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fields.c
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fields.c
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/*** Translated to the C language by N. Kyriazis 20 Aug 2003 ***
Program NEC(input,tape5=input,output,tape11,tape12,tape13,tape14,
tape15,tape16,tape20,tape21)
Numerical Electromagnetics Code (NEC2) developed at Lawrence
Livermore lab., Livermore, CA. (contact G. Burke at 415-422-8414
for problems with the NEC code. For problems with the vax implem-
entation, contact J. Breakall at 415-422-8196 or E. Domning at 415
422-5936)
file created 4/11/80.
***********Notice**********
This computer code material was prepared as an account of work
sponsored by the United States government. Neither the United
States nor the United States Department Of Energy, nor any of
their employees, nor any of their contractors, subcontractors,
or their employees, makes any warranty, express or implied, or
assumes any legal liability or responsibility for the accuracy,
completeness or usefulness of any information, apparatus, product
or process disclosed, or represents that its use would not infringe
privately-owned rights.
******************************************************************/
#include "nec2c.h"
#include "shared.h"
/*common /tmh/ */
static tmh_t tmh;
/*-------------------------------------------------------------------*/
/* compute near e fields of a segment with sine, cosine, and */
/* constant currents. ground effect included. */
void efld( double xi, double yi, double zi, double ai, int ij )
{
#define txk egnd[0]
#define tyk egnd[1]
#define tzk egnd[2]
#define txs egnd[3]
#define tys egnd[4]
#define tzs egnd[5]
#define txc egnd[6]
#define tyc egnd[7]
#define tzc egnd[8]
int ip, ijx;
double xij, yij, rfl, salpr, zij, zp, rhox;
double rhoy, rhoz, rh, r, rmag, cth, px, py;
double xymag, xspec, yspec, rhospc, dmin;
complex double epx, epy, refs, refps, zrsin, zratx, zscrn;
complex double tezs, ters, tezc, terc, tezk, terk, egnd[9];
xij= xi- dataj.xj;
yij= yi- dataj.yj;
ijx= ij;
rfl=-1.;
for( ip = 0; ip < gnd.ksymp; ip++ )
{
if( ip == 1)
ijx=1;
rfl= -rfl;
salpr= dataj.salpj* rfl;
zij= zi- rfl* dataj.zj;
zp= xij* dataj.cabj+ yij* dataj.sabj+ zij* salpr;
rhox= xij- dataj.cabj* zp;
rhoy= yij- dataj.sabj* zp;
rhoz= zij- salpr* zp;
rh= sqrt( rhox* rhox+ rhoy* rhoy+ rhoz* rhoz+ ai* ai);
if( rh <= 1.e-10)
{
rhox=0.;
rhoy=0.;
rhoz=0.;
}
else
{
rhox= rhox/ rh;
rhoy= rhoy/ rh;
rhoz= rhoz/ rh;
}
/* lumped current element approx. for large separations */
r= sqrt( zp* zp+ rh* rh);
if( r >= dataj.rkh)
{
rmag= TP* r;
cth= zp/ r;
px= rh/ r;
txk= cmplx( cos( rmag), -sin( rmag));
py= TP* r* r;
tyk= ETA* cth* txk* cmplx(1.0,-1.0/ rmag)/ py;
tzk= ETA* px* txk* cmplx(1.0, rmag-1.0/ rmag)/(2.* py);
tezk= tyk* cth- tzk* px;
terk= tyk* px+ tzk* cth;
rmag= sin( PI* dataj.s)/ PI;
tezc= tezk* rmag;
terc= terk* rmag;
tezk= tezk* dataj.s;
terk= terk* dataj.s;
txs=CPLX_00;
tys=CPLX_00;
tzs=CPLX_00;
} /* if( r >= dataj.rkh) */
else
{
/* eksc for thin wire approx. or ekscx for extended t.w. approx. */
