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********************************************************************** |
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* |
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* |
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* routine per tracciare la particella di uno STEP |
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* |
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SUBROUTINE GRKUTA (CHARGE,STEP,VECT,VOUT) |
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C. |
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C. ****************************************************************** |
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C. * * |
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C. * Runge-Kutta method for tracking a particle through a magnetic * |
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C. * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * |
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C. * Standards, procedure 25.5.20) * |
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C. * * |
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C. * Input parameters * |
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C. * CHARGE Particle charge * |
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C. * STEP Step size * |
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C. * VECT Initial co-ords,direction cosines,momentum * |
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C. * Output parameters * |
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C. * VOUT Output co-ords,direction cosines,momentum * |
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C. * User routine called * |
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C. * CALL GUFLD(X,F) * |
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C. * * |
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C. * ==>Called by : <USER>, GUSWIM * |
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C. * Authors R.Brun, M.Hansroul ********* * |
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C. * V.Perevoztchikov (CUT STEP implementation) * |
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C. * * |
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C. * * |
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C. ****************************************************************** |
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C. |
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IMPLICIT DOUBLE PRECISION(A-H,O-Z) |
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* |
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REAL VVV(3),FFF(3) |
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REAL*8 CHARGE, STEP, VECT(*), VOUT(*), F(4) |
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REAL*8 XYZT(3), XYZ(3), X, Y, Z, XT, YT, ZT |
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DIMENSION SECXS(4),SECYS(4),SECZS(4),HXP(3) |
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EQUIVALENCE (X,XYZ(1)),(Y,XYZ(2)),(Z,XYZ(3)), |
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+ (XT,XYZT(1)),(YT,XYZT(2)),(ZT,XYZT(3)) |
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* |
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PARAMETER (MAXIT = 1992, MAXCUT = 11) |
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PARAMETER (EC=2.9979251D-4,DLT=1D-4,DLT32=DLT/32) |
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PARAMETER (ZERO=0, ONE=1, TWO=2, THREE=3) |
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PARAMETER (THIRD=ONE/THREE, HALF=ONE/TWO) |
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PARAMETER (PISQUA=.986960440109D+01) |
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PARAMETER (IX=1,IY=2,IZ=3,IPX=4,IPY=5,IPZ=6) |
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|
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*. |
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*. ------------------------------------------------------------------ |
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*. |
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* This constant is for units CM,GEV/C and KGAUSS |
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* |
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ITER = 0 |
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NCUT = 0 |
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DO 10 J=1,7 |
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VOUT(J)=VECT(J) |
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10 CONTINUE |
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PINV = EC * CHARGE / VECT(7) |
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TL = 0. |
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H = STEP |
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* |
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* |
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20 REST = STEP-TL |
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IF (DABS(H).GT.DABS(REST)) H = REST |
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DO I=1,3 |
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VVV(I)=SNGL(VOUT(I)) |
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ENDDO |
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|
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CALL GUFLD(VVV,FFF) |
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DO I=1,3 |
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F(I)=DBLE(FFF(I)) |
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ENDDO |
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* |
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* Start of integration |
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* |
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X = VOUT(1) |
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Y = VOUT(2) |
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Z = VOUT(3) |
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A = VOUT(4) |
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B = VOUT(5) |
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C = VOUT(6) |
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* |
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H2 = HALF * H |
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H4 = HALF * H2 |
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PH = PINV * H |
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PH2 = HALF * PH |
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SECXS(1) = (B * F(3) - C * F(2)) * PH2 |
