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t04.f
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c
c====================================================================================
c
c
SUBROUTINE T04_s (IOPT,PARMOD,PS,X,Y,Z,BX,BY,BZ)
c
c ASSEMBLED: MARCH 25, 2004;
C UPDATED: AUGUST 2 & 31, DECEMBER 27, 2004.
c LATEST MODIFICATIONS/BUGS REMOVED:
c
C (1) MARCH 14, 2005: 79 -> 69 (LINE 94; might cause compilation problems with some Fortran compilers)
c
C (2) JUNE 24, 2006: REPLACED COEFFICIENTS IN
c (i) DATA statement in FUNCTION AP,
C (ii) DATA C_SY statement in SUBROUTINE FULL_RC, and
c (iii) DATA A statement in SUBROUTINE T04_s.
C This correction was needed due to a bug found in the symmetric ring current module.
c Its impact can be significant (up to ~20 nT) only in the innermost magnetosphere (R<=2)
c and only for strongly disturbed conditions; otherwise, the change in the model field
c does not exceed a few percent.
c
c--------------------------------------------------------------------
C A DATA-BASED MODEL OF THE EXTERNAL (I.E., WITHOUT EARTH'S CONTRIBUTION) PART OF THE
C MAGNETOSPHERIC MAGNETIC FIELD, CALIBRATED BY
C (1) SOLAR WIND PRESSURE PDYN (NANOPASCALS),
C (2) DST (NANOTESLA),
C (3) BYIMF,
C (4) BZIMF (NANOTESLA)
C (5-10) INDICES W1 - W6, CALCULATED AS TIME INTEGRALS FROM THE BEGINNING OF A STORM
c SEE THE REFERENCE (3) BELOW, FOR A DETAILED DEFINITION OF THOSE VARIABLES
C
c THE ABOVE 10 INPUT PARAMETERS SHOULD BE PLACED IN THE ELEMENTS
c OF THE ARRAY PARMOD(10).
C
C THE REST OF THE INPUT VARIABLES ARE: THE GEODIPOLE TILT ANGLE PS (RADIANS),
C X,Y,Z - GSM POSITION (RE)
C
c IOPT IS A DUMMY INPUT PARAMETER, INCLUDED TO MAKE THIS SUBROUTINE
C COMPATIBLE WITH THE TRACING SOFTWARE PACKAGE (GEOPACK). IN THIS MODEL,
C THE PARAMETER IOPT DOES NOT AFFECT THE OUTPUT FIELD.
c
C*******************************************************************************************
c** ATTENTION: THE MODEL IS BASED ON DATA TAKEN SUNWARD FROM X=-15Re, AND HENCE BECOMES *
C** INVALID AT LARGER TAILWARD DISTANCES
c
c
c *
C*******************************************************************************************
C
c OUTPUT: GSM COMPONENTS OF THE EXTERNAL MAGNETIC FIELD (BX,BY,BZ, nanotesla)
C COMPUTED AS A SUM OF CONTRIBUTIONS FROM PRINCIPAL FIELD SOURCES
C
c (C) Copr. 2004, Nikolai A. Tsyganenko, USRA/Code 612.3, NASA GSFC
c Greenbelt, MD 20771, USA
c
C REFERENCES:
C
C (1) N. A. Tsyganenko, A new data-based model of the near magnetosphere magnetic field:
c 1. Mathematical structure.
c 2. Parameterization and fitting to observations. JGR v. 107(A8), 1176/1179, doi:10.1029/2001JA000219/220, 2002.
c
c (2) N. A. Tsyganenko, H. J. Singer, J. C. Kasper, Storm-time distortion of the
c inner magnetosphere: How severe can it get ? JGR v. 108(A5), 1209, doi:10.1029/2002JA009808, 2003.
c (3) N. A. Tsyganenko and M. I. Sitnov, Modeling the dynamics of the inner magnetosphere during
c strong geomagnetic storms, J. Geophys. Res., v. 110 (A3), A03208, doi: 10.1029/2004JA010798, 2005.
c----------------------------------------------------------------------
c
c
c 2020.8.7 --change to double by Ribom
REAL*8 PARMOD(10),PS,X,Y,Z,BX,BY,BZ
REAL*8 A(69),PDYN,DST_AST,BXIMF,BYIMF,BZIMF,W1,W2,W3,W4,W5,W6,
* PSS,XX,YY,ZZ,BXCF,BYCF,BZCF,BXT1,BYT1,BZT1,BXT2,BYT2,BZT2,
* BXSRC,BYSRC,BZSRC,BXPRC,BYPRC,BZPRC, BXR11,BYR11,BZR11,
* BXR12,BYR12,BZR12,BXR21,BYR21,BZR21,BXR22,BYR22,BZR22,HXIMF,
* HYIMF,HZIMF,BBX,BBY,BBZ
C
DATA A/1.00000,5.44118,0.891995,9.09684,0.00000,-7.18972,12.2700,
* -4.89408,0.00000,0.870536,1.36081,0.00000,0.688650,0.602330,