if( dataj.iexk != 1)
eksc( dataj.s, zp, rh, TP, ijx, &tezs, &ters,
&tezc, &terc, &tezk, &terk );
else
ekscx( dataj.b, dataj.s, zp, rh, TP, ijx, dataj.ind1, dataj.ind2,
&tezs, &ters, &tezc, &terc, &tezk, &terk);
txs= tezs* dataj.cabj+ ters* rhox;
tys= tezs* dataj.sabj+ ters* rhoy;
tzs= tezs* salpr+ ters* rhoz;
} /* if( r < dataj.rkh) */
txk= tezk* dataj.cabj+ terk* rhox;
tyk= tezk* dataj.sabj+ terk* rhoy;
tzk= tezk* salpr+ terk* rhoz;
txc= tezc* dataj.cabj+ terc* rhox;
tyc= tezc* dataj.sabj+ terc* rhoy;
tzc= tezc* salpr+ terc* rhoz;
if( ip == 1)
{
if( gnd.iperf <= 0)
{
zratx= gnd.zrati;
rmag= r;
xymag= sqrt( xij* xij+ yij* yij);
/* set parameters for radial wire ground screen. */
if( gnd.nradl != 0)
{
xspec=( xi* dataj.zj+ zi* dataj.xj)/( zi+ dataj.zj);
yspec=( yi* dataj.zj+ zi* dataj.yj)/( zi+ dataj.zj);
rhospc= sqrt( xspec* xspec+ yspec* yspec+ gnd.t2* gnd.t2);
if( rhospc <= gnd.scrwl)
{
zscrn= gnd.t1* rhospc* log( rhospc/ gnd.t2);
zratx=( zscrn* gnd.zrati)/( ETA* gnd.zrati+ zscrn);
}
} /* if( gnd.nradl != 0) */
/* calculation of reflection coefficients when ground is specified. */
if( xymag <= 1.0e-6)
{
px=0.;
py=0.;
cth=1.;
zrsin=CPLX_10;
}
else
{
px= -yij/ xymag;
py= xij/ xymag;
cth= zij/ rmag;
zrsin= csqrt(1.0 - zratx*zratx*(1.0 - cth*cth) );
} /* if( xymag <= 1.0e-6) */
refs=( cth- zratx* zrsin)/( cth+ zratx* zrsin);
refps=-( zratx* cth- zrsin)/( zratx* cth+ zrsin);
refps= refps- refs;
epy= px* txk+ py* tyk;
epx= px* epy;
epy= py* epy;
txk= refs* txk+ refps* epx;
tyk= refs* tyk+ refps* epy;
tzk= refs* tzk;
epy= px* txs+ py* tys;
epx= px* epy;
epy= py* epy;
txs= refs* txs+ refps* epx;
tys= refs* tys+ refps* epy;
tzs= refs* tzs;
epy= px* txc+ py* tyc;
epx= px* epy;
epy= py* epy;
txc= refs* txc+ refps* epx;
tyc= refs* tyc+ refps* epy;
tzc= refs* tzc;
} /* if( gnd.iperf <= 0) */
dataj.exk= dataj.exk- txk* gnd.frati;
dataj.eyk= dataj.eyk- tyk* gnd.frati;
dataj.ezk= dataj.ezk- tzk* gnd.frati;
dataj.exs= dataj.exs- txs* gnd.frati;
dataj.eys= dataj.eys- tys* gnd.frati;
dataj.ezs= dataj.ezs- tzs* gnd.frati;
dataj.exc= dataj.exc- txc* gnd.frati;
dataj.eyc= dataj.eyc- tyc* gnd.frati;
dataj.ezc= dataj.ezc- tzc* gnd.frati;
continue;
} /* if( ip == 1) */
dataj.exk= txk;
dataj.eyk= tyk;
dataj.ezk= tzk;
dataj.exs= txs;
dataj.eys= tys;
dataj.ezs= tzs;
dataj.exc= txc;
dataj.eyc= tyc;
dataj.ezc= tzc;
} /* for( ip = 0; ip < gnd.ksymp; ip++ ) */
if( gnd.iperf != 2)
return;
/* field due to ground using sommerfeld/norton */
incom.sn= sqrt( dataj.cabj* dataj.cabj+ dataj.sabj* dataj.sabj);
if( incom.sn >= 1.0e-5)
{
incom.xsn= dataj.cabj/ incom.sn;
incom.ysn= dataj.sabj/ incom.sn;
}
else
{
incom.sn=0.;
incom.xsn=1.;
incom.ysn=0.;
}
/* displace observation point for thin wire approximation */
zij= zi+ dataj.zj;
salpr= -dataj.salpj;
rhox= dataj.sabj* zij- salpr* yij;
rhoy= salpr* xij- dataj.cabj* zij;
rhoz= dataj.cabj* yij- dataj.sabj* xij;
rh= rhox* rhox+ rhoy* rhoy+ rhoz* rhoz;
if( rh <= 1.e-10)
{
incom.xo= xi- ai* incom.ysn;
incom.yo= yi+ ai* incom.xsn;
incom.zo= zi;
}
else
{
rh= ai/ sqrt( rh);
if( rhoz < 0.)
