CN103235186B - Utilize the method and system of spectral measurement arc impedance - Google Patents

Abstract

The invention provides a kind of method and system utilizing spectral measurement arc impedance.Described method comprises: utilize spectrometer to catch the first image that arc channel scioptics assembly formed on spectrometer at least partially to obtain the first spectral line length, described first spectral line length is associated with the described size at least partially of the first image; By comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel; And by utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

Description

Utilize the method and system of spectral measurement arc impedance

Technical field

The present invention relates to the measurement of arc impedance, relate more specifically to the method and system utilizing spectral measurement arc impedance.

Background technology

The measurement of the impedance of very fast transient overvoltage (VFTO) hf electric arc has great importance for the Timeliness coverage of electric system and network failure, measurement and solution.

In the prior art, generally calculate VFTO hf electric arc arc resistance by measurement flame current and arc voltage, particularly, the resistive component of arc voltage is utilized to obtain arc channel resistance divided by flame current, as shown in Equation (1) (see " M.J.Kushner.Arcresistanceoflaser-triggeredsparkgaps [J] .J.Appl.Phys.58,1744 (1985) "):

$R\left(t\right)=\frac{U\left(t\right)-[L_s\left(t\right)\frac{\mathrm{di}\left(t\right)}{\mathrm{dt}}+i\left(t\right)\frac{{\mathrm{dL}}_s\left(t\right)}{\mathrm{dt}}+L_e\frac{\mathrm{di}\left(t\right)}{\mathrm{dt}}]}{i\left(t\right)}---\left(1\right)$

Wherein, R (t) is hf electric arc resistance, and U (t) is measuring voltage, and i (t) is flame current, L _efor the stray inductance of electric arc two end electrodes, L _s(t) arc channel inductance for successively decreasing in time.

Voltage measurement adopts fast-response capacitive divider; Current measurement adopts Luo-coil; The stray inductance of electric arc two end electrodes is estimated according to electrode profile; Arc channel inductance is calculated by channel radius, and can arrange according to loop and adopt different computation models, common model has coaxial transmission line model, as shown in Equation (2):

$L_s=l*\ln \left(\frac{{\mathrm{\ρ}}_2}{{\mathrm{\ρ}}_1}\right)*{10}^{-7}---\left(2\right)$

Wherein, ρ ₂for backflow radius, arranged by loop and determine; ρ ₁for channel radius, by measurements by laser interferometry, as shown in Figure 1, Fig. 1 shows the square ratio juris of the measurement arc channel radius of prior art.The cardinal principle of the measurements by laser interferometry channel radius shown in this figure is as follows.Utilize laser instrument produce beam of laser and from side irradiate discharge channel, received by receiving screen at opposite side, the image obtained as shown in Figure 1, wherein w ₁for channel diameter, w ₂for plasma is to the transition of peripheral gas medium.

But there is following shortcoming in the method:

1) introducing of measurement mechanism can affect the Electric Field Distribution in experiment gap, thus affects formation and the arc voltage of electric arc;

2) the response time difference of voltage and current is difficult to determine, causes result of calculation deviation to be difficult to control;

3) calculating aisle resistance must Measurement channel radius, but in the prior art, time the arc channel radius measurement that becomes measured by the method for laser interferance method or framing camera shooting, cost is high and error is larger;

4) to account for the ratio of arc voltage very little for the voltage resistive component of hf electric arc, and deduct by arc voltage the computing method that perceptual component of voltage obtains resistive voltage and can introduce significant errors, this belongs to the ill-conditioning problem in computing method.

Therefore, need a kind of can high precision and measure the method and system of hf electric arc impedance at low cost.

Summary of the invention

The invention provides a kind of measuring method of non-intervention type, it calculates the diameter of arc channel by the spectrum measuring arc channel, thus calculates the impedance of arc channel.The method overcomes above-mentioned shortcoming of the prior art.

According to an aspect of the present invention, provide a kind of method utilizing spectral measurement arc impedance, comprise: utilize spectrometer to catch the first image that arc channel scioptics assembly formed on spectrometer at least partially to obtain the first spectral line length, described first spectral line length is associated with the described size at least partially of the first image; By comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel; And by utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

According to a further aspect in the invention, additionally provide a kind of system utilizing spectral measurement arc impedance, comprising: lens subassembly, wherein arc channel forms the first image by this lens subassembly; Spectrometer, its for catch described first image at least partially to obtain the first spectral line length, wherein said first spectral line length is associated with the described size at least partially of the first image; Computing unit, it receives the data about described first spectral line length, by comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel, and by utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

Further feature of the present invention will become clear by reference to the following detailed description of accompanying drawing to one exemplary embodiment.

