--------------6291754718F4
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Dear off-line collaborators,
To use R-TAN(PHI)-Z extrapolation of the magnetic field instead of
X-Y-Z extrapolation one should make the following corrections in the
magnetic field extraction program (old nbame: SNAKE):
C
C:: THESE Double precision constants should be defined at the first call
T60 = DSQRT(3.D0)
T30 = 1.D0/T60
C60 = 0.5D0
S60 = T60/2.D0
C-------------------------------
C
C Now one should reflect and rotate if PHI comes out of (0 - 30) deg int
C
---------------------------------------------------------------------------
IF (Y(2) .LT. 0.) THEN
Y(2) = -Y(2)
BXFAC = -1.
ELSE
BXFAC = 1.
ENDIF
C
IF (Y(1) .LT. 0.) THEN
Y(1) = -Y(1)
BYFAC = -1.
ELSE
BYFAC = 1.
ENDIF
C
IREF = 0
IF (Y(1) .EQ. 0.) THEN
IF (Y(2) .GT. 0.) THEN
IREF = 1
X1 = Y(2)*S60
X2 = T30
ELSE
X1 = 0.
X2 = 0.
ENDIF
ELSE
X1 = Y(1)
X2 = Y(2)/X1
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 1
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ENDIF
ENDIF
X(1) = X1
X(2) = X2
X(3) = Y(3)
C
F(1) = 0.
F(2) = 0.
F(3) = 0.
C
C From this poin common Teilor series approximation should be done
C --------------------
C ...
C --------------------
C
C Now the rotation/reflection of the magnetic field back should be done
C ---------------------
IF (IREF .GT. 0) THEN
X1 = F(1)
X2 = F(2)
IF (IREF .GT. 1) THEN
F(1) = - X1*C60 - X2*S60
F(2) = - X1*S60 + X2*C60
F(3) = -F(3)
ELSE
F(1) = X1*C60 - X2*S60
F(2) = X1*S60 + X2*C60
ENDIF
ENDIF
C
IF (BXFAC .LT. 0.) THEN
F(1) = -F(1)
F(3) = -F(3)
ENDIF
C
IF (BYFAC .LT. 0.) THEN
F(2) = -F(2)
F(3) = -F(3)
ENDIF
c
RETURN
END
C ---------------------
As a result of the modification of the program, one can calculate the
toroidal magnetic field
===== (Without double precision for the rotation SIN's and COS's) =====
PHI-test before the angular correction (for Mini Torus Region):
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0. 35.0000, B= 1.70765 5.62041E-04 6.87005E-05
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19194E-02 4.11597E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21134E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342934 -3.79222E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14814E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 -8.74749E-09
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14814E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841091 3.79221E-03
45, X,Y= 24.7487 24.7487, B= 0.872357 -1.02873 4.21134E-03
50, X,Y= 26.8116 22.4976, B= 0.857589 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11599E-04
60, X,Y= 30.3109 17.5000, B= 0.854310 -1.47858 6.87005E-05
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11597E-04
70, X,Y= 32.8892 11.9707, B= 0.651424 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21134E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79221E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14814E-03
90, X,Y= 35.0000 14313E-15,B= 1.19209E-08 -1.11621 8.98363E-09
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14814E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79221E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21134E-03
110, X,Y= 32.8892 -11.9707, B= -0.651424 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11597E-04
120, X,Y= 30.3109 -17.5000, B= -0.854310 -1.47858 -6.87005E-05
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11599E-04
130, X,Y= 26.8116 -22.4976, B= -0.857589 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872357 -1.02873 -4.21134E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841091 -3.79221E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14814E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 8.74749E-09
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14814E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342934 3.79222E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21134E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19194E-02 -4.11597E-04
180, X,Y= 4.28626E-1-35.0000, B= -1.70765 5.62041E-04 -6.87005E-05
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19194E-02 4.11597E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21134E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342934 -3.79222E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14814E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 -8.74749E-09
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14814E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841091 3.79221E-03
225, X,Y= -24.7487 -24.7487, B= -0.872357 1.02873 4.21134E-03
230, X,Y= -26.8116 -22.4976, B= -0.857589 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11599E-04
240, X,Y= -30.3109 -17.5000, B= -0.854310 1.47858 6.87005E-05
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11597E-04
250, X,Y= -32.8892 -11.9707, B= -0.651424 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21134E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79221E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14814E-03
270, X,Y= -35.0000 .4294E-15,B= -1.19209E-08 1.11621 8.98363E-09
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14814E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79221E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21134E-03
290, X,Y= -32.8892 11.9707, B= 0.651424 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11597E-04
300, X,Y= -30.3109 17.5000, B= 0.854310 1.47858 -6.87005E-05
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11599E-04
310, X,Y= -26.8116 22.4976, B= 0.857589 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872357 1.02873 -4.21134E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841091 -3.79221E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14814E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 8.74749E-09
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14814E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342934 3.79222E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21134E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19194E-02 -4.11597E-04
PHI-test after angular correction (double prec.) in rotation of coils:
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0. 35.0000, B= 1.70765 5.62315E-04 6.87478E-05
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19195E-02 4.11568E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21132E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342933 -3.79224E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14813E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 5.80463E-10
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14813E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841090 3.79223E-03
45, X,Y= 24.7487 24.7487, B= 0.872356 -1.02873 4.21132E-03
50, X,Y= 26.8116 22.4976, B= 0.857588 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11571E-04
60, X,Y= 30.3109 17.5000, B= 0.854310 -1.47858 6.87478E-05
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11568E-04
70, X,Y= 32.8892 11.9707, B= 0.651425 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21132E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79223E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14813E-03
90, X,Y= 35.0000 .429E-15,B= 1.4901E-08 -1.11621 -3.44335E-10
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14814E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79222E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21132E-03
110, X,Y= 32.8892 -11.9707, B= -0.651425 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11568E-04
120, X,Y= 30.3109 -17.5000, B= -0.854310 -1.47858 -6.87478E-05
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11571E-04
130, X,Y= 26.8116 -22.4976, B= -0.857588 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872356 -1.02873 -4.21132E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841090 -3.79223E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14813E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 -5.80463E-10
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14813E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342933 3.79224E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21132E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19195E-02 -4.11568E-04
180, X,Y= 4.286E-15-35.0000, = -1.70765 5.62315E-04 -6.87478E-05
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19195E-02 4.11568E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21132E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342933 -3.79224E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14813E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 5.80463E-10
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14813E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841090 3.79223E-03
225, X,Y= -24.7487 -24.7487, B= -0.872356 1.02873 4.21132E-03
230, X,Y= -26.8116 -22.4976, B= -0.857588 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11571E-04
240, X,Y= -30.3109 -17.5000, B= -0.854310 1.47858 6.87478E-05
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11568E-04
250, X,Y= -32.8892 -11.9707, B= -0.651425 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21132E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79223E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14813E-03
270, X,Y= -35.0000 -6.42E-15,B= -1.49012E-08 1.11621 -3.44335E-10
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14813E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79223E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21132E-03
290, X,Y= -32.8892 11.9707, B= 0.651425 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11568E-04
300, X,Y= -30.3109 17.5000, B= 0.854310 1.47858 -6.87478E-05
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11571E-04
310, X,Y= -26.8116 22.4976, B= 0.857588 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872356 1.02873 -4.21132E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841090 -3.79223E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14813E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 -5.80463E-10
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14813E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342933 3.79224E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21132E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19195E-02 -4.11568E-04
Because of the singularity at 0,60,120,180,240 degrees the value of the
By at 0 & 180 degrees is not perfectly zero. It is possible to avoib
this uncertainty only if TAN(PHI) is replased by PHI and the 0-degrees
point is exactly inbetween the n-1 (say -5 degrees) and n-th poin (say 5
degrees). In other cases the bin is assymetric (including our TAN(PHY)
approach) and the value of By is not perfectly 0. There was a special
search for reduction of the By value at x=0. The search included .05 bin
for TAN(PHI) (for which the value of the magnetic field file is equal to
the old one) and the 0.0398 bin version which places the 0 degrees point
exacly inbetween of n-1 and n-th poin. Unfortunatly TAN(PHI) is
assymetric near the poin of TAN(30deg) and that is why
in both cases the result was worse than for the simple .04 step which
was selected for the description of the magnetic field. But he
uncertainty of about 0.04% which you can see in the table is not a
characteristics of the overall approximation. It is typical only for the
bins close to the coil plane. Near the middle plane it is about 4 times
better. In other words the accuracy of the approximation is better then
1.E-4 and becomse 4 times worse approaching the coil plane. In the
region of the drift chamber acceptance the accuracy is better then
2.E-4.