rh= -rh;
incom.xo= xi+ rh* rhox;
incom.yo= yi+ rh* rhoy;
incom.zo= zi+ rh* rhoz;
} /* if( rh <= 1.e-10) */
r= xij* xij+ yij* yij+ zij* zij;
if( r <= .95)
{
double shaf;
/* field from interpolation is integrated over segment */
incom.isnor=1;
dmin= creal(dataj.exk*conj(dataj.exk)) +
creal(dataj.eyk*conj(dataj.eyk)) +
creal(dataj.ezk*conj(dataj.ezk) );
dmin=.01* sqrt( dmin);
shaf=.5* dataj.s;
rom2(- shaf, shaf, egnd, dmin);
}
else
{
/* norton field equations and lumped current element approximation */
incom.isnor=2;
sflds(0., egnd);
} /* if( r <= .95) */
if( r > .95)
{
zp= xij* dataj.cabj+ yij* dataj.sabj+ zij* salpr;
rh= r- zp* zp;
if( rh <= 1.e-10)
dmin=0.;
else
dmin= sqrt( rh/( rh+ ai* ai));
if( dmin <= .95)
{
px=1.- dmin;
terk=( txk* dataj.cabj+ tyk* dataj.sabj+ tzk* salpr)* px;
txk= dmin* txk+ terk* dataj.cabj;
tyk= dmin* tyk+ terk* dataj.sabj;
tzk= dmin* tzk+ terk* salpr;
ters=( txs* dataj.cabj+ tys* dataj.sabj+ tzs* salpr)* px;
txs= dmin* txs+ ters* dataj.cabj;
tys= dmin* tys+ ters* dataj.sabj;
tzs= dmin* tzs+ ters* salpr;
terc=( txc* dataj.cabj+ tyc* dataj.sabj+ tzc* salpr)* px;
txc= dmin* txc+ terc* dataj.cabj;
tyc= dmin* tyc+ terc* dataj.sabj;
tzc= dmin* tzc+ terc* salpr;
} /* if( dmin <= .95) */
} /* if( r > .95) */
dataj.exk= dataj.exk+ txk;
dataj.eyk= dataj.eyk+ tyk;
dataj.ezk= dataj.ezk+ tzk;
dataj.exs= dataj.exs+ txs;
dataj.eys= dataj.eys+ tys;
dataj.ezs= dataj.ezs+ tzs;
dataj.exc= dataj.exc+ txc;
dataj.eyc= dataj.eyc+ tyc;
dataj.ezc= dataj.ezc+ tzc;
return;
}
/*-----------------------------------------------------------------------*/
/* compute e field of sine, cosine, and constant */
/* current filaments by thin wire approximation. */
void eksc( double s, double z, double rh, double xk, int ij,
complex double *ezs, complex double *ers, complex double *ezc,
complex double *erc, complex double *ezk, complex double *erk )
{
double rhk, sh, shk, ss, cs, z1a, z2a, cint, sint;
complex double gz1, gz2, gp1, gp2, gzp1, gzp2;
tmi.ij= ij;
tmi.zpk= xk* z;
rhk= xk* rh;
tmi.rkb2= rhk* rhk;
sh=.5* s;
shk= xk* sh;
ss= sin( shk);
cs= cos( shk);
z2a= sh- z;
z1a=-( sh+ z);
gx( z1a, rh, xk, &gz1, &gp1);
gx( z2a, rh, xk, &gz2, &gp2);
gzp1= gp1* z1a;
gzp2= gp2* z2a;
*ezs= CONST1*(( gz2- gz1)* cs* xk-( gzp2+ gzp1)* ss);
*ezc= -CONST1*(( gz2+ gz1)* ss* xk+( gzp2- gzp1)* cs);
*erk= CONST1*( gp2- gp1)* rh;
intx(- shk, shk, rhk, ij, &cint, &sint);
*ezk= -CONST1*( gzp2- gzp1+ xk* xk* cmplx( cint,- sint));
gzp1= gzp1* z1a;
gzp2= gzp2* z2a;
if( rh >= 1.0e-10)
{
*ers= -CONST1*(( gzp2+ gzp1+ gz2+ gz1)*