* 0.00000,0.316346,1.22728,-0.363620E-01,-0.405821,0.452536,
* 0.755831,0.215662,0.152759,5.96235,23.2036,11.2994,69.9596,
* 0.989596,-0.132131E-01,0.985681,0.344212E-01,1.02389,0.207867,
* 1.51220,0.682715E-01,1.84714,1.76977,1.37690,0.696350,0.343280,
* 3.28846,111.293,5.82287,4.39664,0.383403,0.648176,0.318752E-01,
* 0.581168,1.15070,0.843004,0.394732,0.846509,0.916555,0.550920,
* 0.180725,0.898772,0.387365,2.26596,1.29123,0.436819,1.28211,
* 1.33199,.405553,1.6229,.699074,1.26131,2.42297,.537116,.619441/
c
DATA IOPGEN,IOPTT,IOPB,IOPR/0,0,0,0/
c 2019.7.2 add IOPT
C
PDYN=PARMOD(1)
DST_AST=PARMOD(2)*0.8-13.*SQRT(PDYN)
BYIMF=PARMOD(3)
BZIMF=PARMOD(4)
C
W1=PARMOD (5)
W2=PARMOD (6)
W3=PARMOD (7)
W4=PARMOD (8)
W5=PARMOD (9)
W6=PARMOD(10)
PSS=PS
XX=X
YY=Y
ZZ=Z
C
CALL EXTERN (IOPGEN,IOPTT,IOPB,IOPR,A,69,PDYN,DST_AST,BXIMF,BYIMF,
+ BZIMF,W1,W2,W3,W4,W5,W6,PSS,XX,YY,ZZ,BXCF,BYCF,BZCF,BXT1,BYT1,
+ BZT1,BXT2,BYT2,BZT2,BXSRC,BYSRC,BZSRC,BXPRC,BYPRC,BZPRC, BXR11,
+ BYR11,BZR11,BXR12,BYR12,BZR12,BXR21,BYR21,BZR21,BXR22,BYR22,
+ BZR22,HXIMF,HYIMF,HZIMF,BBX,BBY,BBZ)
C
BX=BBX
BY=BBY
BZ=BBZ
C
RETURN
END
c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c
SUBROUTINE EXTERN (IOPGEN,IOPT,IOPB,IOPR,A,NTOT,
* PDYN,DST,BXIMF,BYIMF,BZIMF,W1,W2,W3,W4,W5,W6,PS,X,Y,Z,
* BXCF,BYCF,BZCF,BXT1,BYT1,BZT1,BXT2,BYT2,BZT2,
* BXSRC,BYSRC,BZSRC,BXPRC,BYPRC,BZPRC, BXR11,BYR11,BZR11,
* BXR12,BYR12,BZR12,BXR21,BYR21,BZR21,BXR22,BYR22,BZR22,HXIMF,
* HYIMF,HZIMF,BX,BY,BZ)
C
C IOPGEN - GENERAL OPTION FLAG: IOPGEN=0 - CALCULATE TOTAL FIELD
C IOPGEN=1 - DIPOLE SHIELDING ONLY
C IOPGEN=2 - TAIL FIELD ONLY
C IOPGEN=3 - BIRKELAND FIELD ONLY
C IOPGEN=4 - RING CURRENT FIELD ONLY
C IOPGEN=5 - INTERCONNECTION FIELD ONLY
C
C IOPT - TAIL FIELD FLAG: IOPT=0 - BOTH MODES
C IOPT=1 - MODE 1 ONLY
C IOPT=2 - MODE 2 ONLY
C
C IOPB - BIRKELAND FIELD FLAG: IOPB=0 - ALL 4 TERMS
C IOPB=1 - REGION 1, MODES 1 AND 2
C IOPB=2 - REGION 2, MODES 1 AND 2
C
C IOPR - RING CURRENT FLAG: IOPR=0 - BOTH SRC AND PRC
C IOPR=1 - SRC ONLY
C IOPR=2 - PRC ONLY
C
IMPLICIT REAL * 8 (A - H, O - Z)
INTEGER IOPGEN,IOPT,IOPB,IOPR,NTOT
REAL*8 PDYN,DST,BXIMF,BYIMF,BZIMF,W1,W2,W3,W4,W5,W6,PS,X,Y,Z,
* BXCF,BYCF,BZCF,BXT1,BYT1,BZT1,BXT2,BYT2,BZT2,
* BXSRC,BYSRC,BZSRC,BXPRC,BYPRC,BZPRC, BXR11,BYR11,BZR11,
* BXR12,BYR12,BZR12,BXR21,BYR21,BZR21,BXR22,BYR22,BZR22,HXIMF,
* HYIMF,HZIMF,BX,BY,BZ
C
REAL*8 A(NTOT)
C
C
COMMON /TAIL/ DXSHIFT1,DXSHIFT2,D,DELTADY
c THE COMMON BLOCKS FORWARD NONLINEAR PARAMETERS
COMMON /BIRKPAR/ XKAPPA1,XKAPPA2
COMMON /RCPAR/ SC_SY,SC_AS,PHI
COMMON /G/ G
COMMON /RH0/ RH0
C
C
DATA A0_A,A0_S0,A0_X0 /34.586D0,1.1960D0,3.4397D0/
c SHUE ET AL. PARAMETERS
DATA DSIG /0.005D0/, RH0,RH2 /7.5D0,-5.2D0/
c
XAPPA=(PDYN/2.)**A(23)
c OVERALL SCALING PARAMETER
RH0=7.5
c TAIL HINGING DISTANCE
c
G= 35.0
c TAIL WARPING PARAMETER
XAPPA3=XAPPA**3
XX=X*XAPPA
YY=Y*XAPPA
ZZ=Z*XAPPA
C
SPS=DSIN(PS)
c
X0=A0_X0/XAPPA
AM=A0_A/XAPPA
S0=A0_S0
c
C CALCULATE "IMF" COMPONENTS OUTSIDE THE MAGNETOPAUSE LAYER (HENCE BEGIN WITH "O")
C THEY ARE NEEDED ONLY IF THE POINT (X,Y,Z) IS WITHIN THE TRANSITION MAGNETOPAUSE LAYER
C OR OUTSIDE THE MAGNETOSPHERE:
C
FACTIMF=A(20)
c
OIMFX=0.D0
OIMFY=BYIMF*FACTIMF
OIMFZ=BZIMF*FACTIMF
c
R=DSQRT(X**2+Y**2+Z**2)
XSS=X
ZSS=Z
1 XSOLD=XSS
c BEGIN ITERATIVE SEARCH OF UNWARPED COORDS (TO FIND SIGMA)
ZSOLD=ZSS
RH=RH0+RH2*(ZSS/R)**2
SINPSAS=SPS/(1.D0+(R/RH)**3)**0.33333333D0
COSPSAS=DSQRT(1.D0-SINPSAS**2)
ZSS=X*SINPSAS+Z*COSPSAS
XSS=X*COSPSAS-Z*SINPSAS
DD=DABS(XSS-XSOLD)+DABS(ZSS-ZSOLD)
IF (DD.GT.1.D-6) GOTO 1
C END OF ITERATIVE SEARCH
RHO2=Y**2+ZSS**2
ASQ=AM**2
XMXM=AM+XSS-X0
IF (XMXM.LT.0.) XMXM=0.