Accompanying drawing explanation

In order to understand the present invention in detail, embodiment is below described now by reference to the accompanying drawings.The similar numeral of element similar in accompanying drawing represents, wherein:

Fig. 1 shows the square ratio juris of the measurement arc channel radius of prior art;

Fig. 2 shows the block diagram of the system of the impedance of measurement arc channel of the present invention;

Fig. 3 shows the circuit diagram of the signal processing circuit in Fig. 2;

Fig. 4 shows the input and output oscillogram of the signal processing circuit in Fig. 3; With

Fig. 5 shows the process flow diagram of the method for the impedance of measurement arc channel of the present invention.

Embodiment

Below with reference to the accompanying drawings in more detail the preferred embodiments of the present invention are described.Note, run through following description, set forth details and more thoroughly understand of the present invention to provide.But the present invention can put into practice when not having these details.In other cases, do not illustrate or describe known element in detail to avoid unnecessarily fuzzy the present invention.Therefore, instructions and accompanying drawing should be considered to illustrative, instead of in the meaning of restriction.

Fig. 2 shows the block diagram of the system of the impedance of measurement arc channel of the present invention.According to Fig. 2, electric current flows into two relative electrodes 1, produces hf electric arc passage between two electrodes 1.Light scioptics assembly 2 imaging on spectrometer that arc channel sends.The side of the reception image input of spectrometer has image capture window, and it typically is the slit of thin-and-long, its long side direction is parallel to the x-axis in figure.

Spectrometer can catch the image that entered by slit to produce spectrum picture.A series of spectral line is comprised in spectrum picture.The information that spectral line reflects comprises the relative intensity of wavelength and respective wavelength, and the intensity brightness of spectral line represents, wavelength and strength information may be used for the electron temperature and the electron density that calculate arc channel.For same light source, the length of each bar spectral line is identical, and the length of spectral line is proportional to the size of the image through slit.Because slit is longilineal, therefore, can think, the length of spectral line is proportional to the length of image in x-axis direction through slit.Such spectrometer is commercially commercially available, the 2300I type spectrometer of such as Princeton instrument company.But should be appreciated that and the present invention is not limited thereto concrete spectrometer type, as long as can catch above-mentioned information thus realize the present invention, the instrument of any other kind or the combination of instrument all should be embodiments of the invention, belong to scope of the present invention.

In practical situations both, because discharge channel is uneven in radial direction, channel center's density is large, and peripheral density is little, and thus, when slit is vertical with luminous object, channel boundary is the clearest, and the error caused is little.Therefore, preferably, make arc channel scioptics assembly imaging perpendicular to the slit of spectrometer, shooting discharge spectrum image, obtains spectral line length now, is designated as l ₁.Note, as shown in the figure, when slit is vertical with luminous object, the image photographed by spectrograph slit corresponds to the width of a portion of arc channel in y-axis direction along x direction, and namely arc channel is at the diameter of this position.

Then the information of reference light source is obtained.At the reference light source of location arrangements one predetermined length of arc channel, such as length is the mercury lamp of 10mm.As mentioned above, length due to the spectral line obtained through the image of spectrograph slit by spectrometer shooting is proportional to the size of the image through slit, and obtain electric arc above at a portion width along the x-axis direction (namely, the diameter of arc channel), therefore in order to the spectral line length of certain part image along the x-axis direction by comparing arc channel and the spectral line length of reference light source are to obtain the diameter of this part of arc channel, here the length direction of reference light source is made along the x-axis direction, and make it image in spectrograph slit, take its spectrum picture, now spectral line length very l ₂.

It should be noted that mercury lamp is herein only example, can other light sources be used, such as xenon lamp etc.The length of reference light source also can change according to concrete practice.

In addition, can the spectral line length of all witness mark light source at every turn.But can from storer the length of the reference light source that direct acquisition has been recorded, spectral line length and positional information etc.