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SECYS(1) = (C * F(1) - A * F(3)) * PH2 |
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SECZS(1) = (A * F(2) - B * F(1)) * PH2 |
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ANG2 = (SECXS(1)**2 + SECYS(1)**2 + SECZS(1)**2) |
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IF (ANG2.GT.PISQUA) GO TO 40 |
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DXT = H2 * A + H4 * SECXS(1) |
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DYT = H2 * B + H4 * SECYS(1) |
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DZT = H2 * C + H4 * SECZS(1) |
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XT = X + DXT |
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YT = Y + DYT |
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ZT = Z + DZT |
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* |
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* Second intermediate point |
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* |
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EST = DABS(DXT)+DABS(DYT)+DABS(DZT) |
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IF (EST.GT.H) GO TO 30 |
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|
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DO I=1,3 |
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VVV(I)=SNGL(XYZT(I)) |
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ENDDO |
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CALL GUFLD(VVV,FFF) |
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DO I=1,3 |
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F(I)=DBLE(FFF(I)) |
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ENDDO |
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C CALL GUFLD(XYZT,F) |
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AT = A + SECXS(1) |
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BT = B + SECYS(1) |
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CT = C + SECZS(1) |
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* |
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SECXS(2) = (BT * F(3) - CT * F(2)) * PH2 |
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SECYS(2) = (CT * F(1) - AT * F(3)) * PH2 |
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SECZS(2) = (AT * F(2) - BT * F(1)) * PH2 |
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AT = A + SECXS(2) |
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BT = B + SECYS(2) |
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CT = C + SECZS(2) |
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SECXS(3) = (BT * F(3) - CT * F(2)) * PH2 |
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SECYS(3) = (CT * F(1) - AT * F(3)) * PH2 |
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SECZS(3) = (AT * F(2) - BT * F(1)) * PH2 |
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DXT = H * (A + SECXS(3)) |
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DYT = H * (B + SECYS(3)) |
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DZT = H * (C + SECZS(3)) |
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XT = X + DXT |
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YT = Y + DYT |
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ZT = Z + DZT |
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AT = A + TWO*SECXS(3) |
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BT = B + TWO*SECYS(3) |
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CT = C + TWO*SECZS(3) |
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* |
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EST = ABS(DXT)+ABS(DYT)+ABS(DZT) |
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IF (EST.GT.2.*ABS(H)) GO TO 30 |
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DO I=1,3 |
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VVV(I)=SNGL(XYZT(I)) |
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ENDDO |
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CALL GUFLD(VVV,FFF) |
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DO I=1,3 |
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F(I)=DBLE(FFF(I)) |
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ENDDO |
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C CALL GUFLD(XYZT,F) |
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* |
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Z = Z + (C + (SECZS(1) + SECZS(2) + SECZS(3)) * THIRD) * H |
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Y = Y + (B + (SECYS(1) + SECYS(2) + SECYS(3)) * THIRD) * H |
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X = X + (A + (SECXS(1) + SECXS(2) + SECXS(3)) * THIRD) * H |
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* |
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SECXS(4) = (BT*F(3) - CT*F(2))* PH2 |
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SECYS(4) = (CT*F(1) - AT*F(3))* PH2 |
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SECZS(4) = (AT*F(2) - BT*F(1))* PH2 |
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A = A+(SECXS(1)+SECXS(4)+TWO * (SECXS(2)+SECXS(3))) * THIRD |
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B = B+(SECYS(1)+SECYS(4)+TWO * (SECYS(2)+SECYS(3))) * THIRD |
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C = C+(SECZS(1)+SECZS(4)+TWO * (SECZS(2)+SECZS(3))) * THIRD |
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* |
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EST = ABS(SECXS(1)+SECXS(4) - (SECXS(2)+SECXS(3))) |
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++ ABS(SECYS(1)+SECYS(4) - (SECYS(2)+SECYS(3))) |
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++ ABS(SECZS(1)+SECZS(4) - (SECZS(2)+SECZS(3))) |
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* |
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IF (EST.GT.DLT .AND. ABS(H).GT.1.E-4) GO TO 30 |
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ITER = ITER + 1 |
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NCUT = 0 |
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* If too many iterations, go to HELIX |
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IF (ITER.GT.MAXIT) GO TO 40 |
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* |
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TL = TL + H |
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IF (EST.LT.(DLT32)) THEN |
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H = H*TWO |
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ENDIF |
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CBA = ONE/ SQRT(A*A + B*B + C*C) |