c THE BOUNDARY IS A CYLINDER TAILWARD OF X=X0-AM
AXX0=XMXM**2
ARO=ASQ+RHO2
SIGMA=DSQRT((ARO+AXX0+SQRT((ARO+AXX0)**2-4.*ASQ*AXX0))/(2.*ASQ))
C
C NOW, THERE ARE THREE POSSIBLE CASES:
C (1) INSIDE THE MAGNETOSPHERE (SIGMA
C (2) IN THE BOUNDARY LAYER
C (3) OUTSIDE THE MAGNETOSPHERE AND B.LAYER
C FIRST OF ALL, CONSIDER THE CASES (1) AND (2):
C
C+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
IF (SIGMA.LT.S0+DSIG) THEN
c CASES (1) OR (2); CALCULATE THE MODEL FIELD
C (WITH THE POTENTIAL "PENETRATED" INTERCONNECTION FIELD):
C+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C
IF (IOPGEN.LE.1) THEN
CALL SHLCAR3X3(XX,YY,ZZ,PS,CFX,CFY,CFZ)
c DIPOLE SHIELDING FIELD
BXCF=CFX*XAPPA3
BYCF=CFY*XAPPA3
BZCF=CFZ*XAPPA3
ELSE
BXCF=0.D0
BYCF=0.D0
BZCF=0.D0
ENDIF
c DONE
IF (IOPGEN.EQ.0.OR.IOPGEN.EQ.2) THEN
DSTT=-20.
IF (DST.LT.DSTT) DSTT=DST
ZNAM=DABS(DSTT)**0.37
DXSHIFT1=A(24)-A(25)/ZNAM
DXSHIFT2=A(26)-A(27)/ZNAM
D=A(36)*DEXP(-W1/A(37)) +A(69)
DELTADY=4.7
CALL DEFORMED (IOPT,PS,XX,YY,ZZ,
c TAIL FIELD (THREE MODES)
* BXT1,BYT1,BZT1,BXT2,BYT2,BZT2)
ELSE
BXT1=0.D0
BYT1=0.D0
BZT1=0.D0
BXT2=0.D0
BYT2=0.D0
BZT2=0.D0
ENDIF
IF (IOPGEN.EQ.0.OR.IOPGEN.EQ.3) THEN
ZNAM=DABS(DST)
IF (DST.GE.-20.D0) ZNAM=20.D0
XKAPPA1=A(32)*(ZNAM/20.D0)**A(33)
XKAPPA2=A(34)*(ZNAM/20.D0)**A(35)
CALL BIRK_TOT (IOPB,PS,XX,YY,ZZ,BXR11,BYR11,BZR11,BXR12,BYR12,
* BZR12,BXR21,BYR21,BZR21,BXR22,BYR22,BZR22)
c BIRKELAND FIELD (TWO MODES FOR R1 AND TWO MODES FOR R2)
ELSE
BXR11=0.D0
BYR11=0.D0
BZR11=0.D0
BXR21=0.D0
BYR21=0.D0
BZR21=0.D0
ENDIF
IF (IOPGEN.EQ.0.OR.IOPGEN.EQ.4) THEN
PHI=A(38)
ZNAM=DABS(DST)
IF (DST.GE.-20.D0) ZNAM=20.D0
SC_SY=A(28)*(20.D0/ZNAM)**A(29) *XAPPA
c
SC_AS=A(30)*(20.D0/ZNAM)**A(31) *XAPPA
c MULTIPLICATION BY XAPPA IS MADE IN ORDER TO MAKE THE SRC AND PRC
c SCALING COMPLETELY INDEPENDENT OF THE GENERAL SCALING DUE TO THE
C MAGNETOPAUSE COMPRESSION/EXPANSION
c
C
CALL FULL_RC(IOPR,PS,XX,YY,ZZ,BXSRC,BYSRC,BZSRC,BXPRC,BYPRC,
* BZPRC)
c SHIELDED RING CURRENT (SRC AND PRC)
ELSE
BXSRC=0.D0
BYSRC=0.D0
BZSRC=0.D0
BXPRC=0.D0
BYPRC=0.D0
BZPRC=0.D0
ENDIF
C
IF (IOPGEN.EQ.0.OR.IOPGEN.EQ.5) THEN
HXIMF=0.D0
HYIMF=BYIMF
HZIMF=BZIMF
c THESE ARE COMPONENTS OF THE PENETRATED FIELD PER UNIT OF THE PENETRATION COEFFICIENT.
C IN OTHER WORDS, THESE ARE DERIVATIVES OF THE PENETRATION FIELD COMPONENTS WITH RESPECT
C TO THE PENETRATION COEFFICIENT. WE ASSUME THAT ONLY TRANSVERSE COMPONENT OF THE
C FIELD PENETRATES INSIDE.
ELSE
HXIMF=0.D0
HYIMF=0.D0
HZIMF=0.D0
ENDIF
C
C-----------------------------------------------------------
C
C NOW, ADD UP ALL THE COMPONENTS:
c
DLP1=(PDYN/2.D0)**A(21)
DLP2=(PDYN/2.D0)**A(22)
TAMP1=A(2)+A(3)*DLP1+A(4)*A(39)*W1/DSQRT(W1**2+A(39)**2)+A(5)*DST
TAMP2=A(6)+A(7)*DLP2+A(8)*A(40)*W2/DSQRT(W2**2+A(40)**2)+A(9)*DST
A_SRC=A(10)+A(11)*A(41)*W3/DSQRT(W3**2+A(41)**2)
* +A(12)*DST
A_PRC=A(13)+A(14)*A(42)*W4/DSQRT(W4**2+A(42)**2)
* +A(15)*DST
A_R11=A(16)+A(17)*A(43)*W5/DSQRT(W5**2+A(43)**2)
A_R21=A(18)+A(19)*A(44)*W6/DSQRT(W6**2+A(44)**2)
BBX=A(1)*BXCF+TAMP1*BXT1+TAMP2*BXT2+A_SRC*BXSRC+A_PRC*BXPRC
* +A_R11*BXR11+A_R21*BXR21+A(20)*HXIMF
BBY=A(1)*BYCF+TAMP1*BYT1+TAMP2*BYT2+A_SRC*BYSRC+A_PRC*BYPRC
* +A_R11*BYR11+A_R21*BYR21+A(20)*HYIMF
BBZ=A(1)*BZCF+TAMP1*BZT1+TAMP2*BZT2+A_SRC*BZSRC+A_PRC*BZPRC
* +A_R11*BZR11+A_R21*BZR21+A(20)*HZIMF
C
C AND WE HAVE THE TOTAL EXTERNAL FIELD.
