/*
* Note: The variables that save our state in this (and other fundtions) are
* not local static variables, but are contained in the Lgm_MagModelInfo
* structure that the user passes to it. This allows the function to be
* thread-safe and re-entrant.
*/
double I_integrand( double s, _qpInfo *qpInfo ) {
Lgm_Vector Bvec;
int reset=1, done, Count;
double f, g, Hremaining, Hdone, H, Htry, Hdid, Hnext, sgn=1.0, sdid, B, dS;
Lgm_MagModelInfo *mInfo;
/*
* Get pointer to our auxilliary data structure.
*/
mInfo = (Lgm_MagModelInfo *)qpInfo;
mInfo->Lgm_I_integrand_u_scale.x = 10.0; mInfo->Lgm_I_integrand_u_scale.y = 1.0; mInfo->Lgm_I_integrand_u_scale.z = 10.0;
if ( mInfo->Lgm_I_integrand_JumpMethod == LGM_RELATIVE_JUMP_METHOD ) {
/*
* Set starting point. If this is the first call for this integral,
* set point to the lower limit.
*/
if ( mInfo->Lgm_I_integrand_FirstCall == TRUE ) {
mInfo->Lgm_I_integrand_FirstCall = FALSE;
mInfo->Lgm_I_integrand_P = mInfo->Pm_South;
mInfo->Lgm_I_integrand_S = 0.0;
dS = s;
} else {
dS = s - mInfo->Lgm_I_integrand_S;
}
if (dS < 0.0) {
H = -dS; sgn = -1.0; // H is a positive qnty
} else {
H = dS; sgn = 1.0;
}
} else if ( mInfo->Lgm_I_integrand_JumpMethod == LGM_ABSOLUTE_JUMP_METHOD ) {
/*
* This strategy starts at start each time. Slower(?), but seems to
* limit roundoff error from accumulating? The speed increase of the
* relative method really depends on how far apart the s points are
* that the integrator is picking. If they are bouncing all over the
* place the relative method still does alot of tracing.
*/
if ( mInfo->Lgm_I_integrand_FirstCall == TRUE ) {
mInfo->Lgm_I_integrand_FirstCall = FALSE;
}
mInfo->Lgm_I_integrand_P = mInfo->Pm_South;
mInfo->Lgm_I_integrand_S = 0.0;
H = s; sgn = 1.0; // H is a positive qnty
} else {
printf("I_integrand: Error, unknown Jump Method ( Lgm_I_integrand_JumpMethod = %d\n", mInfo->Lgm_I_integrand_JumpMethod );
exit(-1);
}
/*
* Get B-field at the given value of s. Need to advance along field line
* by an amount H. May need to do more than one call to get there...
* Setting Htry to be H is an attempt to make the full jump in one call to
* MagStep. For very precise calculations, the number of jumps we do here
* seems to be fairly critical. Making two jumps (i.e. Htry = H/2) and
* limiting Hmax to 0.5 Re seems to work pretty well (perhaps its because
* symetry between mirror points?). Could still play with the max step
* size of 0.5 -- maybe something a bit higher would work just as well and
* be more efficient?
*/
done = FALSE; Count = 0; Htry = 0.5*H; Hdone = 0.0; reset = TRUE;
if (Htry > 0.5) Htry = 0.5;
if ( fabs(mInfo->Lgm_I_integrand_S-s) < 1e-12 ) done = TRUE;
while ( !done ) {
Lgm_MagStep( &mInfo->Lgm_I_integrand_P, &mInfo->Lgm_I_integrand_u_scale, Htry, &Hdid, &Hnext, sgn, &sdid, &reset, mInfo->Bfield, mInfo );
Hdone += Hdid; // positive qnty
mInfo->Lgm_I_integrand_S += sgn*Hdid;
Hremaining = H - Hdone;
if ( Count > 1000 ) {
printf("I_integrand: Warning, early return because Count > 1000. Ill-conditioned integrand?\n");
done = TRUE;
} else if ( fabs(mInfo->Lgm_I_integrand_S-s) < 1e-12 ){
done = TRUE;
} else {
if ( Htry > Hremaining ) Htry = Hremaining;
}
++Count;
}
mInfo->Bfield( &mInfo->Lgm_I_integrand_P, &Bvec, mInfo );
B = Lgm_Magnitude( &Bvec );
/*
* Compute integrand, ( 1 - B/Bm ) ^ (1/2) Make sure 1-B/Bm is not
* negative. If it is, assume its zero. (Note that sometimes (due to
* round-off error) it could be very slightly negative).
