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.
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
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)
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
Radiation field has been c
2magnitude, can ignore.So just obtain the first approximation expression formula of near region electric field
Similarly, can obtain the first approximation expression formula in magnetic field, near region
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
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
Because v is constant, so
Formula (14) substitution formula (12), (13) integration are obtained
Due to τ≤0 o'clock, i (0, τ)=0.In the time of t≤h/v+r/c, formula (15), (16) become
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.