C
C
C NOW, LET US CHECK WHETHER WE HAVE THE CASE (1). IF YES - ALL DONE:
C
IF (SIGMA.LT.S0-DSIG) THEN
c (X,Y,Z) IS INSIDE THE MAGNETOSPHERE
BX=BBX
BY=BBY
BZ=BBZ
ELSE
c THIS IS THE MOST COMPLEX CASE: WE ARE INSIDE
C THE INTERPOLATION REGION
FINT=0.5*(1.-(SIGMA-S0)/DSIG)
FEXT=0.5*(1.+(SIGMA-S0)/DSIG)
C
CALL DIPOLE (PS,X,Y,Z,QX,QY,QZ)
BX=(BBX+QX)*FINT+OIMFX*FEXT -QX
BY=(BBY+QY)*FINT+OIMFY*FEXT -QY
BZ=(BBZ+QZ)*FINT+OIMFZ*FEXT -QZ
c
ENDIF
c THE CASES (1) AND (2) ARE EXHAUSTED; THE ONLY REMAINING
C POSSIBILITY IS NOW THE CASE (3):
C++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
ELSE
CALL DIPOLE (PS,X,Y,Z,QX,QY,QZ)
BX=OIMFX-QX
BY=OIMFY-QY
BZ=OIMFZ-QZ
ENDIF
C
END
c
C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
C
SUBROUTINE SHLCAR3X3(X,Y,Z,PS,BX,BY,BZ)
C
C THIS S/R RETURNS THE SHIELDING FIELD FOR THE EARTH'S DIPOLE,
C REPRESENTED BY 2x3x3=18 "CARTESIAN" HARMONICS, tilted with respect
C to the z=0 plane
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C The 36 coefficients enter in pairs in the amplitudes of the "cartesian"
c harmonics (A(1)-A(36).
c The 14 nonlinear parameters (A(37)-A(50) are the scales Pi,Ri,Qi,and Si
C entering the arguments of exponents, sines, and cosines in each of the
C 18 "Cartesian" harmonics PLUS TWO TILT ANGLES FOR THE CARTESIAN HARMONICS
C (ONE FOR THE PSI=0 MODE AND ANOTHER FOR THE PSI=90 MODE)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
IMPLICIT REAL * 8 (A - H, O - Z)
REAL*8 X,Y,Z,PS,BX,BY,BZ
C
DIMENSION A(50)
DATA A/-901.2327248,895.8011176,817.6208321,-845.5880889,
*-83.73539535,86.58542841,336.8781402,-329.3619944,-311.2947120,
*308.6011161,31.94469304,-31.30824526,125.8739681,-372.3384278,
*-235.4720434,286.7594095,21.86305585,-27.42344605,-150.4874688,
*2.669338538,1.395023949,-.5540427503,-56.85224007,3.681827033,
*-43.48705106,5.103131905,1.073551279,-.6673083508,12.21404266,
*4.177465543,5.799964188,-.3977802319,-1.044652977,.5703560010,
*3.536082962,-3.222069852,9.620648151,6.082014949,27.75216226,
*12.44199571,5.122226936,6.982039615,20.12149582,6.150973118,
*4.663639687,15.73319647,2.303504968,5.840511214,.8385953499E-01,
*.3477844929/
C
P1=A(37)
P2=A(38)
P3=A(39)
R1=A(40)
R2=A(41)
R3=A(42)
Q1=A(43)
Q2=A(44)
Q3=A(45)
S1=A(46)
S2=A(47)
S3=A(48)
T1 =A(49)
T2 =A(50)
C
CPS=DCOS(PS)
SPS=DSIN(PS)
S2PS=2.D0*CPS
C
ST1=DSIN(PS*T1)
CT1=DCOS(PS*T1)
ST2=DSIN(PS*T2)
CT2=DCOS(PS*T2)
X1=X*CT1-Z*ST1
Z1=X*ST1+Z*CT1
X2=X*CT2-Z*ST2
Z2=X*ST2+Z*CT2
C
C
c MAKE THE TERMS IN THE 1ST SUM ("PERPENDICULAR" SYMMETRY):
C
C I=1
C
SQPR= DSQRT(1.D0/P1**2+1.D0/R1**2)
CYP = DCOS(Y/P1)
SYP = DSIN(Y/P1)
CZR = DCOS(Z1/R1)
SZR = DSIN(Z1/R1)
EXPR= DEXP(SQPR*X1)
FX1 =-SQPR*EXPR*CYP*SZR
HY1 = EXPR/P1*SYP*SZR
FZ1 =-EXPR*CYP/R1*CZR
HX1 = FX1*CT1+FZ1*ST1
HZ1 =-FX1*ST1+FZ1*CT1
SQPR= DSQRT(1.D0/P1**2+1.D0/R2**2)
CYP = DCOS(Y/P1)
SYP = DSIN(Y/P1)
CZR = DCOS(Z1/R2)
SZR = DSIN(Z1/R2)
EXPR= DEXP(SQPR*X1)
FX2 =-SQPR*EXPR*CYP*SZR
HY2 = EXPR/P1*SYP*SZR
FZ2 =-EXPR*CYP/R2*CZR
HX2 = FX2*CT1+FZ2*ST1