The double precision was used for the rotation of the coils of the CLAS
toroida magnets when the magnetic field was integrated over all the 6
coils.
To correct hte singularity in the coil plane the double colculation
method was used. In vicinity of the coil plane the magnetic fireld was
calculated first as a a magnetic field of this sector and the second
time as a magnetic field of the neighboring sector. Near the colil plane
calculations of the magnetic field are not friquent so this method does
not incease the extraction time for the magnetic field inside the
acceptance of the drift chambers and should be taken into account (in
terms of the extraction time) only when trajectories crossing the coil
plane are reconstructed (or simulated if this version of program is used
in GSIM).
The resulting correction of the old program is
C------- ============================================= ---------------
C
C:: THESE Double precision constants should be defined at the first call
T60 = DSQRT(3.D0)
T30 = 1.D0/T60
C60 = 0.5D0
S60 = T60/2.D0
C
C:THESE singularity correction constants should be defined at first call
DT1 = 0.015 ! Singularity correction,!change value if DY#0.04 !
DT2 = 1./DT1
C
C-------------------------------
C
C Now one should reflect and rotate if PHI comes out of (0 - 30) deg int
C
------------------------------------------------------------------------
C
IF (Y(2) .LT. 0.) THEN
Y(2) = -Y(2)
BXFAC = -1.
ELSE
BXFAC = 1.
ENDIF
C
IF (Y(1) .LT. 0.) THEN
Y(1) = -Y(1)
BYFAC = -1.
ELSE
BYFAC = 1.
ENDIF
C
IREF = 0
IF (Y(1) .LT. 1.E-7) THEN
IF (Y(2) .GT. 1.E-7) THEN
IDOUB = 2
IREF = 5
X3 = Y(2)*S60
X4 = T30
X1 = Y(2)*S60
X2 = T30
ELSE
X1 = 0.
X2 = 0.
ENDIF
ELSE
X1 = Y(1)
X2 = Y(2)/X1
IF (X2 .GT. DT2 .OR. ABS(X2-T30) .LT. DT1) THEN
IDOUB = 2
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 5
X3 = - Y(1)*C60 + Y(2)*S60
X4 =(Y(1)*S60 + Y(2)*C60)/X3
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 4
X3 = X1
X4 = X2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ELSE ! Near but less then T30
IREF = 4
X3 = X1
X4 = X2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ELSE
IDOUB = 1
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 1
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ENDIF
ENDIF
ENDIF
C
X(1) = X1
X(2) = X2
X(3) = Y(3)
C
F(1) = 0.
F(2) = 0.
F(3) = 0.
B(1) = 0.
B(2) = 0.
B(3) = 0.
C
ISU = 0
C
C Find intercepts for Big + Mini Toruses
C
DO WHILE (IDOUB .GT. 0) ! first IDOUB = 1 .OR. = 2
C
C From this poin common Teilor series approximation should be done
C --------------------
C ...
ISU = ISU + 1 ! If field is extracted successfully (not out of grid)
C ...
C --------------------
C
C Now the rotation/reflection of the magnetic field back should be done
C ---------------------
C
IF (IREF .GT. 0) THEN
X1 = F(1)
X2 = F(2)
IF (IREF .EQ. 2 .OR. IREF .EQ. 4) THEN
F(1) = -X1*C60 - X2*S60
F(2) = -X1*S60 + X2*C60
F(3) = -F(3)
IF (IREF .EQ. 4) IREF = 0
ELSEIF (IREF .EQ. 1 .OR. IREF .EQ. 5) THEN
F(1) = X1*C60 - X2*S60
F(2) = X1*S60 + X2*C60
IF (IREF .EQ. 5) IREF = 3
ELSE ! IREF = 3
F(1) = X1*C60 - X2*S60
F(2) = -X1*S60 - X2*C60
F(3) = -F(3)
ENDIF
ENDIF
C
IDOUB = IDOUB - 1
IF (IDOUB .GT. 0) THEN ! two steps calculation
B(1) = F(1)
B(2) = F(2)
B(3) = F(3)
X(1) = X3
X(2) = X4
X(3) = Y(3)
ELSE
IF (ISU .EQ. 2) THEN
F(1) = (F(1)+B(1))/2
F(2) = (F(2)+B(2))/2
F(3) = (F(3)+B(3))/2
ELSEIF (ISU .EQ. 1) THEN
F(1) = F(1)+B(1)
F(2) = F(2)+B(2)
F(3) = F(3)+B(3)
ENDIF
ENDIF
ENDDO
C
IF (ISU .LE. 0 .OR. ISU .GT. 2) THEN ! Check that field extracted
WRITE(CRMESS,*)'* ISU=',ISU,',X1=',X(1),',X2=',X(2),',Y(1-3)=',Y
CALL RECMES(CRNAME,'I',CRMESS)
RETURN
ENDIF
C
IF (BXFAC .LT. 0.) THEN
F(1) = -F(1)
F(3) = -F(3)
ENDIF
C
IF (BYFAC .LT. 0.) THEN
F(2) = -F(2)
F(3) = -F(3)
ENDIF
c
RETURN
END
C-----------------------------------------------------------------------
C
Now the result of the PHI test is
===================================
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0.00000 35.0000, B= 1.70765 0. 0.
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19195E-02 4.11568E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21132E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342933 -3.79224E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14813E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 5.80463E-10
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14813E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841090 3.79223E-03
45, X,Y= 24.7487 24.7487, B= 0.872356 -1.02873 4.21132E-03
50, X,Y= 26.8116 22.4976, B= 0.857588 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11571E-04
60, X,Y= 30.3109 17.5000, B= 0.853823 -1.47887 0.
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11568E-04
70, X,Y= 32.8892 11.9707, B= 0.651425 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21132E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79223E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14813E-03
90, X,Y= 35.0000 2.14313E-15,B= 1.49012E-08 -1.11621 -3.44335E-10
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14813E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79223E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21132E-03
110, X,Y= 32.8892 -11.9707, B= -0.651425 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11568E-04
120, X,Y= 30.3109 -17.5000, B= -0.853823 -1.47887 0.
