reached, and the position of the second layer of plasma is determined; wherein, this round of inversion is three layers of plasma plus a metal boundary, the three layers of plasma density are ne0, ne1 and ne2 respectively, the first layer of plasma and the second layer of plasma correspond to the cutoff frequencies f1 and f2 respectively, and the positions are and S506, determine whether the completion of arrive If yes, then go to step S6, otherwise, add 1 to the value of i and return to step S502 to iteratively invert the plasma density rising edge profile. In each round, a layer of local penetrable thickness is added. That is, in the i-th round, when determining the thickness of the l-th layer of electron density, a metal plate is placed after the l+i-1 layer. arrive The value remains unchanged from the previous inversion result. The value of the reflection coefficient phase Closest to the actual reflection coefficient phase, complete the arrive Iterative update of , where Indicates the position of the 0th layer in the i-th round, represents the first layer position in round i, Indicates the second-level position in round i, Indicates the position of the N-i+1th layer in the i-th round, and They represent the l+1th layer position and the l+i-1th layer position in the i-th round respectively.

4. The method for diagnosing parameters of non-uniform plasmas based on the microwave local penetration effect according to claim 3, characterized in that: The thickness d0 is expressed as follows: Here, k0 represents the free space wave number.

5. The method for diagnosing parameters of non-uniform plasmas based on the microwave local penetration effect according to claim 3, characterized in that: The expression of the equivalent transmission line model is as follows: Among them, R l and R l+1 They represent the reflection coefficients of the lth layer and the l+1th layer inside the equivalent transmission line model, respectively. l and k l+1 denote the wave vectors along the incident direction in the lth layer and the l+1th layer, j denotes the imaginary unit, μ l and μ l+1 Represent the magnetic permeability of the lth layer and the magnetic permeability of the l+1th layer, R l(l+1) and P l(l+1) Both represent two intermediate parameters, R0 represents the final reflection coefficient of the equivalent transmission line model to the outside, represents the reflection coefficient phase, d l Represents the position coordinates of the lth layer.

Images