HZ2 =-FX2*ST1+FZ2*CT1
SQPR= DSQRT(1.D0/P1**2+1.D0/R3**2)
CYP = DCOS(Y/P1)
SYP = DSIN(Y/P1)
CZR = DCOS(Z1/R3)
SZR = DSIN(Z1/R3)
EXPR= DEXP(SQPR*X1)
FX3 =-EXPR*CYP*(SQPR*Z1*CZR+SZR/R3*(X1+1.D0/SQPR))
HY3 = EXPR/P1*SYP*(Z1*CZR+X1/R3*SZR/SQPR)
FZ3 =-EXPR*CYP*(CZR*(1.D0+X1/R3**2/SQPR)-Z1/R3*SZR)
HX3 = FX3*CT1+FZ3*ST1
HZ3 =-FX3*ST1+FZ3*CT1
C
C I=2:
C
SQPR= DSQRT(1.D0/P2**2+1.D0/R1**2)
CYP = DCOS(Y/P2)
SYP = DSIN(Y/P2)
CZR = DCOS(Z1/R1)
SZR = DSIN(Z1/R1)
EXPR= DEXP(SQPR*X1)
FX4 =-SQPR*EXPR*CYP*SZR
HY4 = EXPR/P2*SYP*SZR
FZ4 =-EXPR*CYP/R1*CZR
HX4 = FX4*CT1+FZ4*ST1
HZ4 =-FX4*ST1+FZ4*CT1
SQPR= DSQRT(1.D0/P2**2+1.D0/R2**2)
CYP = DCOS(Y/P2)
SYP = DSIN(Y/P2)
CZR = DCOS(Z1/R2)
SZR = DSIN(Z1/R2)
EXPR= DEXP(SQPR*X1)
FX5 =-SQPR*EXPR*CYP*SZR
HY5 = EXPR/P2*SYP*SZR
FZ5 =-EXPR*CYP/R2*CZR
HX5 = FX5*CT1+FZ5*ST1
HZ5 =-FX5*ST1+FZ5*CT1
SQPR= DSQRT(1.D0/P2**2+1.D0/R3**2)
CYP = DCOS(Y/P2)
SYP = DSIN(Y/P2)
CZR = DCOS(Z1/R3)
SZR = DSIN(Z1/R3)
EXPR= DEXP(SQPR*X1)
FX6 =-EXPR*CYP*(SQPR*Z1*CZR+SZR/R3*(X1+1.D0/SQPR))
HY6 = EXPR/P2*SYP*(Z1*CZR+X1/R3*SZR/SQPR)
FZ6 =-EXPR*CYP*(CZR*(1.D0+X1/R3**2/SQPR)-Z1/R3*SZR)
HX6 = FX6*CT1+FZ6*ST1
HZ6 =-FX6*ST1+FZ6*CT1
C
C I=3:
C
SQPR= DSQRT(1.D0/P3**2+1.D0/R1**2)
CYP = DCOS(Y/P3)
SYP = DSIN(Y/P3)
CZR = DCOS(Z1/R1)
SZR = DSIN(Z1/R1)
EXPR= DEXP(SQPR*X1)
FX7 =-SQPR*EXPR*CYP*SZR
HY7 = EXPR/P3*SYP*SZR
FZ7 =-EXPR*CYP/R1*CZR
HX7 = FX7*CT1+FZ7*ST1
HZ7 =-FX7*ST1+FZ7*CT1
SQPR= DSQRT(1.D0/P3**2+1.D0/R2**2)
CYP = DCOS(Y/P3)
SYP = DSIN(Y/P3)
CZR = DCOS(Z1/R2)
SZR = DSIN(Z1/R2)
EXPR= DEXP(SQPR*X1)
FX8 =-SQPR*EXPR*CYP*SZR
HY8 = EXPR/P3*SYP*SZR
FZ8 =-EXPR*CYP/R2*CZR
HX8 = FX8*CT1+FZ8*ST1
HZ8 =-FX8*ST1+FZ8*CT1
SQPR= DSQRT(1.D0/P3**2+1.D0/R3**2)
CYP = DCOS(Y/P3)
SYP = DSIN(Y/P3)
CZR = DCOS(Z1/R3)
SZR = DSIN(Z1/R3)
EXPR= DEXP(SQPR*X1)
FX9 =-EXPR*CYP*(SQPR*Z1*CZR+SZR/R3*(X1+1.D0/SQPR))
HY9 = EXPR/P3*SYP*(Z1*CZR+X1/R3*SZR/SQPR)
FZ9 =-EXPR*CYP*(CZR*(1.D0+X1/R3**2/SQPR)-Z1/R3*SZR)
HX9 = FX9*CT1+FZ9*ST1
HZ9 =-FX9*ST1+FZ9*CT1
A1=A(1)+A(2)*CPS
A2=A(3)+A(4)*CPS
A3=A(5)+A(6)*CPS
A4=A(7)+A(8)*CPS
A5=A(9)+A(10)*CPS
A6=A(11)+A(12)*CPS
A7=A(13)+A(14)*CPS
A8=A(15)+A(16)*CPS
A9=A(17)+A(18)*CPS
BX=A1*HX1+A2*HX2+A3*HX3+A4*HX4+A5*HX5+A6*HX6+A7*HX7+A8*HX8+A9*HX9
BY=A1*HY1+A2*HY2+A3*HY3+A4*HY4+A5*HY5+A6*HY6+A7*HY7+A8*HY8+A9*HY9
BZ=A1*HZ1+A2*HZ2+A3*HZ3+A4*HZ4+A5*HZ5+A6*HZ6+A7*HZ7+A8*HZ8+A9*HZ9
c MAKE THE TERMS IN THE 2ND SUM ("PARALLEL" SYMMETRY):
C
C I=1
C
SQQS= DSQRT(1.D0/Q1**2+1.D0/S1**2)
CYQ = DCOS(Y/Q1)
SYQ = DSIN(Y/Q1)
CZS = DCOS(Z2/S1)
SZS = DSIN(Z2/S1)
EXQS= DEXP(SQQS*X2)
FX1 =-SQQS*EXQS*CYQ*CZS *SPS
HY1 = EXQS/Q1*SYQ*CZS *SPS
FZ1 = EXQS*CYQ/S1*SZS *SPS
HX1 = FX1*CT2+FZ1*ST2
HZ1 =-FX1*ST2+FZ1*CT2
SQQS= DSQRT(1.D0/Q1**2+1.D0/S2**2)
CYQ = DCOS(Y/Q1)
SYQ = DSIN(Y/Q1)
CZS = DCOS(Z2/S2)
SZS = DSIN(Z2/S2)
EXQS= DEXP(SQQS*X2)
FX2 =-SQQS*EXQS*CYQ*CZS *SPS
HY2 = EXQS/Q1*SYQ*CZS *SPS
FZ2 = EXQS*CYQ/S2*SZS *SPS
HX2 = FX2*CT2+FZ2*ST2
HZ2 =-FX2*ST2+FZ2*CT2
SQQS= DSQRT(1.D0/Q1**2+1.D0/S3**2)
CYQ = DCOS(Y/Q1)
SYQ = DSIN(Y/Q1)
CZS = DCOS(Z2/S3)
SZS = DSIN(Z2/S3)