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11571E-04
130, X,Y= 26.8116 -22.4976, B= -0.857588 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872356 -1.02873 -4.21132E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841090 -3.79223E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14813E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 -5.80463E-10
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14813E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342933 3.79224E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21132E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19195E-02 -4.11568E-04
180, X,Y=4.28626E-15 -35.0000, B= -1.70765 0. 0.
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19195E-02 4.11568E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21132E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342933 -3.79224E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14813E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 5.80463E-10
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14813E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841090 3.79223E-03
225, X,Y= -24.7487 -24.7487, B= -0.872356 1.02873 4.21132E-03
230, X,Y= -26.8116 -22.4976, B= -0.857588 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11571E-04
240, X,Y= -30.3109 -17.5000, B= -0.853823 1.47887 0.
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11568E-04
250, X,Y= -32.8892 -11.9707, B= -0.651425 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21132E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79223E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14813E-03
270, X,Y= -35.0000 -6.4294E-15,B= -1.49012E-08 1.11621 -3.44335E-10
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14813E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79223E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21132E-03
290, X,Y= -32.8892 11.9707, B= 0.651425 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11568E-04
300, X,Y= -30.3109 17.5000, B= 0.853823 1.47887 0.
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11571E-04
310, X,Y= -26.8116 22.4976, B= 0.857588 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872356 1.02873 -4.21132E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841090 -3.79223E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14813E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 -5.80463E-10
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14813E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342933 3.79224E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21132E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19195E-02 -4.11568E-04
The singularity compensation is restricted by ATAN(0.015)=0.86 degrees.
Let us look what happens on this boundary:
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
-1.20, X,Y= -0.732985 34.9923, B= 1.70168 -1.59870E-03 -2.33824E-04
-1.16, X,Y= -0.708555 34.9928, B= 1.70218 -1.80251E-03 -2.40749E-04
-1.12, X,Y= -0.684125 34.9933, B= 1.70268 -2.00758E-03 -2.47658E-04
-1.08, X,Y= -0.659695 34.9938, B= 1.70315 -2.21437E-03 -2.54556E-04
-1.04, X,Y= -0.635265 34.9942, B= 1.70361 -2.42232E-03 -2.61438E-04
-1.00, X,Y= -0.610834 34.9947, B= 1.70406 -2.63184E-03 -2.68312E-04
-0.96, X,Y= -0.586403 34.9951, B= 1.70449 -2.84290E-03 -2.75174E-04
-0.92, X,Y= -0.561972 34.9955, B= 1.70491 -3.05525E-03 -2.82015E-04
-0.88, X,Y= -0.537540 34.9959, B= 1.70531 -3.26921E-03 -2.88854E-04
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
-0.84, X,Y= -0.513108 34.9962, B= 1.70745 3.26859E-03 3.10967E-05
-0.80, X,Y= -0.488676 34.9966, B= 1.70766 2.89020E-03 2.01474E-05
-0.76, X,Y= -0.464244 34.9969, B= 1.70786 2.51577E-03 9.27673E-06
-0.72, X,Y= -0.439811 34.9972, B= 1.70568 6.49418E-03 2.24787E-04
-0.68, X,Y= -0.415379 34.9975, B= 1.70590 6.13022E-03 2.12224E-04
-0.64, X,Y= -0.390946 34.9978, B= 1.70610 5.76683E-03 1.99673E-04
-0.60, X,Y= -0.366512 34.9981, B= 1.70628 5.40390E-03 1.87134E-04
-0.56, X,Y= -0.342079 34.9983, B= 1.70646 5.04145E-03 1.74606E-04
-0.52, X,Y= -0.317646 34.9986, B= 1.70662 4.67951E-03 1.62091E-04
-0.48, X,Y= -0.293212 34.9988, B= 1.70677 4.31796E-03 1.49585E-04
-0.44, X,Y= -0.268778 34.9990, B= 1.70691 3.95682E-03 1.37087E-04
-0.40, X,Y= -0.244344 34.9991, B= 1.70704 3.59595E-03 1.24598E-04
-0.36, X,Y= -0.219910 34.9993, B= 1.70716 3.23543E-03 1.12116E-04
-0.32, X,Y= -0.195476 34.9995, B= 1.70726 2.87519E-03 9.96401E-05
-0.28, X,Y= -0.171042 34.9996, B= 1.70735 2.51521E-03 8.71722E-05
-0.24, X,Y= -0.146607 34.9997, B= 1.70743 2.15551E-03 7.47089E-05
-0.20, X,Y= -0.122173 34.9998, B= 1.70750 1.79598E-03 6.22516E-05
-0.16, X,Y= -0.097738 34.9999, B= 1.70755 1.43656E-03 4.97955E-05
-0.12, X,Y= -0.073304 34.9999, B= 1.70759 1.07737E-03 3.73444E-05
-0.08, X,Y= -0.048869 35.0000, B= 1.70762 7.18173E-04 2.48945E-05
-0.04, X,Y= -0.024435 35.0000, B= 1.70764 3.59084E-04 1.24471E-05
-----------------------------------------------------------------------
0.00, X,Y= 0.000000 35.0000, B= 1.70765 0.00000 0.00000
-----------------------------------------------------------------------
0.04, X,Y= 0.024435 35.0000, B= 1.70764 -3.59084E-04 -1.24471E-05
0.08, X,Y= 0.048869 35.0000, B= 1.70762 -7.18173E-04 -2.48945E-05
0.12, X,Y= 0.073304 34.9999, B= 1.70759 -1.07737E-03 -3.73444E-05
0.16, X,Y= 0.097738 34.9999, B= 1.70755 -1.43656E-03 -4.97955E-05
0.20, X,Y= 0.122173 34.9998, B= 1.70750 -1.79598E-03 -6.22516E-05
0.24, X,Y= 0.146607 34.9997, B= 1.70743 -2.15551E-03 -7.47089E-05
0.28, X,Y= 0.171042 34.9996, B= 1.70735 -2.51521E-03 -8.71722E-05
0.32, X,Y= 0.195476 34.9995, B= 1.70726 -2.87519E-03 -9.96401E-05
