CN103852647A - Approximate analysis expressing method for lightning return stroke electromagnetic field - Google Patents

Abstract

The invention provides an approximate analytic expression method for describing the electromagnetic field returned by lightning on the ground surface. The approximate analytical expression of lightning return electromagnetic field is composed of four approximate analytical expressions of lightning near-area electric field, near-area magnetic field, far-area electric field and far-area magnetic field. This group of approximate analytical expressions is based on the transmission line model of the lightning return process, and is obtained by approximate processing of the exact analytical expressions of the lightning return electromagnetic field obtained by the dipole method. In this group of approximate analytical expressions, whether it is the near field or the far field, the electromagnetic field of the lightning return on the surface can be approximately expressed as the product of the current function at the bottom of the channel and a factor related to distance. This group of approximate analytical expressions for lightning return electromagnetic field provides a theoretical basis for the approximate calculation of lightning return electromagnetic field, the development of laboratory lightning return electric field and magnetic field simulators, and the long-distance evaluation of lightning return parameters.

Description

A kind of approximate analysis expression of Electromagnetic Fields of Lightning Return Stroke

Technical field

The invention provides the approximate analysis expression formula of one group of earth's surface Electromagnetic Fields of Lightning Return Stroke, is the product of lightning channel base current and and Range-based factor by Electromagnetic Fields of Lightning Return Stroke approximate representation.The method can be applicable to approximate treatment, the development of thunder and lightning electro-magnetic environment simulator and the remote approximate evaluation of Fields of Lightning Return Stroke parameter of earth's surface Electromagnetic Fields of Lightning Return Stroke.

Background technology

Be accompanied by the develop rapidly of infotech, the electromagnetic susceptibility of various electronic equipments is more and more higher, and the Lightning Electromagnetic Pulse (LEMP) that Return stroke of ground flash produces endangers source as a kind of typical case of electromagnetic susceptibility product and caused people's extensive concern.The contingency occurring due to thunder and lightning is very strong, and very difficult actual measurement obtains fighting back parameatal Lightning Electromagnetic Fields distribution situation, and more feasible method is that Fields of Lightning Return Stroke process is carried out calculating its electromagnetic field after theoretical modeling.Thunder discharge model can be divided into aerodynamics model, electromagnetic model, distributed circuit model and engineering model four classes.Wherein, engineering model is described as longitudinal current the function of height and time, is most widely used.At present, engineering model mainly comprises BG model, TL model, TCS model, MTLL model, MTLE model and DU model etc.Except the direction of motion and producing method of electric current, the key distinction of different engineering models is that the velocity of propagation of return stroke current is different with the attenuation law along passage.Solution of electro-magnetic field analysis method based on these engineering models mainly contains the separation of variable, conformal mapping method, monopole method and dipole technique etc.Wherein, the error of monopole technology is compared with recommendation greatly and not; Analytic solution and measured result by the ground Lightning Electromagnetic Fields to being obtained by dipole theory contrast, and confirm that dipole method has good computational accuracy.Therefore, dipole technique is widely used in antenna theory and Electromagnetic Calculation.

On above-mentioned basis of Electromagnetic Fields of Lightning Return Stroke being carried out to theoretical modeling and calculating, for further meeting the security test demand of the electromagnetic susceptibility products such as electronic and electrical equipment under thunder and lightning electromagnetic environment, need to carry out laboratory simulation to typical LEMP environment, in view of the lightning surge analogue technique in current laboratory comparatively ripe, the direct method that realizes so LEMP simulation is exactly to set up contacting between LEMP and Fields of Lightning Return Stroke channel bottom electric current, utilizes lightning surge analogue technique to realize the simulation of LEMP environment.The researchist of Florida university of the U.S. finds also to have proved theoretically the characteristic that LEMP far zone field and channel bottom electric current are approximate, thinks that the LEMP far zone field waveform in certain distance can carry out approximate representation with fighting back channel bottom current waveform; And find the approximate characteristic between electric field derivative and base current derivative in an artificially triggered lightning experiment.This just links up LEMP and Fields of Lightning Return Stroke channel bottom electric current.For further setting up theoretically earth's surface LEMP field wave shape and fighting back the relation between channel bottom current waveform, taking TL model as basis, carry out approximate processing by the LEMP field to being obtained by dipole method, provide a kind of utilization and fought back channel bottom current waveform and describe the approximate analysis expression formula of earth's surface Electromagnetic Fields of Lightning Return Stroke, and set it as the theoretical foundation of earth's surface LEMP approximate treatment and thunder and lightning electric field, the development of magnetic simulation device.