ss-( z2a* gz2- z1a* gz1)* cs*xk)/ rh;
*erc= -CONST1*(( gzp2- gzp1+ gz2- gz1)*
cs+( z2a* gz2+ z1a* gz1)* ss*xk)/ rh;
return;
}
*ers = CPLX_00;
*erc = CPLX_00;
return;
}
/*-----------------------------------------------------------------------*/
/* compute e field of sine, cosine, and constant current */
/* filaments by extended thin wire approximation. */
void ekscx( double bx, double s, double z,
double rhx, double xk, int ij, int inx1, int inx2,
complex double *ezs, complex double *ers, complex double *ezc,
complex double *erc, complex double *ezk, complex double *erk )
{
int ira;
double b, rh, sh, rhk, shk, ss, cs, z1a;
double z2a, a2, bk, bk2, cint, sint;
complex double gz1, gz2, gzp1, gzp2, gr1, gr2;
complex double grp1, grp2, grk1, grk2, gzz1, gzz2;
if( rhx >= bx)
{
rh= rhx;
b= bx;
ira=0;
}
else
{
rh= bx;
b= rhx;
ira=1;
}
sh=.5* s;
tmi.ij= ij;
tmi.zpk= xk* z;
rhk= xk* rh;
tmi.rkb2= rhk* rhk;
shk= xk* sh;
ss= sin( shk);
cs= cos( shk);
z2a= sh- z;
z1a=-( sh+ z);
a2= b* b;
if( inx1 != 2)
gxx( z1a, rh, b, a2, xk, ira, &gz1,
&gzp1, &gr1, &grp1, &grk1, &gzz1);
else
{
gx( z1a, rhx, xk, &gz1, &grk1);
gzp1= grk1* z1a;
gr1= gz1/ rhx;
grp1= gzp1/ rhx;
grk1= grk1* rhx;
gzz1= CPLX_00;
}
if( inx2 != 2)
gxx( z2a, rh, b, a2, xk, ira, &gz2,
&gzp2, &gr2, &grp2, &grk2, &gzz2);
else
{
gx( z2a, rhx, xk, &gz2, &grk2);
gzp2= grk2* z2a;
gr2= gz2/ rhx;
grp2= gzp2/ rhx;
grk2= grk2* rhx;
gzz2= CPLX_00;
}
*ezs= CONST1*(( gz2- gz1)* cs* xk-( gzp2+ gzp1)* ss);
*ezc= -CONST1*(( gz2+ gz1)* ss* xk+( gzp2- gzp1)* cs);
*ers= -CONST1*(( z2a* grp2+ z1a* grp1+ gr2+ gr1)*ss
-( z2a* gr2- z1a* gr1)* cs* xk);
*erc= -CONST1*(( z2a* grp2- z1a* grp1+ gr2- gr1)*cs
+( z2a* gr2+ z1a* gr1)* ss* xk);
*erk= CONST1*( grk2- grk1);
intx(- shk, shk, rhk, ij, &cint, &sint);
bk= b* xk;
bk2= bk* bk*.25;
*ezk= -CONST1*( gzp2- gzp1+ xk* xk*(1.- bk2)*
cmplx( cint,- sint)-bk2*( gzz2- gzz1));
return;
}
/*-----------------------------------------------------------------------*/
/* integrand for h field of a wire */
void gh( double zk, double *hr, double *hi)
{
double rs, r, ckr, skr, rr2, rr3;
rs= zk- tmh.zpka;
rs= tmh.rhks+ rs* rs;
r= sqrt( rs);
ckr= cos( r);
skr= sin( r);
rr2=1./ rs;
rr3= rr2/ r;
*hr= skr* rr2+ ckr* rr3;
*hi= ckr* rr2- skr* rr3;
return;
}
/*-----------------------------------------------------------------------*/
/* gwave computes the electric field, including ground wave, of a */
/* current element over a ground plane using formulas of k.a. norton */
/* (proc. ire, sept., 1937, pp.1203,1236.) */
void gwave( complex double *erv, complex double *ezv,