0.36, X,Y= 0.219910 34.9993, B= 1.70716 -3.23543E-03 -1.12116E-04
0.40, X,Y= 0.244344 34.9991, B= 1.70704 -3.59595E-03 -1.24598E-04
0.44, X,Y= 0.268778 34.9990, B= 1.70691 -3.95682E-03 -1.37087E-04
0.48, X,Y= 0.293212 34.9988, B= 1.70677 -4.31796E-03 -1.49585E-04
0.52, X,Y= 0.317646 34.9986, B= 1.70662 -4.67951E-03 -1.62091E-04
0.56, X,Y= 0.342079 34.9983, B= 1.70646 -5.04145E-03 -1.74606E-04
0.60, X,Y= 0.366512 34.9981, B= 1.70628 -5.40390E-03 -1.87134E-04
0.64, X,Y= 0.390946 34.9978, B= 1.70610 -5.76683E-03 -1.99673E-04
0.68, X,Y= 0.415379 34.9975, B= 1.70590 -6.13022E-03 -2.12224E-04
0.72, X,Y= 0.439811 34.9972, B= 1.70568 -6.49418E-03 -2.24787E-04
0.76, X,Y= 0.464244 34.9969, B= 1.70786 -2.51577E-03 -9.27673E-06
0.80, X,Y= 0.488676 34.9966, B= 1.70766 -2.89020E-03 -2.01474E-05
0.84, X,Y= 0.513108 34.9962, B= 1.70745 -3.26859E-03 -3.10967E-05
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
0.88, X,Y= 0.537540 34.9959, B= 1.70531 3.26921E-03 2.88854E-04
0.92, X,Y= 0.561972 34.9955, B= 1.70491 3.05525E-03 2.82015E-04
0.96, X,Y= 0.586403 34.9951, B= 1.70449 2.84290E-03 2.75174E-04
1.00, X,Y= 0.610834 34.9947, B= 1.70406 2.63184E-03 2.68312E-04
1.04, X,Y= 0.635265 34.9942, B= 1.70361 2.42232E-03 2.61438E-04
1.08, X,Y= 0.659695 34.9938, B= 1.70315 2.21437E-03 2.54556E-04
1.12, X,Y= 0.684125 34.9933, B= 1.70268 2.00758E-03 2.47658E-04
1.16, X,Y= 0.708555 34.9928, B= 1.70218 1.80251E-03 2.40749E-04
1.20, X,Y= 0.732985 34.9923, B= 1.70168 1.59870E-03 2.33824E-04
It should be compared with not corrected values:
0.00, X,Y= 0.000000 35.0000, B= 1.70765 5.62315E-04 6.87478E-05
-----------------------------------------------------------------------
0.04, X,Y= 0.024435 35.0000, B= 1.70744 2.07498E-04 5.63614E-05
0.08, X,Y= 0.048869 35.0000, B= 1.70722 -1.38887E-04 4.40943E-05
0.12, X,Y= 0.073304 34.9999, B= 1.70698 -4.76881E-04 3.19459E-05
0.16, X,Y= 0.097738 34.9999, B= 1.70674 -8.06391E-04 1.99172E-05
0.20, X,Y= 0.122173 34.9998, B= 1.70648 -1.12761E-03 8.00240E-06
0.24, X,Y= 0.146607 34.9997, B= 1.70621 -1.44057E-03 -3.79162E-06
0.28, X,Y= 0.171042 34.9996, B= 1.70593 -1.74513E-03 -1.54713E-05
0.32, X,Y= 0.195476 34.9995, B= 1.70563 -2.04154E-03 -2.70348E-05
0.36, X,Y= 0.219910 34.9993, B= 1.70533 -2.32967E-03 -3.84868E-05
0.40, X,Y= 0.244344 34.9991, B= 1.70501 -2.60966E-03 -4.98253E-05
0.44, X,Y= 0.268778 34.9990, B= 1.70468 -2.88147E-03 -6.10492E-05
0.48, X,Y= 0.293212 34.9988, B= 1.70434 -3.14508E-03 -7.21607E-05
0.52, X,Y= 0.317646 34.9986, B= 1.70399 -3.40061E-03 -8.31608E-05
0.56, X,Y= 0.342079 34.9983, B= 1.70362 -3.64808E-03 -9.40477E-05
0.60, X,Y= 0.366512 34.9981, B= 1.70325 -3.88753E-03 -1.04829E-04
0.64, X,Y= 0.390946 34.9978, B= 1.70286 -4.11908E-03 -1.15502E-04
0.68, X,Y= 0.415379 34.9975, B= 1.70246 -4.34254E-03 -1.26066E-04
0.72, X,Y= 0.439811 34.9972, B= 1.70205 -4.55811E-03 -1.36520E-04
0.76, X,Y= 0.464244 34.9969, B= 1.70642 3.92014E-03 3.09307E-04
0.80, X,Y= 0.488676 34.9966, B= 1.70607 3.70177E-03 3.02506E-04
0.84, X,Y= 0.513108 34.9962, B= 1.70570 3.48468E-03 2.95684E-04
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
0.88, X,Y= 0.537540 34.9959, B= 1.70531 3.26921E-03 2.88854E-04
0.92, X,Y= 0.561972 34.9955, B= 1.70491 3.05525E-03 2.82015E-04
0.96, X,Y= 0.586403 34.9951, B= 1.70449 2.84290E-03 2.75174E-04
1.00, X,Y= 0.610834 34.9947, B= 1.70406 2.63184E-03 2.68312E-04
1.04, X,Y= 0.635265 34.9942, B= 1.70361 2.42232E-03 2.61438E-04
1.08, X,Y= 0.659695 34.9938, B= 1.70315 2.21437E-03 2.54556E-04
1.12, X,Y= 0.684125 34.9933, B= 1.70268 2.00758E-03 2.47658E-04
1.16, X,Y= 0.708555 34.9928, B= 1.70218 1.80251E-03 2.40749E-04
1.20, X,Y= 0.732985 34.9923, B= 1.70168 1.59870E-03 2.33824E-04
1.24, X,Y= 0.757414 34.9918, B= 1.70115 1.39611E-03 2.26876E-04
1.28, X,Y= 0.781842 34.9913, B= 1.70062 1.19529E-03 2.19934E-04
1.32, X,Y= 0.806271 34.9907, B= 1.70006 9.95510E-04 2.12958E-04
1.36, X,Y= 0.830699 34.9901, B= 1.69950 7.97267E-04 2.05974E-04
1.40, X,Y= 0.855126 34.9896, B= 1.69892 6.00510E-04 1.98986E-04
1.44, X,Y= 0.879553 34.9889, B= 1.69832 4.04906E-04 1.91968E-04
1.48, X,Y= 0.903980 34.9883, B= 1.69771 2.10831E-04 1.84945E-04
1.52, X,Y= 0.928406 34.9877, B= 1.69708 1.78487E-05 1.77893E-04
1.56, X,Y= 0.952832 34.9870, B= 1.69644 -1.73826E-04 1.70824E-04
1.60, X,Y= 0.977257 34.9864, B= 1.69579 -3.63868E-04 1.63752E-04
It is clear that it is not enough to correct the field in the range of
about 0.5 of the TAN(PHI) step (0.86 degrees). It seems reasonable to
make a singularity correction for about 1.5 of the step. But to make
this the magnetic field should be recalculated not for the 17 but for 18
nodes (one more step over 30 degrees). But this kind of the
recalculation can be done only next weekend... if any good approximation
of the field is necessary at less then 2.7 degrees from the coil plane.
Mikhail 7/13/97
--------------6291754718F4
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Content-Transfer-Encoding: 7bit
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To use R-TAN(PHI)-Z extrapolation instead of X-Y-Z extrapolation of
the magnetic field one should make the following correction in the
magnetic field extraction program (old nbame: SNAKE).
C
C:: THESE Double precision constants should be defined at the first call
T60 = DSQRT(3.D0)
T30 = 1.D0/T60
C60 = 0.5D0
S60 = T60/2.D0
C-------------------------------
C
C Now one should reflect and rotate if PHI comes out of (0 - 30) deg interval
C ---------------------------------------------------------------------------
IF (Y(2) .LT. 0.) THEN
Y(2) = -Y(2)
BXFAC = -1.
ELSE
BXFAC = 1.
ENDIF
C
IF (Y(1) .LT. 0.) THEN
Y(1) = -Y(1)
BYFAC = -1.