Summary of the invention

The technical problem to be solved in the present invention is directly perceived, the approximate contact of setting up between earth's surface Electromagnetic Fields of Lightning Return Stroke and channel bottom current waveform, solve current thunder and lightning electromagnetic environment analogue technique and the realistic problem such as can comply with without standard, for the development of relevant simulator provides a kind of theoretical foundation.

For solving the problems of the technologies described above, the present invention is taking the Electromagnetic Fields of Lightning Return Stroke model of vertical channel as basis, be ideal conducting plane depending on the earth, accurate and analytical expression by the earth's surface Electromagnetic Fields of Lightning Return Stroke to being obtained by dipole technique is carried out approximate processing, reject in Electromagnetic Fields of Lightning Return Stroke accurate and analytical expression base current function model has been chosen to comparatively responsive current integration item and current differential item, set up directly perceived between earth's surface Electromagnetic Fields of Lightning Return Stroke expression formula and channel bottom current expression, approximate contact, between both expression formulas, only differ one with the factor of Range-based, concrete approximate expression is:

Wherein, E _z, H _φrepresent respectively vertical electric field and poloidal magnetic field that Fields of Lightning Return Stroke produces on ground, and i (0, t) represent Fields of Lightning Return Stroke channel bottom electric current, ε ₀represent the permittivity in vacuum, v, c represent respectively counterattack speed and the light velocity of lightning channel electric current, and r represents the horizontal range between Fields of Lightning Return Stroke passage and observation station.In far-field region, the ratio of the mould value of Electric and magnetic fields is

the Electromagnetic Fields of Lightning Return Stroke that is far field can be approximately plane wave.

Advantage of the present invention is:

1) this group Electromagnetic Fields of Lightning Return Stroke approximate analysis expression formula has been rejected calculation of complex and negligible current integration item and differential term in accurate expression, reduce the requirement to return stroke current function model when Electromagnetic Fields of Lightning Return Stroke is calculated, greatly simplified the calculating of earth's surface LEMP.

2) can reflect comparatively intuitively the corresponding relation between Electromagnetic Fields of Lightning Return Stroke waveform and channel bottom current waveform, the simulation and the long-range detection Fields of Lightning Return Stroke parameter that can be laboratory Electromagnetic Fields of Lightning Return Stroke provide theoretical foundation.

Brief description of the drawings

Below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

Fig. 1 is the computation model of vertical channel Electromagnetic Fields of Lightning Return Stroke.

Fig. 2 is apart from the approximate comparison of wave shape figure of accurate electromagnetic field and its two-stage in the distance of counterattack path 10 m.

Fig. 3 is apart from the approximate comparison of wave shape figure of accurate electromagnetic field and its two-stage in the distance of counterattack passage 50km.

Embodiment

Fig. 1 is the computation model of vertical channel Electromagnetic Fields of Lightning Return Stroke: the vertical antenna that it is L that Fields of Lightning Return Stroke passage can be approximated to be perpendicular to the length on ground, return stroke current at the uniform velocity transmits along passage, suppose that the earth is the infinitely-great surface level of conductance, according to dipole technique, fight back any point (r on passage peripheral ground, φ, 0) general expression of the counterattack electromagnetic field of locating under cylindrical coordinate is