complex double *erh, complex double *ezh, complex double *eph )
{
double sppp, sppp2, cppp2, cppp, spp, spp2, cpp2, cpp;
complex double rk1, rk2, t1, t2, t3, t4, p1, rv;
complex double omr, w, f, q1, rh, v, g, xr1, xr2;
complex double x1, x2, x3, x4, x5, x6, x7;
sppp= gwav.zmh/ gwav.r1;
sppp2= sppp* sppp;
cppp2=1.- sppp2;
if( cppp2 < 1.0e-20)
cppp2=1.0e-20;
cppp= sqrt( cppp2);
spp= gwav.zph/ gwav.r2;
spp2= spp* spp;
cpp2=1.- spp2;
if( cpp2 < 1.0e-20)
cpp2=1.0e-20;
cpp= sqrt( cpp2);
rk1= -TPJ* gwav.r1;
rk2= -TPJ* gwav.r2;
t1=1. -gwav.u2* cpp2;
t2= csqrt( t1);
t3=(1. -1./ rk1)/ rk1;
t4=(1. -1./ rk2)/ rk2;
p1= rk2* gwav.u2* t1/(2.* cpp2);
rv=( spp- gwav.u* t2)/( spp+ gwav.u* t2);
omr=1.- rv;
w=1./ omr;
w=(4.0 + I*0.0)* p1* w* w;
fbar( w, &f );
q1= rk2* t1/(2.* gwav.u2* cpp2);
rh=( t2- gwav.u* spp)/( t2+ gwav.u* spp);
v=1./(1.+ rh);
v=(4.0 + I*0.0)* q1* v* v;
fbar( v, &g );
xr1= gwav.xx1/ gwav.r1;
xr2= gwav.xx2/ gwav.r2;
x1= cppp2* xr1;
x2= rv* cpp2* xr2;
x3= omr* cpp2* f* xr2;
x4= gwav.u* t2* spp*2.* xr2/ rk2;
x5= xr1* t3*(1.-3.* sppp2);
x6= xr2* t4*(1.-3.* spp2);
*ezv=( x1+ x2+ x3- x4- x5- x6)* (-CONST4);
x1= sppp* cppp* xr1;
x2= rv* spp* cpp* xr2;
x3= cpp* omr* gwav.u* t2* f* xr2;
x4= spp* cpp* omr* xr2/ rk2;
x5=3.* sppp* cppp* t3* xr1;
x6= cpp* gwav.u* t2* omr* xr2/ rk2*.5;
x7=3.* spp* cpp* t4* xr2;
*erv=-( x1+ x2- x3+ x4- x5+ x6- x7)* (-CONST4);
*ezh=-( x1- x2+ x3- x4- x5- x6+ x7)* (-CONST4);
x1= sppp2* xr1;
x2= rv* spp2* xr2;
x4= gwav.u2* t1* omr* f* xr2;
x5= t3*(1.-3.* cppp2)* xr1;
x6= t4*(1.-3.* cpp2)*(1.- gwav.u2*(1.+ rv)- gwav.u2* omr* f)* xr2;
x7= gwav.u2* cpp2* omr*(1.-1./ rk2)*( f*( gwav.u2* t1- spp2-1./ rk2)+1./rk2)* xr2;
*erh=( x1- x2- x4- x5+ x6+ x7)* (-CONST4);
x1= xr1;
x2= rh* xr2;
x3=( rh+1.)* g* xr2;
x4= t3* xr1;
x5= t4*(1.- gwav.u2*(1.+ rv)- gwav.u2* omr* f)* xr2;
x6=.5* gwav.u2* omr*( f*( gwav.u2* t1- spp2-1./ rk2)+1./ rk2)* xr2/ rk2;
*eph=-( x1- x2+ x3- x4+ x5+ x6)* (-CONST4);
return;
}
/*-----------------------------------------------------------------------*/
/* segment end contributions for thin wire approx. */
void gx( double zz, double rh, double xk,
complex double *gz, complex double *gzp)
{
double r, r2, rkz;
r2= zz* zz+ rh* rh;
r= sqrt( r2);
rkz= xk* r;
*gz= cmplx( cos( rkz),- sin( rkz))/ r;
*gzp= -cmplx(1.0, rkz)* *gz/ r2;
return;
}
/*-----------------------------------------------------------------------*/
/* segment end contributions for ext. thin wire approx. */
void gxx( double zz, double rh, double a,
double a2, double xk, int ira, complex double *g1,