ELSE
BYFAC = 1.
ENDIF
C
IREF = 0
IF (Y(1) .EQ. 0.) THEN
IF (Y(2) .GT. 0.) THEN
IREF = 1
X1 = Y(2)*S60
X2 = T30
ELSE
X1 = 0.
X2 = 0.
ENDIF
ELSE
X1 = Y(1)
X2 = Y(2)/X1
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 1
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ENDIF
ENDIF
X(1) = X1
X(2) = X2
X(3) = Y(3)
C
F(1) = 0.
F(2) = 0.
F(3) = 0.
C
C From this poin common Teilor series approximation should be done (as an old)
C --------------------
C ...
C --------------------
C
C Now the rotation/reflection of the magnetic field back should be done
C ---------------------
IF (IREF .GT. 0) THEN
X1 = F(1)
X2 = F(2)
IF (IREF .GT. 1) THEN
F(1) = - X1*C60 - X2*S60
F(2) = - X1*S60 + X2*C60
F(3) = -F(3)
ELSE
F(1) = X1*C60 - X2*S60
F(2) = X1*S60 + X2*C60
ENDIF
ENDIF
C
IF (BXFAC .LT. 0.) THEN
F(1) = -F(1)
F(3) = -F(3)
ENDIF
C
IF (BYFAC .LT. 0.) THEN
F(2) = -F(2)
F(3) = -F(3)
ENDIF
c
RETURN
END
C ---------------------
Result of modification of the program, calculating the toroidal magnetic field
===== (Double precision for the rotation SIN's and COS's) ====================
PHI-test before the angular correction (for Mini Torus Region):
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0. 35.0000, B= 1.70765 5.62041E-04 6.87005E-05
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19194E-02 4.11597E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21134E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342934 -3.79222E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14814E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 -8.74749E-09
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14814E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841091 3.79221E-03
45, X,Y= 24.7487 24.7487, B= 0.872357 -1.02873 4.21134E-03
50, X,Y= 26.8116 22.4976, B= 0.857589 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11599E-04
60, X,Y= 30.3109 17.5000, B= 0.854310 -1.47858 6.87005E-05
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11597E-04
70, X,Y= 32.8892 11.9707, B= 0.651424 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21134E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79221E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14814E-03
90, X,Y= 35.0000 2.14313E-15,B= 1.19209E-08 -1.11621 8.98363E-09
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14814E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79221E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21134E-03
110, X,Y= 32.8892 -11.9707, B= -0.651424 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11597E-04
120, X,Y= 30.3109 -17.5000, B= -0.854310 -1.47858 -6.87005E-05
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11599E-04
130, X,Y= 26.8116 -22.4976, B= -0.857589 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872357 -1.02873 -4.21134E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841091 -3.79221E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14814E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 8.74749E-09
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14814E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342934 3.79222E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21134E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19194E-02 -4.11597E-04
180, X,Y= 4.28626E-15 -35.0000, B= -1.70765 5.62041E-04 -6.87005E-05
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19194E-02 4.11597E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21134E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342934 -3.79222E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14814E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 -8.74749E-09
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14814E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841091 3.79221E-03
225, X,Y= -24.7487 -24.7487, B= -0.872357 1.02873 4.21134E-03
230, X,Y= -26.8116 -22.4976, B= -0.857589 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11599E-04
240, X,Y= -30.3109 -17.5000, B= -0.854310 1.47858 6.87005E-05
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11597E-04
250, X,Y= -32.8892 -11.9707, B= -0.651424 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21134E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79221E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14814E-03
270, X,Y= -35.0000 -6.4294E-15,B= -1.19209E-08 1.11621 8.98363E-09
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14814E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79221E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21134E-03
290, X,Y= -32.8892 11.9707, B= 0.651424 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11597E-04
300, X,Y= -30.3109 17.5000, B= 0.854310 1.47858 -6.87005E-05
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11599E-04
310, X,Y= -26.8116 22.4976, B= 0.857589 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872357 1.02873 -4.21134E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841091 -3.79221E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14814E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 8.74749E-09
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14814E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342934 3.79222E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21134E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19194E-02 -4.11597E-04
PHI-test after the angular correction (double precision) in rotation of coils:
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0. 35.0000, B= 1.70765 5.62315E-04 6.87478E-05
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19195E-02 4.11568E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21132E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342933 -3.79224E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14813E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 5.80463E-10
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14813E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841090 3.79223E-03
45, X,Y= 24.7487 24.7487, B= 0.872356 -1.02873 4.21132E-03
50, X,Y= 26.8116 22.4976, B= 0.857588 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11571E-04
60, X,Y= 30.3109 17.5000, B= 0.854310 -1.47858 6.87478E-05
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11568E-04
70, X,Y= 32.8892 11.9707, B= 0.651425 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21132E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79223E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14813E-03
90, X,Y= 35.0000 2.14313E-15,B= 1.4901E-08 -1.11621 -3.44335E-10
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14814E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79222E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21132E-03
110, X,Y= 32.8892 -11.9707, B= -0.651425 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11568E-04
120, X,Y= 30.3109 -17.5000, B= -0.854310 -1.47858 -6.87478E-05
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11571E-04
130, X,Y= 26.8116 -22.4976, B= -0.857588 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872356 -1.02873 -4.21132E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841090 -3.79223E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14813E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 -5.80463E-10
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14813E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342933 3.79224E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21132E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19195E-02 -4.11568E-04
180, X,Y= 4.286E-15 -35.0000, B= -1.70765 5.62315E-04 -6.87478E-05
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19195E-02 4.11568E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21132E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342933 -3.79224E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14813E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 5.80463E-10
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14813E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841090 3.79223E-03
225, X,Y= -24.7487 -24.7487, B= -0.872356 1.02873 4.21132E-03
230, X,Y= -26.8116 -22.4976, B= -0.857588 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11571E-04
240, X,Y= -30.3109 -17.5000, B= -0.854310 1.47858 6.87478E-05
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11568E-04
250, X,Y= -32.8892 -11.9707, B= -0.651425 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21132E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79223E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14813E-03
270, X,Y= -35.0000 -6.42E-15,B= -1.49012E-08 1.11621 -3.44335E-10
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14813E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79223E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21132E-03
290, X,Y= -32.8892 11.9707, B= 0.651425 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11568E-04
300, X,Y= -30.3109 17.5000, B= 0.854310 1.47858 -6.87478E-05
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11571E-04
310, X,Y= -26.8116 22.4976, B= 0.857588 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872356 1.02873 -4.21132E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841090 -3.79223E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14813E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 -5.80463E-10
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14813E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342933 3.79224E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21132E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19195E-02 -4.11568E-04
Because of the singularity at 0,60,120,180,240 degrees the value of the
By at 0 & 180 degrees is not perfectly zero. It is possible to avoib this
uncertainty only if TAN(PHI) is replased by PHI and the 0-degrees point is
exactly inbetween the n-1 (say -5 degrees) and n-th poin (say 5 degrees). In
other cases the bin is assymetric (including our TAN(PHY) approach) and the
value of By is not perfectly 0. There was a special search for reduction of the
By value at x=0. The search included .05 bin for TAN(PHI) (for which the
value of the magnetic field file is equal to the old one) and the 0.0398 bin
version which places the 0 degrees point exacly inbetween of n-1 and n-th poin.