As mentioned above, by comparing the spectral line length of certain part image along the x-axis direction of arc channel and the spectral line length of reference light source to obtain the diameter of this part of arc channel.When being represented by formula, the diameter d that following formula (3) calculates certain part of hf electric arc passage can be provided:

$d=10*\frac{l_1}{l_2}\left(\mathrm{mm}\right)---\left(3\right)$

Finally, the impedance of certain part of arc channel is calculated by following formula:

$\frac{4}{\mathrm{\σ}\×\mathrm{\π}\×d^2}---\left(4\right)$

Wherein, σ is the conductivity of certain part of arc channel, and d is the diameter of this part of arc channel.

Alternatively, σ can obtain in the following manner.

First, electron temperature is calculated.Two spectral lines of the predetermined ion in chosen spectrum picture, two spectral lines of such as monovalence fluorine ion, using degree ratioing technigue calculates electron temperature T _e, electron temperature T can be calculated by following formula _e:

$\frac{I_1}{I_2}=\frac{A_1{g}_1{\mathrm{\λ}}_2}{A_2{g}_2{\mathrm{\λ}}_1}*\exp (-\frac{E_1-E_2}{{\mathrm{kT}}_e})---\left(5\right)$

Wherein, k is Boltzmann constant, I ₁and I ₂the radiation intensity of two predetermined spectral lines respectively, A ₁and A ₂the transition probability of two predetermined spectral lines respectively, g ₁and g ₂the statistical weight of two predetermined spectral lines respectively, λ ₁and λ ₂the radiation wavelength of two predetermined spectral lines respectively, E ₁and E ₂the excitation energy of two predetermined spectral lines respectively.Electron temperature T can be obtained according to above formula _e.Different kinds of ions will be comprised when it be known to those skilled in the art that arc discharge.Here choosing fluorine ion is consider that the above-mentioned line parameters of fluorine ion easily to obtain in this area and known.But as mentioned above, owing to may comprise different kinds of ions in electrical discharge arc passage, therefore those skilled in the art can choose other ions that can measure and obtain to calculate electron temperature T _e.

Then electron density n is calculated _e, it is directly proportional to spectral line halfwidth, is shown below:

n _e=C*Δλ（6）

Wherein, C is Stark broadening factor, is constant; Electron density n can be obtained according to above formula _e.

For spectral line halfwidth, preferably choose and calculate electron temperature T _ethe halfwidth of the spectral line of Shi Suoyong.Here, of choosing in above-mentioned two spectral lines of monovalence fluorine ion calculates halfwidth.

Then conductivity is calculated.Here utilize Spitzer correction formula to calculate conductivity, as follows:

${\mathrm{\σ}}_0=1.53*{10}^{-2}*\frac{T^{3/2}}{\ln {(1+1.4*{{\mathrm{\Λ}}_m}^2)}^{1/2}}---\left(7\right)$

Wherein,

Λ _m=1.24*10 ⁷*1.05*T ^3/2/n _e ^1/2（8）

Note, those skilled in the art can utilize other method multiple and formula to calculate conductivity, the Z & L model etc. of such as Zollweg and Liebermann etc., see " quadrate lope woods. the Primary Study [D] of pulsed discharge plasma electromagnetic property. Institutes Of Technology Of Nanjing .2008.06 ".

In addition, all can measure conductivity at every turn.But can direct acquisition has been recorded from storer conductivity information.Such as, when discharging condition is identical, the conductivity parameters obtained before can directly utilizing.

So far, utilize formula (4), the impedance of certain part of arc channel can be calculated.

Because arc discharge can be decayed along with passage of time, starting the channel impedance of moment in order to measure arc discharge, the operation of spectrometer can being made synchronous with arc discharge by synchronously triggering.Continue below to describe the method for synchronous triggering and corresponding device with reference to figure 1.

As shown in Figure 1, the synchronous triggering loop of spectrometer comprises: as the B-dot coil of sensor, signal processing circuit and shielded cable.

B-dot coil is installed on main discharge near circuitry, be in same plane with discharge circuit, when the main discharge circuit discharging of being used for being coupled is initial, electric current is uprushed the magnetic field produced, and substantially can produce a voltage rise signal without time delay at main discharge circuital current initial time.In one embodiment, B-dot coil can be single turn air core coil, and such as utilize enameled wire coiling to form, its output terminal is connected to the input end of signal processing circuit by shielded cable.The magnetic field of coupling is converted into electric signal and exports by B-dot coil.