complex double *g1p, complex double *g2,
complex double *g2p, complex double *g3, complex double *gzp )
{
double r, r2, r4, rk, rk2, rh2, t1, t2;
complex double gz, c1, c2, c3;
r2= zz* zz+ rh* rh;
r= sqrt( r2);
r4= r2* r2;
rk= xk* r;
rk2= rk* rk;
rh2= rh* rh;
t1=.25* a2* rh2/ r4;
t2=.5* a2/ r2;
c1= cmplx(1.0, rk);
c2=3.* c1- rk2;
c3= cmplx(6.0, rk)* rk2-15.* c1;
gz= cmplx( cos( rk),- sin( rk))/ r;
*g2= gz*(1.+ t1* c2);
*g1= *g2- t2* c1* gz;
gz= gz/ r2;
*g2p= gz*( t1* c3- c1);
*gzp= t2* c2* gz;
*g3= *g2p+ *gzp;
*g1p= *g3* zz;
if( ira != 1)
{
*g3=( *g3+ *gzp)* rh;
*gzp= -zz* c1* gz;
if( rh <= 1.0e-10)
{
*g2=0.;
*g2p=0.;
return;
}
*g2= *g2/ rh;
*g2p= *g2p* zz/ rh;
return;
} /* if( ira != 1) */
t2=.5* a;
*g2= -t2* c1* gz;
*g2p= t2* gz* c2/ r2;
*g3= rh2* *g2p- a* gz* c1;
*g2p= *g2p* zz;
*gzp= -zz* c1* gz;
return;
}
/*-----------------------------------------------------------------------*/
/* hfk computes the h field of a uniform current */
/* filament by numerical integration */
void hfk( double el1, double el2, double rhk,
double zpkx, double *sgr, double *sgi )
{
int nx = 1, nma = 65536, nts = 4;
int ns, nt;
int flag = TRUE;
double rx = 1.0e-4;
double z, ze, s, ep, zend, dz=0., zp, dzot=0., t00r, g1r, g5r=0, t00i;
double g1i, g5i=0., t01r, g3r=0, t01i, g3i=0, t10r, t10i, te1i, te1r, t02r;
double g2r, g4r, t02i, g2i, g4i, t11r, t11i, t20r, t20i, te2i, te2r;
tmh.zpka= zpkx;
tmh.rhks= rhk* rhk;
z= el1;
ze= el2;
s= ze- z;
ep= s/(10.* nma);
zend= ze- ep;
*sgr=0.0;
*sgi=0.0;
ns= nx;
nt=0;
gh( z, &g1r, &g1i);
while( TRUE )
{
if( flag )
{
dz= s/ ns;
zp= z+ dz;
if( zp > ze )
{
dz= ze- z;
if( fabs(dz) <= ep )
{
*sgr= *sgr* rhk*.5;
*sgi= *sgi* rhk*.5;
return;
}
}
dzot= dz*.5;
zp= z+ dzot;
gh( zp, &g3r, &g3i);
zp= z+ dz;
gh( zp, &g5r, &g5i);
} /* if( flag ) */
t00r=( g1r+ g5r)* dzot;
t00i=( g1i+ g5i)* dzot;
t01r=( t00r+ dz* g3r)*0.5;
t01i=( t00i+ dz* g3i)*0.5;
t10r=(4.0* t01r- t00r)/3.0;
t10i=(4.0* t01i- t00i)/3.0;
test( t01r, t10r, &te1r, t01i, t10i, &te1i, 0.);
if( (te1i <= rx) && (te1r <= rx) )
{
*sgr= *sgr+ t10r;
*sgi= *sgi+ t10i;
nt += 2;
z += dz;
if( z >= zend)
{
*sgr= *sgr* rhk*.5;
*sgi= *sgi* rhk*.5;
return;
}
g1r= g5r;
g1i= g5i;
if( nt >= nts)
if( ns > nx)
{
ns= ns/2;
nt=1;
}
flag = TRUE;
continue;
} /* if( (te1i <= rx) && (te1r <= rx) ) */
zp= z+ dz*0.25;
gh( zp, &g2r, &g2i);
zp= z+ dz*0.75;
gh( zp, &g4r, &g4i);
t02r=( t01r+ dzot*( g2r+ g4r))*0.5;
t02i=( t01i+ dzot*( g2i+ g4i))*0.5;
t11r=(4.0* t02r- t01r)/3.0;
t11i=(4.0* t02i- t01i)/3.0;
t20r=(16.0* t11r- t10r)/15.0;
t20i=(16.0* t11i- t10i)/15.0;