$E_z=\frac{1}{4{\mathrm{\&pi;\&epsiv;}}_0}{\&Integral;}_{-h}^h[\frac{{2z}^{\&prime;2}-r^2}{R^5}{\&Integral;}_{-\&infin;}^{t}i(z^{\&prime;},t-R/c)\mathrm{dt}+\frac{{2z}^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{{\mathrm{cR}}^4}i(z^{\&prime;},t-R/c)-\frac{r^2}{c^2{\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">R</figure-callout>}}^3}\frac{\&PartialD;i(z^{\&prime;},t-R/c)}{\&PartialD;t}]{\mathrm{dz}}^{\&prime;}---\left(1\right)$

$H_{\mathrm{\&phi;}}=\frac{1}{4\mathrm{\&pi;}}{\&Integral;}_{-h}^h[\frac{r}{R^3}i(z^{\&prime;},t-R/c)+\frac{\mathrm{<figure-callout\; id="2"\; label="r\; cR"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">r</figure-callout>}}{{\mathrm{cR}}^{}}\frac{\&PartialD;i(z^{\&prime;},t-R/c)}{\&PartialD;t}]{\mathrm{dz}}^{\&prime;}---\left(2\right)$

Wherein, E _zvertical electric field, H _φbe poloidal magnetic field, r is the horizontal range of observation station apart from counterattack passage, and z ' is any point of fighting back in passage, and h is the height of z ' apart from earth's surface,

for the distance between field point and electric current infinitesimal, c is the light velocity, and i is return stroke current.In formula (1), the 1st, the 2nd, the 3rd is respectively electrostatic field, induction field, radiation field; In formula (2), the 1st, the 2nd is respectively induction field, radiation field.To simplify the analysis, adopt transmission line (TL) model of Fields of Lightning Return Stroke, the mathematic(al) representation of return stroke current is

i(z′，t)＝u(t-z′/v)·i(0，t-z′/v) (3)

Wherein, u (t-z '/v) be step function, v is current wave velocity of propagation.

The near field producing for Fields of Lightning Return Stroke, order

according to TL model, the current integration item in electrostatic field component in formula (1)

${\&Integral;}_{-\&infin;}^{t}i(z^{\&prime;},\mathrm{\&tau;}-R/c)\mathrm{d\&tau;}={\&Integral;}_{-\&infin;}^{t}i(0,\mathrm{\&tau;}-R/c-z^{\&prime;}/v)\mathrm{d\&tau;}=f(0,t-R/c-z^{\&prime;}/v)-f\left(\mathrm{0,0}\right)=F(t-R/c-z^{\&prime;}/v)---\left(4\right)$

In near field, suppose r < < H, along with z ' increase, 1/R is tending towards 0 very soon.Like this F (t-R/c-z '/v) can the first approximation in t-r/c place Taylor expansion carry out linear expression by it,

F(t-R/c-z′/v)＝F(t-r/c)-F′(t-r/c)×[(t-r/c)-(t-R/c-z′/v)]+o(c ^-2) (5)

≈F(t-r/c)-i(0，t-r/c)×[(R-r)/c+z′/v]

, electrostatic field and induction field can be distinguished approximate representation and be

$E_z^{\&prime;}\left(\mathrm{electrostatic}\right)\&ap;\frac{F(t-r/c)}{2{\mathrm{\&pi;\&epsiv;}}_0}\frac{h}{R{\left(h\right)}^3}-\frac{i(0,t-r/c)}{{2\mathrm{\&pi;\&epsiv;}}_0}[\frac{1}{c}(\frac{\mathrm{rh}}{R{\left(h\right)}^3}-\frac{3h}{2R{\left(h\right)}^2}+\frac{{\tan }^{-1}\frac{h}{r}}{2r})+\frac{1}{v}(\frac{r^2}{R{\left(h\right)}^3}-\frac{2}{R\left(h\right)}+\frac{1}{r})]---\left(6\right)$