Unfortunatly TAN(PHI) is assymetric near the poin of TAN(30deg) and that is why
in both cases the result was worse than for the simple .04 step which was
selected for the description of the magnetic field. But he uncertainty of
about 0.04% which you can see in the table is not a characteristics of the
overall approximation. It is typical only for the bins close to the coil plane.
Near the middle plane it is about 4 times better. In other words the accuracy
of the approximation is better then 1.E-4 and becomse 4 times worse approaching
the coil plane. In the region of the drift chamber acceptance the accuracy is
better then 2.E-4.
The double precision was used for the rotation of the coils of the CLS
toroida magnets when the magnetic field was integrated over all the 6 coils.
To correct hte singularity in the coil plane the double colculation
method was used. In vicinity of the coil plane the magnetic fireld was
calculated first as a a magnetic field of this sector and the second time as
a magnetic field of the neighboring sector. Near the colil plane calculations
of the magnetic field are not friquent so this method does not incease the
extraction time for the magnetic field inside the acceptance of the drift
chambers and should be taken into account (in terms of the extraction time)
only when trajectories crossing the coil plane are reconstructed (or simulated
if this version of program is used in GSIM).
The resulting correction of the old program is
C---============================================== ----------------------
C
C:: THESE Double precision constants should be defined at the first call
T60 = DSQRT(3.D0)
T30 = 1.D0/T60
C60 = 0.5D0
S60 = T60/2.D0
C
C:: THESE singularity correction constants should be defined at the first call
DT1 = 0.015 ! Singularity corrrection,!!change value if DY .NE. 0.04 !!
DT2 = 1./DT1
C
C-------------------------------
C
C Now one should reflect and rotate if PHI comes out of (0 - 30) deg interval
C ---------------------------------------------------------------------------
C
IF (Y(2) .LT. 0.) THEN
Y(2) = -Y(2)
BXFAC = -1.
ELSE
BXFAC = 1.
ENDIF
C
IF (Y(1) .LT. 0.) THEN
Y(1) = -Y(1)
BYFAC = -1.
ELSE
BYFAC = 1.
ENDIF
C
IREF = 0
IF (Y(1) .LT. 1.E-7) THEN
IF (Y(2) .GT. 1.E-7) THEN
IDOUB = 2
IREF = 5
X3 = Y(2)*S60
X4 = T30
X1 = Y(2)*S60
X2 = T30
ELSE
X1 = 0.
X2 = 0.
ENDIF
ELSE
X1 = Y(1)
X2 = Y(2)/X1
IF (X2 .GT. DT2 .OR. ABS(X2-T30) .LT. DT1) THEN
IDOUB = 2
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 5
X3 = - Y(1)*C60 + Y(2)*S60
X4 =(Y(1)*S60 + Y(2)*C60)/X3
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 4
X3 = X1
X4 = X2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ELSE ! Near but less then T30
IREF = 4
X3 = X1
X4 = X2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ELSE
IDOUB = 1
IF (X2 .GT. T30) THEN
IF (X2 .GT. T60) THEN
IREF = 1
X1 = Y(1)*C60 + Y(2)*S60
X2 =(-Y(1)*S60 + Y(2)*C60)/X1
ELSE
IREF = 2
X1 = Y(1)*C60 + Y(2)*S60
X2 =(Y(1)*S60 - Y(2)*C60)/X1
ENDIF
ENDIF
ENDIF
ENDIF
C
X(1) = X1
X(2) = X2
X(3) = Y(3)
C
F(1) = 0.
F(2) = 0.
F(3) = 0.
B(1) = 0.
B(2) = 0.
B(3) = 0.
C
ISU = 0
C
C Find intercepts for Big + Mini Toruses
C
DO WHILE (IDOUB .GT. 0) ! first IDOUB = 1 .OR. = 2
C
C From this poin common Teilor series approximation should be done (as an old)
C --------------------
C ...
ISU = ISU + 1 ! If field is extracted successfully (not out of grid)
C ...
C --------------------
C
C Now the rotation/reflection of the magnetic field back should be done
C ---------------------
C
IF (IREF .GT. 0) THEN
X1 = F(1)
X2 = F(2)
IF (IREF .EQ. 2 .OR. IREF .EQ. 4) THEN
F(1) = -X1*C60 - X2*S60
F(2) = -X1*S60 + X2*C60
F(3) = -F(3)
IF (IREF .EQ. 4) IREF = 0
ELSEIF (IREF .EQ. 1 .OR. IREF .EQ. 5) THEN
F(1) = X1*C60 - X2*S60
F(2) = X1*S60 + X2*C60
IF (IREF .EQ. 5) IREF = 3
ELSE ! IREF = 3
F(1) = X1*C60 - X2*S60
F(2) = -X1*S60 - X2*C60
F(3) = -F(3)
ENDIF
ENDIF
C
IDOUB = IDOUB - 1
IF (IDOUB .GT. 0) THEN ! two steps calculation
B(1) = F(1)
B(2) = F(2)
B(3) = F(3)
X(1) = X3
X(2) = X4
X(3) = Y(3)
ELSE
IF (ISU .EQ. 2) THEN
F(1) = (F(1)+B(1))/2
F(2) = (F(2)+B(2))/2
F(3) = (F(3)+B(3))/2
ELSEIF (ISU .EQ. 1) THEN
F(1) = F(1)+B(1)
F(2) = F(2)+B(2)
F(3) = F(3)+B(3)
ENDIF
ENDIF
ENDDO
C
IF (ISU .LE. 0 .OR. ISU .GT. 2) THEN ! Check that mag. field is extracted
WRITE(CRMESS,*)'*Fail ISU=',ISU,', X1=',X(1),', X2=',X(2),', Y(1-3)=',Y
CALL RECMES(CRNAME,'I',CRMESS)
RETURN
ENDIF
C
IF (BXFAC .LT. 0.) THEN
F(1) = -F(1)
F(3) = -F(3)
ENDIF
C
IF (BYFAC .LT. 0.) THEN
F(2) = -F(2)
F(3) = -F(3)
ENDIF
c
RETURN
END
C------------------------------------------------------------------------------
C
Now the result of the PHI test is
===================================
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
0, X,Y= 0.00000 35.0000, B= 1.70765 0. 0.
5, X,Y= 3.05045 34.8668, B= 1.65964 -1.19195E-02 4.11568E-04
10, X,Y= 6.07769 34.4683, B= 1.50901 -0.119029 -2.12194E-03
15, X,Y= 9.05867 33.8074, B= 1.32709 -0.241115 -4.21132E-03
20, X,Y= 11.9707 32.8892, B= 1.16920 -0.342933 -3.79224E-03
25, X,Y= 14.7916 31.7208, B= 1.05067 -0.445736 -2.14813E-03
30, X,Y= 17.5000 30.3109, B= 0.966667 -0.558105 5.80463E-10
35, X,Y= 20.0752 28.6703, B= 0.911355 -0.687041 2.14813E-03
40, X,Y= 22.4976 26.8116, B= 0.881589 -0.841090 3.79223E-03
45, X,Y= 24.7487 24.7487, B= 0.872356 -1.02873 4.21132E-03
50, X,Y= 26.8116 22.4976, B= 0.857588 -1.24733 2.12195E-03
55, X,Y= 28.6703 20.0752, B= 0.840144 -1.43133 -4.11571E-04
60, X,Y= 30.3109 17.5000, B= 0.853823 -1.47887 0.