test( t11r, t20r, &te2r, t11i, t20i, &te2i, 0.);
if( (te2i > rx) || (te2r > rx) )
{
nt=0;
if( ns >= nma)
fprintf( output_fp, "\n STEP SIZE LIMITED AT Z= %10.5f", z );
else
{
ns= ns*2;
dz= s/ ns;
dzot= dz*0.5;
g5r= g3r;
g5i= g3i;
g3r= g2r;
g3i= g2i;
flag = FALSE;
continue;
}
} /* if( (te2i > rx) || (te2r > rx) ) */
*sgr= *sgr+ t20r;
*sgi= *sgi+ t20i;
nt++;
z += dz;
if( z >= zend)
{
*sgr= *sgr* rhk*.5;
*sgi= *sgi* rhk*.5;
return;
}
g1r= g5r;
g1i= g5i;
if( nt >= nts)
if( ns > nx)
{
ns= ns/2;
nt=1;
}
flag = TRUE;
} /* while( TRUE ) */
}
/*-----------------------------------------------------------------------*/
/* hintg computes the h field of a patch current */
void hintg( double xi, double yi, double zi )
{
int ip;
double rx, ry, rfl, xymag, pxx, pyy, cth;
double rz, rsq, r, rk, cr, sr, t1zr, t2zr;
complex double gam, f1x, f1y, f1z, f2x, f2y, f2z, rrv, rrh;
rx= xi- dataj.xj;
ry= yi- dataj.yj;
rfl=-1.;
dataj.exk=CPLX_00;
dataj.eyk=CPLX_00;
dataj.ezk=CPLX_00;
dataj.exs=CPLX_00;
dataj.eys=CPLX_00;
dataj.ezs=CPLX_00;
for( ip = 1; ip <= gnd.ksymp; ip++ )
{
rfl= -rfl;
rz= zi- dataj.zj* rfl;
rsq= rx* rx+ ry* ry+ rz* rz;
if( rsq < 1.0e-20)
continue;
r = sqrt( rsq );
rk= TP* r;
cr= cos( rk);
sr= sin( rk);
gam=-( cmplx(cr,-sr)+rk*cmplx(sr,cr) )/( FPI*rsq*r )* dataj.s;
dataj.exc= gam* rx;
dataj.eyc= gam* ry;
dataj.ezc= gam* rz;
t1zr= dataj.t1zj* rfl;
t2zr= dataj.t2zj* rfl;
f1x= dataj.eyc* t1zr- dataj.ezc* dataj.t1yj;
f1y= dataj.ezc* dataj.t1xj- dataj.exc* t1zr;
f1z= dataj.exc* dataj.t1yj- dataj.eyc* dataj.t1xj;
f2x= dataj.eyc* t2zr- dataj.ezc* dataj.t2yj;
f2y= dataj.ezc* dataj.t2xj- dataj.exc* t2zr;
f2z= dataj.exc* dataj.t2yj- dataj.eyc* dataj.t2xj;
if( ip != 1)
{
if( gnd.iperf == 1)
{
f1x= -f1x;
f1y= -f1y;
f1z= -f1z;
f2x= -f2x;
f2y= -f2y;
f2z= -f2z;
}
else
{
xymag= sqrt( rx* rx+ ry* ry);
if( xymag <= 1.0e-6)
{
pxx=0.;
pyy=0.;
cth=1.;
rrv=CPLX_10;
}
else
{
pxx= -ry/ xymag;
pyy= rx/ xymag;
cth= rz/ r;
rrv= csqrt(1.- gnd.zrati* gnd.zrati*(1.- cth* cth));
} /* if( xymag <= 1.0e-6) */
rrh= gnd.zrati* cth;
rrh=( rrh- rrv)/( rrh+ rrv);
rrv= gnd.zrati* rrv;
rrv=-( cth- rrv)/( cth+ rrv);
gam=( f1x* pxx+ f1y* pyy)*( rrv- rrh);
f1x= f1x* rrh+ gam* pxx;
f1y= f1y* rrh+ gam* pyy;
f1z= f1z* rrh;
gam=( f2x* pxx+ f2y* pyy)*( rrv- rrh);
f2x= f2x* rrh+ gam* pxx;
f2y= f2y* rrh+ gam* pyy;
f2z= f2z* rrh;
} /* if( gnd.iperf == 1) */
} /* if( ip != 1) */
dataj.exk += f1x;
dataj.eyk += f1y;
dataj.ezk += f1z;
dataj.exs += f2x;
dataj.eys += f2y;
dataj.ezs += f2z;
} /* for( ip = 1; ip <= gnd.ksymp; ip++ ) */
return;
}