The electric signal exported from B-dot coil is connected to the input end of signal processing circuit by a short shielded cable, electric signal is shaped as predetermined voltage by signal processing circuit, such as 4V, square-wave signal, and be connected to spectrometer synchronous triggering signal input end, for triggering spectrometer action by a shielded cable.

Signal processing circuit as shown in Figure 3, it comprise the voltage for limiting described electric signal voltage limiting module 31 and for carrying out shaping to electric signal to export the switch module 33 of square-wave pulse signal.Voltage limiting module 31 comprises the diode D be connected in series ₁with diode string D _s.Switch module can be various transistor well-known to those skilled in the art, such as MOSFET, and it controls pole and is connected to diode D ₁with diode string D _sbetween node, the signal after rectification by its output stage (such as, source electrode) export.Signal processing circuit can also comprise filtration module 32 between voltage limiting module 31 and switch module 33, and it carries out filtering to described electric signal and filtered signal is exported to switch module 33.This filtration module 32 can comprise resistor R ₁with capacitor C ₁.Signal processing circuit can also comprise output load part 34, and it is connected to the output stage of switch module, for square-wave pulse signal is outputted to spectrometer with suitable voltage.The input signal of signal processing circuit and output signal are as shown in Figure 4.

As mentioned above, arc discharge can be decayed along with passage of time, and therefore, the channel impedance of each time point after from arc discharge is change.The present invention can measure the channel impedance of arc discharge at each time point place further.Be described in detail below.

After the signal that signal processing circuit exports is input to spectrometer, can by this signal delay regular hour t, so that spectrometer caught action t time delay.This time delay t is adjustable.Such as, this time delay t can carry control software design winspec32 by spectrometer and provide, and range of adjustment is 0 to infinitely great.By the method, spectrometer can obtain the spectrum picture of different electric discharge developing stage, obtains the arc channel impedance of different discharge regime thus.

In addition, as shown in Figure 2, along the y-axis direction, and the image capture slit of spectrometer is parallel to x-axis to the arc channel between two electrodes.The diameter of an arc channel part along the y-axis direction that what therefore spectrometer once captured is.Because arc channel diameter is along the y-axis direction not uniform, thus cause impedance to be also uneven, therefore, invention also contemplates that this problem, the diameter of one step surveying arc channel different piece along the y-axis direction of going forward side by side, thus the impedance calculating different piece.Be described in detail below.

By supporting that the micrometer caliper on the displacement platform of spectrometer carrys out the height of minute adjustment displacement platform, thus the height of spectrograph slit can be regulated.Then the step of above measurements and calculations is repeated, to measure the impedance at arc channel diverse location place along the y-axis direction.

Such as, utilize said method, utilize formula (7), obtain multiple Conductivity Calculation value by repetitive measurement.Then utilize approximating method known in the art, such as Lorentz fit, obtain arc channel conductivityσ (y) along the y-axis direction.This matching can realize with different computational tools, the product " Origin8.6 " of such as OriginLab company, or Matlab etc.

Conductivityσ (y) being multiplied by channel cross-sectional area gets reciprocal in arc channel length direction upper integral, can obtain the impedance at least partially of the hf electric arc passage in corresponding moment, as follows:

$r=\underset{y-}{\overset{y+}{\∫}}\frac{4}{\mathrm{\σ}\left(y\right)\×\mathrm{\π}\×d^2}*\mathrm{dy}---\left(9\right)$

According to this equation, when y gets different values, the impedance of the different piece of arc channel can be obtained.

The method utilizing spectral measurement arc impedance is according to an embodiment of the invention described below in conjunction with Fig. 5.Fig. 5 shows the process flow diagram of the method.

The method starts from 500.

510, utilize spectrometer to catch the first image that arc channel scioptics assembly formed on spectrometer at least partially to obtain the first spectral line length.

520, by comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel.Here reference spectrum line length by directly obtaining from storer, also by being placed on the position of arc channel with reference to light source, can utilize spectrometer measurement spectrum to obtain.

530, by utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

The method ends at step 540.

In addition, in further alternative embodiment, there is the impedance of moment to measure arc discharge, sensor can be utilized to sense the initial current signal causing electric arc, to trigger the operation of spectrometer, thus make spectrometer synchronously measure arc channel.