*/
g = 1.0 - B/mInfo->Bm;
f = (g > 0.0) ? sqrt( g ) : 0.0;
++mInfo->Lgm_n_I_integrand_Calls;
return( f );
}
int main(){
long int Date;
double UTC;
Lgm_Vector u, B, CurlB;
Lgm_MagModelInfo *mInfo;
int i, j;
Date = 20050831;
UTC = 9.0;
mInfo = Lgm_InitMagInfo( );
Lgm_Set_Coord_Transforms( Date, UTC, mInfo->c );
mInfo->Bfield = Lgm_B_TS04;
//mInfo->Bfield = Lgm_B_OP77;
//mInfo->Bfield = Lgm_B_T89;
mInfo->Bfield = Lgm_B_TS04;
mInfo->Bfield = Lgm_B_igrf;
mInfo->Bfield = Lgm_B_cdip;
mInfo->Bfield = Lgm_B_edip;
mInfo->Bfield = Lgm_B_T89;
mInfo->P = 4.1011111111111118;
mInfo->Dst = 7.7777777777777777;
mInfo->By = 3.7244444444444444;
mInfo->Bz = -0.12666666666666665;
mInfo->W[0] = 0.12244444444444445;
mInfo->W[1] = 0.2514;
mInfo->W[2] = 0.089266666666666661;
mInfo->W[3] = 0.047866666666666668;
mInfo->W[4] = 0.22586666666666666;
mInfo->W[5] = 1.0461333333333334;
printf("%13s", "Kp");
printf(" %13s", "Ux (Re)");
printf(" %13s", "Uy (Re)");
printf(" %13s", "Uz (Re)");
printf(" %13s", "Bx (nT)");
printf(" %13s", "By (nT)");
printf(" %13s", "Bz (nT)");
printf(" %13s", "Bmag (nT)");
printf(" %16s", "CurlB_x (nT/Re)");
printf(" %16s", "CurlB_y (nT/Re)");
printf(" %16s", "CurlB_z (nT/Re)\n");
for (i=0; i<=5; i++) {
mInfo->Kp = i;
u.x = -6.6; u.y = 0.0; u.z = 0.0;
mInfo->Bfield( &u, &B, mInfo );
Lgm_CurlB( &u, &CurlB, LGM_DERIV_SIX_POINT, 1e-3, mInfo );
printf( "%13i", mInfo->Kp);
printf( " %13g %13g %13g", u.x, u.y, u.z );
printf( " %13g %13g %13g", B.x, B.y, B.z );
printf( " %13g", Lgm_Magnitude( &B ) );
printf( " %16g %16g %16g \n", CurlB.x, CurlB.y, CurlB.z );
}
for (j=0; j<100; j++){
mInfo->Kp = 3;
for (i=0; i<13; i++) {
u.x = -1. - (double)i * 0.5;
u.y = 1.0; u.z = -1.0;
mInfo->Bfield( &u, &B, mInfo );
Lgm_CurlB( &u, &CurlB, LGM_DERIV_SIX_POINT, 1e-3, mInfo );
printf( "%13i", mInfo->Kp);
printf( " %13g %13g %13g", u.x, u.y, u.z );
printf( " %13g %13g %13g", B.x, B.y, B.z );
printf( " %13g", Lgm_Magnitude( &B ) );
printf( " %16g %16g %16g \n", CurlB.x, CurlB.y, CurlB.z );
}
}
{
Lgm_Vector v;
mInfo->Lgm_VelStep_T = 100e-3; // 100keV
mInfo->Lgm_VelStep_q = -LGM_e; // electron change
mInfo->Lgm_VelStep_E0 = LGM_Ee0; // electron mass
mInfo->Lgm_VelStep_Bm = sqrt(B.x*B.x + B.y*B.y + B.z*B.z); // b mirror [nT]
mInfo->Lgm_VelStep_h = 1e-3; // step size in Re
mInfo->Lgm_VelStep_DerivScheme = LGM_DERIV_FOUR_POINT;
printf("\nT=%lf q=%lf E0=%lf Bm=%lf h=%lf DerivScheme=%d\n",
mInfo->Lgm_VelStep_T,
mInfo->Lgm_VelStep_q, mInfo->Lgm_VelStep_E0, mInfo->Lgm_VelStep_Bm, mInfo->Lgm_VelStep_h,
mInfo->Lgm_VelStep_DerivScheme );
Lgm_GradAndCurvDriftVel(&u, &v, mInfo);
printf("\nThe drift velocity [km/s in GSM] for a locally mirroring 100 keV electron is:\n");
Lgm_PrintVector(&v);
}
Lgm_FreeMagInfo( mInfo );
exit(0);
}