$E_z^{\&prime;}\left(\mathrm{induction}\right)\&ap;\frac{i(0,t-r/c)}{{2\mathrm{\&pi;\&epsiv;}}_{0}c}[\frac{{\tan }^{-1}(h/r)}{2r}-\frac{3h}{2R{\left(h\right)}^2}]---\left(7\right)$

Radiation field has been c ²magnitude, can ignore.So just obtain the first approximation expression formula of near region electric field

$E_z^{\&prime;}\&ap;-\frac{F(t-r/c)}{{2\mathrm{\&pi;\&epsiv;}}_0}\frac{h}{R{\left(h\right)}^3}-\frac{i(0,t-r/c)}{{2\mathrm{\&pi;\&epsiv;}}_0}\&times;[\frac{\mathrm{rh}}{\mathrm{cR}{\left(h\right)}^3}+\frac{1}{v}[\frac{r^2}{R{\left(h\right)}^3}-\frac{2}{R\left(h\right)}+\frac{1}{r}\left]\right]---\left(8\right)$

Similarly, can obtain the first approximation expression formula in magnetic field, near region

$H_{\mathrm{\&phi;}}^{\&prime;}\&ap;H_{\mathrm{\&phi;}}^{\&prime;}\left(\mathrm{induction}\right)=\frac{1}{2\mathrm{\&pi;}}i(0,t-r/c){\&Integral;}_0^{\mathrm{<figure-callout\; id="3"\; label="h\; r\; R"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">h</figure-callout>}}\frac{r}{R^{}}\frac{{}^3}{}{\mathrm{dz}}^{\&prime;}=\frac{1}{2\mathrm{\&pi;r}}i(0,t-r/c)\frac{h}{R\left(h\right)}---\left(9\right)$

R < < H during due near field, along with the increase of time, electric current rises more and more higher in passage, and R (h) will level off to h; And ignore the R in formula (8) ^-1item and R ^-3, just can obtain the two stage approach expression formula of near region Electromagnetic Fields of Lightning Return Stroke

$E_z^{\&prime;\&prime;}\&ap;-\frac{1}{2{\mathrm{\&pi;\&epsiv;}}_0\mathrm{vr}}i(0,t-r/c)---\left(10\right)$

$H_{\mathrm{\&phi;}}^{\&prime;\&prime;}\&ap;\frac{1}{2\mathrm{\&pi;r}}i(0,t-r/c)---\left(11\right)$

The far zone field producing for Fields of Lightning Return Stroke, when R ≈ r and r > > L, the principal ingredient of LEMP electromagnetic field is radiation field, electrostatic field item and induction field item are tending towards 0.For the engineering model of transmission line type, because wavefront is continuous, formula (1), (2) are simplified, have

$E_z^{\&prime;\&prime;}\&ap;E_z^{\&prime;}=E_z\left(\mathrm{radiation}\right)\&ap;-\frac{1}{2{\mathrm{\&pi;\&epsiv;}}_0{c}^{2}r}{\&Integral;}_0^h\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}/v)}{\&PartialD;t}{\mathrm{dz}}^{\&prime;}---\left(12\right)$

$H_{\mathrm{\&phi;}}^{\&prime;\&prime;}\&ap;H_{\mathrm{\&phi;}}^{\&prime;\&prime;}=H_{\mathrm{\&phi;}}\left(\mathrm{radiation}\right)\&ap;\frac{1}{2\mathrm{\&pi;cr}}{\&Integral;}_0^h\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}v)}{\&PartialD;t}{\mathrm{dz}}^{\&prime;}---\left(13\right)$

Because v is constant, so

$\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}/v)}{\&PartialD;t}=-v\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}/v)}{{\&PartialD;z}^{\&prime;}}---\left(14\right)$

Formula (14) substitution formula (12), (13) integration are obtained

$E_z^{\&prime;\&prime;}\&ap;\frac{v}{{2\mathrm{\&pi;\&epsiv;}}_0{c}^{2}r}{\&Integral;}_0^h\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}/v)}{{\&PartialD;z}^{\&prime;}}{\mathrm{dz}}^{\&prime;}=-\frac{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">v</figure-callout>}}{{2\mathrm{\&pi;\&epsiv;}}_0{c}^{2}r}\&times;[i(0,t-r/c)-i(0,t-r/c-h/v)]---\left(15\right)$