EXQS= DEXP(SQQS*X2)
FX3 =-SQQS*EXQS*CYQ*CZS *SPS
HY3 = EXQS/Q1*SYQ*CZS *SPS
FZ3 = EXQS*CYQ/S3*SZS *SPS
HX3 = FX3*CT2+FZ3*ST2
HZ3 =-FX3*ST2+FZ3*CT2
C
C I=2
C
SQQS= DSQRT(1.D0/Q2**2+1.D0/S1**2)
CYQ = DCOS(Y/Q2)
SYQ = DSIN(Y/Q2)
CZS = DCOS(Z2/S1)
SZS = DSIN(Z2/S1)
EXQS= DEXP(SQQS*X2)
FX4 =-SQQS*EXQS*CYQ*CZS *SPS
HY4 = EXQS/Q2*SYQ*CZS *SPS
FZ4 = EXQS*CYQ/S1*SZS *SPS
HX4 = FX4*CT2+FZ4*ST2
HZ4 =-FX4*ST2+FZ4*CT2
SQQS= DSQRT(1.D0/Q2**2+1.D0/S2**2)
CYQ = DCOS(Y/Q2)
SYQ = DSIN(Y/Q2)
CZS = DCOS(Z2/S2)
SZS = DSIN(Z2/S2)
EXQS= DEXP(SQQS*X2)
FX5 =-SQQS*EXQS*CYQ*CZS *SPS
HY5 = EXQS/Q2*SYQ*CZS *SPS
FZ5 = EXQS*CYQ/S2*SZS *SPS
HX5 = FX5*CT2+FZ5*ST2
HZ5 =-FX5*ST2+FZ5*CT2
SQQS= DSQRT(1.D0/Q2**2+1.D0/S3**2)
CYQ = DCOS(Y/Q2)
SYQ = DSIN(Y/Q2)
CZS = DCOS(Z2/S3)
SZS = DSIN(Z2/S3)
EXQS= DEXP(SQQS*X2)
FX6 =-SQQS*EXQS*CYQ*CZS *SPS
HY6 = EXQS/Q2*SYQ*CZS *SPS
FZ6 = EXQS*CYQ/S3*SZS *SPS
HX6 = FX6*CT2+FZ6*ST2
HZ6 =-FX6*ST2+FZ6*CT2
C
C I=3
C
SQQS= DSQRT(1.D0/Q3**2+1.D0/S1**2)
CYQ = DCOS(Y/Q3)
SYQ = DSIN(Y/Q3)
CZS = DCOS(Z2/S1)
SZS = DSIN(Z2/S1)
EXQS= DEXP(SQQS*X2)
FX7 =-SQQS*EXQS*CYQ*CZS *SPS
HY7 = EXQS/Q3*SYQ*CZS *SPS
FZ7 = EXQS*CYQ/S1*SZS *SPS
HX7 = FX7*CT2+FZ7*ST2
HZ7 =-FX7*ST2+FZ7*CT2
SQQS= DSQRT(1.D0/Q3**2+1.D0/S2**2)
CYQ = DCOS(Y/Q3)
SYQ = DSIN(Y/Q3)
CZS = DCOS(Z2/S2)
SZS = DSIN(Z2/S2)
EXQS= DEXP(SQQS*X2)
FX8 =-SQQS*EXQS*CYQ*CZS *SPS
HY8 = EXQS/Q3*SYQ*CZS *SPS
FZ8 = EXQS*CYQ/S2*SZS *SPS
HX8 = FX8*CT2+FZ8*ST2
HZ8 =-FX8*ST2+FZ8*CT2
SQQS= DSQRT(1.D0/Q3**2+1.D0/S3**2)
CYQ = DCOS(Y/Q3)
SYQ = DSIN(Y/Q3)
CZS = DCOS(Z2/S3)
SZS = DSIN(Z2/S3)
EXQS= DEXP(SQQS*X2)
FX9 =-SQQS*EXQS*CYQ*CZS *SPS
HY9 = EXQS/Q3*SYQ*CZS *SPS
FZ9 = EXQS*CYQ/S3*SZS *SPS
HX9 = FX9*CT2+FZ9*ST2
HZ9 =-FX9*ST2+FZ9*CT2
A1=A(19)+A(20)*S2PS
A2=A(21)+A(22)*S2PS
A3=A(23)+A(24)*S2PS
A4=A(25)+A(26)*S2PS
A5=A(27)+A(28)*S2PS
A6=A(29)+A(30)*S2PS
A7=A(31)+A(32)*S2PS
A8=A(33)+A(34)*S2PS
A9=A(35)+A(36)*S2PS
BX=BX+A1*HX1+A2*HX2+A3*HX3+A4*HX4+A5*HX5+A6*HX6+A7*HX7+A8*HX8
* +A9*HX9
BY=BY+A1*HY1+A2*HY2+A3*HY3+A4*HY4+A5*HY5+A6*HY6+A7*HY7+A8*HY8
* +A9*HY9
BZ=BZ+A1*HZ1+A2*HZ2+A3*HZ3+A4*HZ4+A5*HZ5+A6*HZ6+A7*HZ7+A8*HZ8
* +A9*HZ9
C
RETURN
END
c
c############################################################################
c
C
SUBROUTINE DEFORMED (IOPT,PS,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2)
C
C IOPT - TAIL FIELD MODE FLAG: IOPT=0 - THE TWO TAIL MODES ARE ADDED UP
C IOPT=1 - MODE 1 ONLY
C IOPT=2 - MODE 2 ONLY
C
C CALCULATES GSM COMPONENTS OF TWO UNIT-AMPLITUDE TAIL FIELD MODES,
C TAKING INTO ACCOUNT BOTH EFFECTS OF DIPOLE TILT:
C WARPING IN Y-Z (DONE BY THE S/R WARPED) AND BENDING IN X-Z (DONE BY THIS SUBROUTINE)
C
IMPLICIT REAL*8 (A-H,O-Z)
INTEGER IOPT
REAL*8 PS,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2
COMMON /RH0/ RH0
DATA RH2,IEPS /-5.2D0,3/
C
C RH0,RH1,RH2, AND IEPS CONTROL THE TILT-RELATED DEFORMATION OF THE TAIL FIELD
C
SPS=DSIN(PS)
CPS=DSQRT(1.D0-SPS**2)
R2=X**2+Y**2+Z**2
R=SQRT(R2)
ZR=Z/R
RH=RH0+RH2*ZR**2
DRHDR=-ZR/R*2.D0*RH2*ZR
DRHDZ= 2.D0*RH2*ZR/R
C
RRH=R/RH