65, X,Y= 31.7208 14.7916, B= 0.819499 -1.44325 4.11568E-04
70, X,Y= 32.8892 11.9707, B= 0.651425 -1.36636 -2.12195E-03
75, X,Y= 33.8074 9.05867, B= 0.454732 -1.26985 -4.21132E-03
80, X,Y= 34.4683 6.07769, B= 0.287611 -1.18402 -3.79223E-03
85, X,Y= 34.8668 3.05045, B= 0.139318 -1.13278 -2.14813E-03
90, X,Y= 35.0000 2.14313E-15,B= 1.49012E-08 -1.11621 -3.44335E-10
95, X,Y= 34.8668 -3.05045, B= -0.139318 -1.13278 2.14813E-03
100, X,Y= 34.4683 -6.07769, B= -0.287611 -1.18402 3.79223E-03
105, X,Y= 33.8074 -9.05867, B= -0.454732 -1.26985 4.21132E-03
110, X,Y= 32.8892 -11.9707, B= -0.651425 -1.36636 2.12195E-03
115, X,Y= 31.7208 -14.7916, B= -0.819499 -1.44325 -4.11568E-04
120, X,Y= 30.3109 -17.5000, B= -0.853823 -1.47887 0.
125, X,Y= 28.6703 -20.0752, B= -0.840144 -1.43133 4.11571E-04
130, X,Y= 26.8116 -22.4976, B= -0.857588 -1.24733 -2.12195E-03
135, X,Y= 24.7487 -24.7487, B= -0.872356 -1.02873 -4.21132E-03
140, X,Y= 22.4976 -26.8116, B= -0.881589 -0.841090 -3.79223E-03
145, X,Y= 20.0752 -28.6703, B= -0.911355 -0.687041 -2.14813E-03
150, X,Y= 17.5000 -30.3109, B= -0.966667 -0.558105 -5.80463E-10
155, X,Y= 14.7916 -31.7208, B= -1.05067 -0.445736 2.14813E-03
160, X,Y= 11.9707 -32.8892, B= -1.16920 -0.342933 3.79224E-03
165, X,Y= 9.05867 -33.8074, B= -1.32709 -0.241115 4.21132E-03
170, X,Y= 6.07769 -34.4683, B= -1.50901 -0.119029 2.12194E-03
175, X,Y= 3.05045 -34.8668, B= -1.65964 -1.19195E-02 -4.11568E-04
180, X,Y=4.28626E-15 -35.0000, B= -1.70765 0. 0.
185, X,Y= -3.05045 -34.8668, B= -1.65964 1.19195E-02 4.11568E-04
190, X,Y= -6.07769 -34.4683, B= -1.50901 0.119029 -2.12194E-03
195, X,Y= -9.05867 -33.8074, B= -1.32709 0.241115 -4.21132E-03
200, X,Y= -11.9707 -32.8892, B= -1.16920 0.342933 -3.79224E-03
205, X,Y= -14.7916 -31.7208, B= -1.05067 0.445736 -2.14813E-03
210, X,Y= -17.5000 -30.3109, B= -0.966667 0.558105 5.80463E-10
215, X,Y= -20.0752 -28.6703, B= -0.911355 0.687041 2.14813E-03
220, X,Y= -22.4976 -26.8116, B= -0.881589 0.841090 3.79223E-03
225, X,Y= -24.7487 -24.7487, B= -0.872356 1.02873 4.21132E-03
230, X,Y= -26.8116 -22.4976, B= -0.857588 1.24733 2.12195E-03
235, X,Y= -28.6703 -20.0752, B= -0.840144 1.43133 -4.11571E-04
240, X,Y= -30.3109 -17.5000, B= -0.853823 1.47887 0.
245, X,Y= -31.7208 -14.7916, B= -0.819499 1.44325 4.11568E-04
250, X,Y= -32.8892 -11.9707, B= -0.651425 1.36636 -2.12195E-03
255, X,Y= -33.8074 -9.05867, B= -0.454732 1.26985 -4.21132E-03
260, X,Y= -34.4683 -6.07769, B= -0.287611 1.18402 -3.79223E-03
265, X,Y= -34.8668 -3.05045, B= -0.139318 1.13278 -2.14813E-03
270, X,Y= -35.0000 -6.4294E-15,B= -1.49012E-08 1.11621 -3.44335E-10
275, X,Y= -34.8668 3.05045, B= 0.139318 1.13278 2.14813E-03
280, X,Y= -34.4683 6.07769, B= 0.287611 1.18402 3.79223E-03
285, X,Y= -33.8074 9.05867, B= 0.454732 1.26985 4.21132E-03
290, X,Y= -32.8892 11.9707, B= 0.651425 1.36636 2.12195E-03
295, X,Y= -31.7208 14.7916, B= 0.819499 1.44325 -4.11568E-04
300, X,Y= -30.3109 17.5000, B= 0.853823 1.47887 0.
305, X,Y= -28.6703 20.0752, B= 0.840144 1.43133 4.11571E-04
310, X,Y= -26.8116 22.4976, B= 0.857588 1.24733 -2.12195E-03
315, X,Y= -24.7487 24.7487, B= 0.872356 1.02873 -4.21132E-03
320, X,Y= -22.4976 26.8116, B= 0.881589 0.841090 -3.79223E-03
325, X,Y= -20.0752 28.6703, B= 0.911355 0.687041 -2.14813E-03
330, X,Y= -17.5000 30.3109, B= 0.966667 0.558105 -5.80463E-10
335, X,Y= -14.7916 31.7208, B= 1.05067 0.445736 2.14813E-03
340, X,Y= -11.9707 32.8892, B= 1.16920 0.342933 3.79224E-03
345, X,Y= -9.05867 33.8074, B= 1.32709 0.241115 4.21132E-03
350, X,Y= -6.07769 34.4683, B= 1.50901 0.119029 2.12194E-03
355, X,Y= -3.05045 34.8668, B= 1.65964 1.19195E-02 -4.11568E-04
The singularity compensation is restricted by ATAN(0.015)=0.86 degrees.