$H_{\mathrm{\&phi;}}^{\&prime;\&prime;}\&ap;-\frac{v}{2\mathrm{\&pi;cr}}{\&Integral;}_0^h\frac{\&PartialD;i(0,t-r/c-z^{\&prime;}/v)}{{\&PartialD;z}^{\&prime;}}{\mathrm{dz}}^{\&prime;}=\frac{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HSA00000817120100013.png"\; state="\{\{state\}\}">v</figure-callout>}}{2\mathrm{\&pi;cr}}\&times;[i(0,t-r/c)-i(0,t-r/c-h/v)]---\left(16\right)$

Due to τ≤0 o'clock, i (0, τ)=0.In the time of t≤h/v+r/c, formula (15), (16) become

$E_z^{\&prime;\&prime;}(r,t)\&ap;E_z\left(\mathrm{radiation}\right)\&ap;-\frac{v}{{2\mathrm{\&pi;\&epsiv;}}_0{c}^{2}r}i(0,t-r/c)---\left(17\right)$

$H_{\mathrm{\&phi;}}^{\&prime;\&prime;}(r,t)\&ap;H_{\mathrm{\&phi;}}\left(\mathrm{radiation}\right)\&ap;\frac{v}{2\mathrm{\&pi;cr}}i(0,t-r/c)---\left(18\right)$

Formula (10), (11) and formula (17), (18) are respectively the approximate analysis expression formula in thunder and lightning near region, earth's surface electric field, magnetic field, near region, far field electric field, magnetic field, far field.Wherein, the negative sign in electric field expression formula represents the direction of electric field and the opposite direction of current flowing.

Fig. 2 is apart from accurately the electromagnetic field comparison of wave shape figure approximate with its two-stage: Fig. 1 (a) and (b) the corresponding exact solution E that fights back Electromagnetic Calculation of waveform difference of middle numbering 1,2,3 in the distance of counterattack path 10 m _z, H _φ, first order approximate solution E ' _z, H ' _φ, and second order approximate solution E " _z, H " _φwaveform.

Fig. 3 be distance fight back in the distance of passage 50km the accurate electromagnetic field comparison of wave shape figure approximate with its two-stage: Fig. 2 (a) and (b) middle 1,2,3 the waveform of numbering represent respectively to fight back the exact solution E of Electromagnetic Calculation _z, H _φ, first order approximate solution (radiation field) E ' _z, H ' _φ, and second order approximate solution (base current of scale) E " _z, H " _φwaveform.

The comparing result of approximate expression waveform and exact solution waveform shows, no matter is near field region or far-field region, as long as return stroke current does not arrive counterattack channel roof, the waveform of electromagnetic field is just approximate consistent with the waveform of fighting back channel bottom electric current.

Claims (2)

1. An approximate analytical expression method that is applied to describe the lightning return electromagnetic field on the surface, is characterized in that: The approximate analytic expression of the surface lightning return electromagnetic field described in the present invention is made up of 4 approximate analytic expressions of lightning near area electric field, near area magnetic field, far area electric field and far area magnetic field; Based on the transmission line model, it is obtained through the approximate processing of the exact analytical expression of the lightning return electromagnetic field obtained by the dipole method; in this group of approximate analytical expressions, the surface lightning return electromagnetic field is equal to It can be approximately expressed as the product of the current at the bottom of the channel and a factor related to the distance. When the observation distance is determined, the waveforms of the lightning electric field and magnetic field have similar characteristics to the current waveform at the bottom of the return strike channel. 2. Applying the above-mentioned approximate analytical expression method of the lightning return electromagnetic field to the approximate calculation of the lightning return electromagnetic field, the theoretical basis for the development of the laboratory lightning return electric field and magnetic field simulator, etc., are also protected by this patent.

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