F=1.D0/(1.D0+RRH**IEPS)**(1.D0/IEPS)
DFDR=-RRH**(IEPS-1)*F**(IEPS+1)/RH
DFDRH=-RRH*DFDR
c
SPSAS=SPS*F
CPSAS=DSQRT(1.D0-SPSAS**2)
C
XAS=X*CPSAS-Z*SPSAS
ZAS=X*SPSAS+Z*CPSAS
C
FACPS=SPS/CPSAS*(DFDR+DFDRH*DRHDR)/R
PSASX=FACPS*X
PSASY=FACPS*Y
PSASZ=FACPS*Z+SPS/CPSAS*DFDRH*DRHDZ
C
DXASDX=CPSAS-ZAS*PSASX
DXASDY=-ZAS*PSASY
DXASDZ=-SPSAS-ZAS*PSASZ
DZASDX=SPSAS+XAS*PSASX
DZASDY=XAS*PSASY
DZASDZ=CPSAS+XAS*PSASZ
FAC1=DXASDZ*DZASDY-DXASDY*DZASDZ
FAC2=DXASDX*DZASDZ-DXASDZ*DZASDX
FAC3=DZASDX*DXASDY-DXASDX*DZASDY
C
C DEFORM:
C
CALL WARPED(IOPT,PS,XAS,Y,ZAS,BXAS1,BYAS1,BZAS1,BXAS2,BYAS2,BZAS2)
C
BX1=BXAS1*DZASDZ-BZAS1*DXASDZ +BYAS1*FAC1
BY1=BYAS1*FAC2
BZ1=BZAS1*DXASDX-BXAS1*DZASDX +BYAS1*FAC3
BX2=BXAS2*DZASDZ-BZAS2*DXASDZ +BYAS2*FAC1
BY2=BYAS2*FAC2
BZ2=BZAS2*DXASDX-BXAS2*DZASDX +BYAS2*FAC3
RETURN
END
C
C------------------------------------------------------------------
c
C
SUBROUTINE WARPED (IOPT,PS,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2)
C
C CALCULATES GSM COMPONENTS OF THE WARPED FIELD FOR TWO TAIL UNIT MODES.
C THE WARPING DEFORMATION IS IMPOSED ON THE UNWARPED FIELD, COMPUTED
C BY THE S/R "UNWARPED". THE WARPING PARAMETERS WERE TAKEN FROM THE
C RESULTS OF GEOTAIL OBSERVATIONS (TSYGANENKO ET AL. [1998]).
C NB # 6, P.106, OCT 12, 2000.
C
C IOPT - TAIL FIELD MODE FLAG: IOPT=0 - THE TWO TAIL MODES ARE ADDED UP
C IOPT=1 - MODE 1 ONLY
C IOPT=2 - MODE 2 ONLY
C
IMPLICIT REAL*8 (A-H,O-Z)
C
INTEGER IOPT
REAL*8 PS,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2
COMMON /G/ G
DGDX=0.D0
XL=20.D0
DXLDX=0.D0
SPS=DSIN(PS)
RHO2=Y**2+Z**2
RHO=DSQRT(RHO2)
IF (Y.EQ.0.D0.AND.Z.EQ.0.D0) THEN
PHI=0.D0
CPHI=1.D0
SPHI=0.D0
ELSE
PHI=DATAN2(Z,Y)
CPHI=Y/RHO
SPHI=Z/RHO
ENDIF
RR4L4=RHO/(RHO2**2+XL**4)
F=PHI+G*RHO2*RR4L4*CPHI*SPS
DFDPHI=1.D0-G*RHO2*RR4L4*SPHI*SPS
DFDRHO=G*RR4L4**2*(3.D0*XL**4-RHO2**2)*CPHI*SPS
DFDX=RR4L4*CPHI*SPS*(DGDX*RHO2-G*RHO*RR4L4*4.D0*XL**3*DXLDX)
CF=DCOS(F)
SF=DSIN(F)
YAS=RHO*CF
ZAS=RHO*SF
CALL UNWARPED (IOPT,X,YAS,ZAS,BX_AS1,BY_AS1,BZ_AS1,
* BX_AS2,BY_AS2,BZ_AS2)
BRHO_AS = BY_AS1*CF+BZ_AS1*SF
c DEFORM THE 1ST MODE
BPHI_AS = -BY_AS1*SF+BZ_AS1*CF
BRHO_S = BRHO_AS*DFDPHI
BPHI_S = BPHI_AS-RHO*(BX_AS1*DFDX+BRHO_AS*DFDRHO)
BX1 = BX_AS1*DFDPHI
BY1 = BRHO_S*CPHI-BPHI_S*SPHI
BZ1 = BRHO_S*SPHI+BPHI_S*CPHI
c DONE
BRHO_AS = BY_AS2*CF+BZ_AS2*SF
c DEFORM THE 2ND MODE
BPHI_AS = -BY_AS2*SF+BZ_AS2*CF
BRHO_S = BRHO_AS*DFDPHI
BPHI_S = BPHI_AS-RHO*(BX_AS2*DFDX+BRHO_AS*DFDRHO)
BX2 = BX_AS2*DFDPHI
BY2 = BRHO_S*CPHI-BPHI_S*SPHI
BZ2 = BRHO_S*SPHI+BPHI_S*CPHI
c DONE
RETURN
END
C
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C
SUBROUTINE UNWARPED (IOPT,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2)
C IOPT - TAIL FIELD MODE FLAG: IOPT=0 - THE TWO TAIL MODES ARE ADDED UP
C IOPT=1 - MODE 1 ONLY
C IOPT=2 - MODE 2 ONLY
C
C CALCULATES GSM COMPONENTS OF THE SHIELDED FIELD OF TWO TAIL MODES WITH UNIT
C AMPLITUDES, WITHOUT ANY WARPING OR BENDING. NONLINEAR PARAMETERS OF THE MODES
C ARE FORWARDED HERE VIA A COMMON BLOCK /TAIL/.