In addition, in further alternative embodiment, in order to measure after arc discharge occurs until the impedance of the random time point of electric arc extinction, the operation of spectrometer can be triggered after by the initial current signal delay schedule time, at least to obtain the diameter at least partially of the arc channel at different time points place.

In addition, in further alternative embodiment, in order to the impedance at the diverse location place and different piece of measuring arc channel, the position of spectrometer can be adjusted along the direction being parallel to arc channel at least to obtain the diameter at the diverse location place of arc channel, thus calculate the impedance of the part of the different length of arc channel.

As mentioned above, the invention provides a kind of measuring method of non-intervention type, calculated the diameter of arc channel by arc channel emission spectrum, and utilize conductivity to calculate the impedance of arc channel.The present invention utilizes optical method for measuring to obtain reflecting the parameter of microscopic particle motion state, thus calculates channel impedance, there is not the problem of voltage, current measurement introducing.And utilize the light source of known dimensions and discharge channel imaging contrast higher to the way precision obtaining channel diameter, and cost is not high.Utilize technical scheme provided by the present invention, can also measure the impedance of arc channel at the impedance of each discharge regime and/or the specific part of arc channel, this provides the practicality of greater flexibility and Geng Gao for arc channel impedance measurement.

Claims (20)

1. utilize a method for spectral measurement arc impedance, comprising:

Utilize spectrometer to catch the first image that arc channel scioptics assembly formed on spectrometer at least partially to obtain the first spectral line length, described first spectral line length is associated with the described size at least partially of the first image;

By comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel; And

By utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

2. the method for claim 1, wherein said first image is perpendicular to the long side direction of the image capture window on spectrometer.

3. the method for claim 1, by utilizing spectrometer to catch, the second image that reference light source scioptics assembly formed on spectrometer obtains wherein said reference spectrum line length, and wherein the second image is positioned at the image capture window on spectrometer.

4. the method for claim 1, also comprises:

The position of spectrometer is adjusted at least to obtain the diameter at the diverse location place of arc channel along the direction being parallel to arc channel.

5. the method as described in claim 1 or 4, also comprises:

Utilizing causes the initial current signal of described electric arc to trigger the operation of spectrometer.

6. method as claimed in claim 5, also comprises:

Trigger the operation of spectrometer after by the initial current signal delay schedule time, at least to obtain the diameter at least partially of the arc channel at different time points place.

7. the method for claim 1, wherein calculates the impedance at least partially of arc channel by following formula:

$\frac{4}{\mathrm{\σ}\×\mathrm{\π}\×d^2}$

Wherein, σ is the conductivity at least partially of arc channel, and d is the diameter at least partially of arc channel.

8. method as claimed in claim 7, wherein calculates the conductivity at least partially of arc channel by following formula:

$\mathrm{\σ}=1.53*{10}^{-2}*\frac{T^{3/2}}{\ln {(1+1.4*{{\mathrm{\Λ}}_m}^2)}^{1/2}}$

Wherein Λ _m=1.24*10 ⁷* 1.05*T ^3/2/ n _e ^1/2, T is the electron temperature of arc channel, n _efor the electron density of arc channel.

9. method as claimed in claim 8, wherein by using two predetermined spectral lines of predetermined ion, utilizes following formula to calculate electron temperature T:

$\frac{I_1}{I_2}=\frac{A_1{g}_1{\mathrm{\λ}}_2}{A_2{g}_2{\mathrm{\λ}}_1}*\exp (-\frac{E_1-E_2}{\mathrm{kT}})$

Wherein, k is Boltzmann constant, I ₁and I ₂the radiation intensity of two predetermined spectral lines respectively, A ₁and A ₂the transition probability of two predetermined spectral lines respectively, g ₁and g ₂the statistical weight of two predetermined spectral lines respectively, λ ₁and λ ₂the radiation wavelength of two predetermined spectral lines respectively, E ₁and E ₂the excitation energy of two predetermined spectral lines respectively, and

The electron density n of arc channel is calculated by following formula _e:

n _e＝C*Δλ

Wherein C is stark broadening factor, and Δ λ is spectral line halfwidth.