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VOUT(1) = X |
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VOUT(2) = Y |
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VOUT(3) = Z |
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VOUT(4) = CBA*A |
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VOUT(5) = CBA*B |
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VOUT(6) = CBA*C |
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REST = STEP - TL |
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IF (STEP.LT.0.) REST = -REST |
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IF (REST .GT. 1.E-5*DABS(STEP)) GO TO 20 |
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* |
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GO TO 999 |
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* |
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** CUT STEP |
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30 NCUT = NCUT + 1 |
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* If too many cuts , go to HELIX |
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IF (NCUT.GT.MAXCUT) GO TO 40 |
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H = H*HALF |
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GO TO 20 |
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* |
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** ANGLE TOO BIG, USE HELIX |
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40 F1 = F(1) |
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F2 = F(2) |
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F3 = F(3) |
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F4 = DSQRT(F1**2+F2**2+F3**2) |
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RHO = -F4*PINV |
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TET = RHO * STEP |
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IF(TET.NE.0.) THEN |
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HNORM = ONE/F4 |
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F1 = F1*HNORM |
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F2 = F2*HNORM |
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F3 = F3*HNORM |
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* |
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HXP(1) = F2*VECT(IPZ) - F3*VECT(IPY) |
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HXP(2) = F3*VECT(IPX) - F1*VECT(IPZ) |
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HXP(3) = F1*VECT(IPY) - F2*VECT(IPX) |
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HP = F1*VECT(IPX) + F2*VECT(IPY) + F3*VECT(IPZ) |
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* |
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RHO1 = ONE/RHO |
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SINT = DSIN(TET) |
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COST = TWO*DSIN(HALF*TET)**2 |
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* |
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G1 = SINT*RHO1 |
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G2 = COST*RHO1 |
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G3 = (TET-SINT) * HP*RHO1 |
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G4 = -COST |
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G5 = SINT |
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G6 = COST * HP |
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|
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VOUT(IX) = VECT(IX) + (G1*VECT(IPX) + G2*HXP(1) + G3*F1) |
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VOUT(IY) = VECT(IY) + (G1*VECT(IPY) + G2*HXP(2) + G3*F2) |
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VOUT(IZ) = VECT(IZ) + (G1*VECT(IPZ) + G2*HXP(3) + G3*F3) |
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VOUT(IPX) = VECT(IPX) + (G4*VECT(IPX) + G5*HXP(1) + G6*F1) |
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VOUT(IPY) = VECT(IPY) + (G4*VECT(IPY) + G5*HXP(2) + G6*F2) |
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VOUT(IPZ) = VECT(IPZ) + (G4*VECT(IPZ) + G5*HXP(3) + G6*F3) |
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* |
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ELSE |
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VOUT(IX) = VECT(IX) + STEP*VECT(IPX) |
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VOUT(IY) = VECT(IY) + STEP*VECT(IPY) |
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VOUT(IZ) = VECT(IZ) + STEP*VECT(IPZ) |
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* |
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ENDIF |
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* |
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999 END |
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* |
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* |
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|
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********************************************************************** |
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* |
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* gives the value of the magnetic field in the tracking point |
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* |
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********************************************************************** |
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subroutine gufld(v,f) !coordinates in cm, B field in kGauss |
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real v(3),f(3) !coordinates in cm, B field in kGauss, error in kGauss |
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real*8 vv(3),ff(3) !inter_B.f works in double precision |
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do i=1,3 |
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vv(i)=v(i)/100. !inter_B.f works in meters |
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enddo |
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c inter_B: coordinates in m, B field in Tesla |
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call inter_B(vv(1),vv(2),vv(3),ff) |
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do i=1,3 !change back the field in kGauss |
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f(i)=ff(i)*10. |
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enddo |
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|
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return |
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end |
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