C
IMPLICIT REAL*8 (A-H,O-Z)
INTEGER IOPT
REAL*8 PS,X,Y,Z,BX1,BY1,BZ1,BX2,BY2,BZ2
C
DIMENSION A1(60),A2(60)
c TAIL SHIELDING FIELD PARAMETERS FOR THE MODES #1 & #2
COMMON /TAIL/ DXSHIFT1,DXSHIFT2,D0,DELTADY
c ATTENTION: HERE D0 & DELTADY ARE INCLUDED IN /TAIL/
C AND EXCLUDED FROM DATA
DATA DELTADX1,ALPHA1,XSHIFT1
* /1.D0,1.1D0,6.D0/
DATA DELTADX2,ALPHA2,XSHIFT2
* /0.D0,.25D0,4.D0/
DATA A1/-25.45869857,57.35899080,317.5501869,-2.626756717,
*-93.38053698,-199.6467926,-858.8129729,34.09192395,845.4214929,
*-29.07463068,47.10678547,-128.9797943,-781.7512093,6.165038619,
*167.8905046,492.0680410,1654.724031,-46.77337920,-1635.922669,
*40.86186772,-.1349775602,-.9661991179E-01,-.1662302354,
*.002810467517,.2487355077,.1025565237,-14.41750229,-.8185333989,
*11.07693629,.7569503173,-9.655264745,112.2446542,777.5948964,
*-5.745008536,-83.03921993,-490.2278695,-1155.004209,39.08023320,
*1172.780574,-39.44349797,-14.07211198,-40.41201127,-313.2277343,
*2.203920979,8.232835341,197.7065115,391.2733948,-18.57424451,
*-437.2779053,23.04976898,11.75673963,13.60497313,4.691927060,
*18.20923547,27.59044809,6.677425469,1.398283308,2.839005878,
*31.24817706,24.53577264/
DATA A2/-287187.1962,4970.499233,410490.1952,-1347.839052,
*-386370.3240,3317.983750,-143462.3895,5706.513767,171176.2904,
*250.8882750,-506570.8891,5733.592632,397975.5842,9771.762168,
*-941834.2436,7990.975260,54313.10318,447.5388060,528046.3449,
*12751.04453,-21920.98301,-21.05075617,31971.07875,3012.641612,
*-301822.9103,-3601.107387,1797.577552,-6.315855803,142578.8406,
*13161.93640,804184.8410,-14168.99698,-851926.6360,-1890.885671,
*972475.6869,-8571.862853,26432.49197,-2554.752298,-482308.3431,
*-4391.473324,105155.9160,-1134.622050,-74353.53091,-5382.670711,
*695055.0788,-916.3365144,-12111.06667,67.20923358,-367200.9285,
*-21414.14421,14.75567902,20.75638190,59.78601609,16.86431444,
*32.58482365,23.69472951,17.24977936,13.64902647,68.40989058,
*11.67828167/
DATA XM1,XM2/2*-12.D0/
IF (IOPT.EQ.2) GOTO 1
XSC1=(X-XSHIFT1-DXSHIFT1)*ALPHA1-XM1*(ALPHA1-1.D0)
YSC1=Y*ALPHA1
ZSC1=Z*ALPHA1
D0SC1=D0*ALPHA1
c HERE WE USE A SINGLE VALUE D0 OF THE THICKNESS FOR BOTH MODES
CALL TAILDISK(D0SC1,DELTADX1,DELTADY,XSC1,YSC1,ZSC1,FX1,FY1,FZ1)
CALL SHLCAR5X5(A1,X,Y,Z,DXSHIFT1,HX1,HY1,HZ1)
BX1=FX1+HX1
BY1=FY1+HY1
BZ1=FZ1+HZ1
IF (IOPT.EQ.1) THEN
BX2=0.D0
BY2=0.D0
BZ2=0.D0
RETURN
ENDIF
1 XSC2=(X-XSHIFT2-DXSHIFT2)*ALPHA2-XM2*(ALPHA2-1.D0)
YSC2=Y*ALPHA2
ZSC2=Z*ALPHA2
D0SC2=D0*ALPHA2
c HERE WE USE A SINGLE VALUE D0 OF THE THICKNESS FOR BOTH MODES
CALL TAILDISK(D0SC2,DELTADX2,DELTADY,XSC2,YSC2,ZSC2,FX2,FY2,FZ2)
CALL SHLCAR5X5(A2,X,Y,Z,DXSHIFT2,HX2,HY2,HZ2)
BX2=FX2+HX2
BY2=FY2+HY2
BZ2=FZ2+HZ2
IF (IOPT.EQ.2) THEN
BX1=0.D0
BY1=0.D0
BZ1=0.D0
RETURN
ENDIF
RETURN
END
C
C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
C
SUBROUTINE TAILDISK(D0,DELTADX,DELTADY,X,Y,Z,BX,BY,BZ)
c
c THIS SUBROUTINE COMPUTES THE COMPONENTS OF THE TAIL CURRENT FIELD,
C SIMILAR TO THAT DESCRIBED BY TSYGANENKO AND PEREDO (1994). THE
C DIFFERENCE IS THAT NOW WE USE SPACEWARPING, AS DESCRIBED IN OUR
C PAPER ON MODELING BIRKELAND CURRENTS (TSYGANENKO AND STERN, 1996)
C INSTEAD OF SHEARING IT IN THE SPIRIT OF T89 TAIL MODEL.
C
IMPLICIT REAL*8 (A-H,O-Z)
REAL*8 D0,DELTADX,DELTADY,X,Y,Z,BX,BY,BZ
c
DIMENSION F(5),B(5),C(5)
C
DATA F /-71.09346626D0,-1014.308601D0,-1272.939359D0,
* -3224.935936D0,-44546.86232D0/
DATA B /10.90101242D0,12.68393898D0,13.51791954D0,14.86775017D0,
* 15.12306404D0/
DATA C /.7954069972D0,.6716601849D0,1.174866319D0,2.565249920D0,