/*-----------------------------------------------------------------------*/
/* hsfld computes the h field for constant, sine, and */
/* cosine current on a segment including ground effects. */
void hsfld( double xi, double yi, double zi, double ai )
{
int ip;
double xij, yij, rfl, salpr, zij, zp, rhox, rhoy, rhoz, rh, phx;
double phy, phz, rmag, xymag, xspec, yspec, rhospc, px, py, cth;
complex double hpk, hps, hpc, qx, qy, qz, rrv, rrh, zratx;
xij= xi- dataj.xj;
yij= yi- dataj.yj;
rfl=-1.;
for( ip = 0; ip < gnd.ksymp; ip++ )
{
rfl= -rfl;
salpr= dataj.salpj* rfl;
zij= zi- rfl* dataj.zj;
zp= xij* dataj.cabj+ yij* dataj.sabj+ zij* salpr;
rhox= xij- dataj.cabj* zp;
rhoy= yij- dataj.sabj* zp;
rhoz= zij- salpr* zp;
rh= sqrt( rhox* rhox+ rhoy* rhoy+ rhoz* rhoz+ ai* ai);
if( rh <= 1.0e-10)
{
dataj.exk=0.;
dataj.eyk=0.;
dataj.ezk=0.;
dataj.exs=0.;
dataj.eys=0.;
dataj.ezs=0.;
dataj.exc=0.;
dataj.eyc=0.;
dataj.ezc=0.;
continue;
}
rhox= rhox/ rh;
rhoy= rhoy/ rh;
rhoz= rhoz/ rh;
phx= dataj.sabj* rhoz- salpr* rhoy;
phy= salpr* rhox- dataj.cabj* rhoz;
phz= dataj.cabj* rhoy- dataj.sabj* rhox;
hsflx( dataj.s, rh, zp, &hpk, &hps, &hpc);
if( ip == 1 )
{
if( gnd.iperf != 1 )
{
zratx= gnd.zrati;
rmag= sqrt( zp* zp+ rh* rh);
xymag= sqrt( xij* xij+ yij* yij);
/* set parameters for radial wire ground screen. */
if( gnd.nradl != 0)
{
xspec=( xi* dataj.zj+ zi* dataj.xj)/( zi+ dataj.zj);
yspec=( yi* dataj.zj+ zi* dataj.yj)/( zi+ dataj.zj);
rhospc= sqrt( xspec* xspec+ yspec* yspec+ gnd.t2* gnd.t2);
if( rhospc <= gnd.scrwl)
{
rrv= gnd.t1* rhospc* log( rhospc/ gnd.t2);
zratx=( rrv* gnd.zrati)/( ETA* gnd.zrati+ rrv);
}
}
/* calculation of reflection coefficients when ground is specified. */
if( xymag <= 1.0e-6)
{
px=0.;
py=0.;
cth=1.;
rrv=CPLX_10;
}
else
{
px= -yij/ xymag;
py= xij/ xymag;
cth= zij/ rmag;
rrv= csqrt(1.- zratx* zratx*(1.- cth* cth));
}
rrh= zratx* cth;
rrh=-( rrh- rrv)/( rrh+ rrv);
rrv= zratx* rrv;
rrv=( cth- rrv)/( cth+ rrv);
qy=( phx* px+ phy* py)*( rrv- rrh);
qx= qy* px+ phx* rrh;
qy= qy* py+ phy* rrh;
qz= phz* rrh;
dataj.exk= dataj.exk- hpk* qx;
dataj.eyk= dataj.eyk- hpk* qy;
dataj.ezk= dataj.ezk- hpk* qz;
dataj.exs= dataj.exs- hps* qx;
dataj.eys= dataj.eys- hps* qy;
dataj.ezs= dataj.ezs- hps* qz;
dataj.exc= dataj.exc- hpc* qx;
dataj.eyc= dataj.eyc- hpc* qy;
dataj.ezc= dataj.ezc- hpc* qz;
continue;
} /* if( gnd.iperf != 1 ) */
dataj.exk= dataj.exk- hpk* phx;
dataj.eyk= dataj.eyk- hpk* phy;
dataj.ezk= dataj.ezk- hpk* phz;
dataj.exs= dataj.exs- hps* phx;
dataj.eys= dataj.eys- hps* phy;
dataj.ezs= dataj.ezs- hps* phz;
dataj.exc= dataj.exc- hpc* phx;