10. method as claimed in claim 8 or 9, also comprises:

The function (σ (y)) of conductivity along the direction of arc channel of arc channel is obtained by Lorentz fit method; And

The impedance at least partially of arc channel is calculated by following formula:

$r=\underset{y-}{\overset{y+}{\∫}}\frac{4}{\mathrm{\σ}\left(y\right)\×\mathrm{\π}\×d^2}*\mathrm{dy}.$

11. 1 kinds of systems utilizing spectral measurement arc impedance, comprising:

Lens subassembly, wherein arc channel forms the first image by this lens subassembly;

Spectrometer, its for catch described first image at least partially to obtain the first spectral line length, wherein said first spectral line length is associated with the described size at least partially of the first image;

Computing unit, it receives the data about described first spectral line length, by comparing the first spectral line length and reference spectrum line length to calculate the diameter at least partially of arc channel, and by utilizing the diameter at least partially of arc channel and the conductivity at least partially of arc channel that calculate, calculate the impedance at least partially of arc channel.

12. systems as claimed in claim 11, wherein said first image is perpendicular to the long side direction of the image capture window on spectrometer.

13. systems as claimed in claim 11, also comprise:

Reference light source,

Wherein by utilize spectrometer to catch the second image that reference light source scioptics assembly formed on spectrometer to obtain described reference spectrum line length, wherein the second image is positioned at the image capture window on spectrometer.

14. systems as claimed in claim 11, also comprise:

Spectrometer position regulator, it adjusts the position of spectrometer along the direction being parallel to arc channel, thus obtains the diameter at the diverse location place of arc channel.

15. systems as described in claim 11 or 14, also comprise:

Sensor, it is for sensing the initial current signal causing described electric arc; And

Signal processing circuit, it is for the treatment of sensed current signal and output to spectrometer, thus triggers the operation of spectrometer.

16. systems as claimed in claim 15, wherein said signal processing circuit comprises:

Voltage limiting module, it limits the voltage of described current signal;

Filtration module, it carries out filtering to described current signal;

Switch module, it carries out shaping to described filtered current signal; With

Output unit, the signal after its output Shaping.

17. systems as claimed in claim 15, also comprise:

Time delay elements, it is connected between described signal processing circuit and described spectrometer, for triggering the operation of spectrometer after by the initial current signal delay schedule time, to obtain the diameter at least partially of the arc channel at different time points place.

18. systems as claimed in claim 11, wherein computing unit calculates the impedance at least partially of arc channel by following formula:

$\frac{4}{\mathrm{\σ}\×\mathrm{\π}\×d^2}$

Wherein, σ is the conductivity at least partially of arc channel, and d is the diameter at least partially of arc channel.

19. systems as claimed in claim 18, wherein computing unit calculates the conductivity at least partially of arc channel by following formula:

$\mathrm{\σ}=1.53*{10}^{-2}*\frac{T^{3/2}}{\ln {(1+1.4*{{\mathrm{\Λ}}_m}^2)}^{1/2}}$

Wherein Λ _m=1.24*10 ⁷* 1.05*T ^3/2/ n _e ^1/2, T is the electron temperature of arc channel, n _efor the electron density of arc channel,

Wherein by using two predetermined spectral lines of predetermined ion, utilize following formula to calculate electron temperature T:

$\frac{I_1}{I_2}=\frac{A_1{g}_1{\mathrm{\λ}}_2}{A_2{g}_2{\mathrm{\λ}}_1}*\exp (-\frac{E_1-E_2}{\mathrm{kT}})$

Wherein, k is Boltzmann constant, I ₁and I ₂the radiation intensity of two predetermined spectral lines respectively, A ₁and A ₂the transition probability of two predetermined spectral lines respectively, g ₁and g ₂the statistical weight of two predetermined spectral lines respectively, λ ₁and λ ₂the radiation wavelength of two predetermined spectral lines respectively, E ₁and E ₂the excitation energy of two predetermined spectral lines respectively, and

The electron density n of arc channel is calculated by following formula _e:

n _e＝C*Δλ

Wherein C is stark broadening factor, and Δ λ is spectral line halfwidth.

20. systems as claimed in claim 19, wherein computing unit obtains the function (σ (y)) of conductivity along the direction of arc channel of arc channel by Lorentz fit method, and is calculated the impedance at least partially of arc channel by following formula:

$r=\underset{y-}{\overset{y+}{\∫}}\frac{4}{\mathrm{\σ}\left(y\right)\×\mathrm{\π}\×d^2}*\mathrm{dy}.$