Let us look what happens on this boundary:
A(DEG) X(cm) Y(cm) Bx(cm) By(cm) Bz(cm)
-1.20, X,Y= -0.732985 34.9923, B= 1.70168 -1.59870E-03 -2.33824E-04
-1.16, X,Y= -0.708555 34.9928, B= 1.70218 -1.80251E-03 -2.40749E-04
-1.12, X,Y= -0.684125 34.9933, B= 1.70268 -2.00758E-03 -2.47658E-04
-1.08, X,Y= -0.659695 34.9938, B= 1.70315 -2.21437E-03 -2.54556E-04
-1.04, X,Y= -0.635265 34.9942, B= 1.70361 -2.42232E-03 -2.61438E-04
-1.00, X,Y= -0.610834 34.9947, B= 1.70406 -2.63184E-03 -2.68312E-04
-0.96, X,Y= -0.586403 34.9951, B= 1.70449 -2.84290E-03 -2.75174E-04
-0.92, X,Y= -0.561972 34.9955, B= 1.70491 -3.05525E-03 -2.82015E-04
-0.88, X,Y= -0.537540 34.9959, B= 1.70531 -3.26921E-03 -2.88854E-04
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
-0.84, X,Y= -0.513108 34.9962, B= 1.70745 3.26859E-03 3.10967E-05 C
-0.80, X,Y= -0.488676 34.9966, B= 1.70766 2.89020E-03 2.01474E-05
-0.76, X,Y= -0.464244 34.9969, B= 1.70786 2.51577E-03 9.27673E-06 O
-0.72, X,Y= -0.439811 34.9972, B= 1.70568 6.49418E-03 2.24787E-04
-0.68, X,Y= -0.415379 34.9975, B= 1.70590 6.13022E-03 2.12224E-04 R
-0.64, X,Y= -0.390946 34.9978, B= 1.70610 5.76683E-03 1.99673E-04
-0.60, X,Y= -0.366512 34.9981, B= 1.70628 5.40390E-03 1.87134E-04 R
-0.56, X,Y= -0.342079 34.9983, B= 1.70646 5.04145E-03 1.74606E-04
-0.52, X,Y= -0.317646 34.9986, B= 1.70662 4.67951E-03 1.62091E-04 E
-0.48, X,Y= -0.293212 34.9988, B= 1.70677 4.31796E-03 1.49585E-04
-0.44, X,Y= -0.268778 34.9990, B= 1.70691 3.95682E-03 1.37087E-04 C
-0.40, X,Y= -0.244344 34.9991, B= 1.70704 3.59595E-03 1.24598E-04
-0.36, X,Y= -0.219910 34.9993, B= 1.70716 3.23543E-03 1.12116E-04 T
-0.32, X,Y= -0.195476 34.9995, B= 1.70726 2.87519E-03 9.96401E-05
-0.28, X,Y= -0.171042 34.9996, B= 1.70735 2.51521E-03 8.71722E-05 E
-0.24, X,Y= -0.146607 34.9997, B= 1.70743 2.15551E-03 7.47089E-05
-0.20, X,Y= -0.122173 34.9998, B= 1.70750 1.79598E-03 6.22516E-05 D
-0.16, X,Y= -0.097738 34.9999, B= 1.70755 1.43656E-03 4.97955E-05
-0.12, X,Y= -0.073304 34.9999, B= 1.70759 1.07737E-03 3.73444E-05 .
-0.08, X,Y= -0.048869 35.0000, B= 1.70762 7.18173E-04 2.48945E-05
-0.04, X,Y= -0.024435 35.0000, B= 1.70764 3.59084E-04 1.24471E-05 .
-----------------------------------------------------------------------
0.00, X,Y= 0.000000 35.0000, B= 1.70765 0.00000 0.00000 .
-----------------------------------------------------------------------
0.04, X,Y= 0.024435 35.0000, B= 1.70764 -3.59084E-04 -1.24471E-05 .
0.08, X,Y= 0.048869 35.0000, B= 1.70762 -7.18173E-04 -2.48945E-05
0.12, X,Y= 0.073304 34.9999, B= 1.70759 -1.07737E-03 -3.73444E-05 .
0.16, X,Y= 0.097738 34.9999, B= 1.70755 -1.43656E-03 -4.97955E-05
0.20, X,Y= 0.122173 34.9998, B= 1.70750 -1.79598E-03 -6.22516E-05 C
0.24, X,Y= 0.146607 34.9997, B= 1.70743 -2.15551E-03 -7.47089E-05
0.28, X,Y= 0.171042 34.9996, B= 1.70735 -2.51521E-03 -8.71722E-05 O
0.32, X,Y= 0.195476 34.9995, B= 1.70726 -2.87519E-03 -9.96401E-05
0.36, X,Y= 0.219910 34.9993, B= 1.70716 -3.23543E-03 -1.12116E-04 R
0.40, X,Y= 0.244344 34.9991, B= 1.70704 -3.59595E-03 -1.24598E-04
0.44, X,Y= 0.268778 34.9990, B= 1.70691 -3.95682E-03 -1.37087E-04 R
0.48, X,Y= 0.293212 34.9988, B= 1.70677 -4.31796E-03 -1.49585E-04
0.52, X,Y= 0.317646 34.9986, B= 1.70662 -4.67951E-03 -1.62091E-04 E
0.56, X,Y= 0.342079 34.9983, B= 1.70646 -5.04145E-03 -1.74606E-04
0.60, X,Y= 0.366512 34.9981, B= 1.70628 -5.40390E-03 -1.87134E-04 C
0.64, X,Y= 0.390946 34.9978, B= 1.70610 -5.76683E-03 -1.99673E-04
0.68, X,Y= 0.415379 34.9975, B= 1.70590 -6.13022E-03 -2.12224E-04 T
0.72, X,Y= 0.439811 34.9972, B= 1.70568 -6.49418E-03 -2.24787E-04
0.76, X,Y= 0.464244 34.9969, B= 1.70786 -2.51577E-03 -9.27673E-06 E
0.80, X,Y= 0.488676 34.9966, B= 1.70766 -2.89020E-03 -2.01474E-05
0.84, X,Y= 0.513108 34.9962, B= 1.70745 -3.26859E-03 -3.10967E-05 D
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
0.88, X,Y= 0.537540 34.9959, B= 1.70531 3.26921E-03 2.88854E-04
0.92, X,Y= 0.561972 34.9955, B= 1.70491 3.05525E-03 2.82015E-04
0.96, X,Y= 0.586403 34.9951, B= 1.70449 2.84290E-03 2.75174E-04
1.00, X,Y= 0.610834 34.9947, B= 1.70406 2.63184E-03 2.68312E-04
1.04, X,Y= 0.635265 34.9942, B= 1.70361 2.42232E-03 2.61438E-04
1.08, X,Y= 0.659695 34.9938, B= 1.70315 2.21437E-03 2.54556E-04
1.12, X,Y= 0.684125 34.9933, B= 1.70268 2.00758E-03 2.47658E-04
1.16, X,Y= 0.708555 34.9928, B= 1.70218 1.80251E-03 2.40749E-04
1.20, X,Y= 0.732985 34.9923, B= 1.70168 1.59870E-03 2.33824E-04
It should be compared with not corrected values:
0.00, X,Y= 0.000000 35.0000, B= 1.70765 5.62315E-04 6.87478E-05
-----------------------------------------------------------------------
0.04, X,Y= 0.024435 35.0000, B= 1.70744 2.07498E-04 5.63614E-05
0.08, X,Y= 0.048869 35.0000, B= 1.70722 -1.38887E-04 4.40943E-05
0.12, X,Y= 0.073304 34.9999, B= 1.70698 -4.76881E-04 3.19459E-05
0.16, X,Y= 0.097738 34.9999, B= 1.70674 -8.06391E-04 1.99172E-05
0.20, X,Y= 0.122173 34.9998, B= 1.70648 -1.12761E-03 8.00240E-06
0.24, X,Y= 0.146607 34.9997, B= 1.70621 -1.44057E-03 -3.79162E-06
0.28, X,Y= 0.171042 34.9996, B= 1.70593 -1.74513E-03 -1.54713E-05
0.32, X,Y= 0.195476 34.9995, B= 1.70563 -2.04154E-03 -2.70348E-05
0.36, X,Y= 0.219910 34.9993, B= 1.70533 -2.32967E-03 -3.84868E-05
0.40, X,Y= 0.244344 34.9991, B= 1.70501 -2.60966E-03 -4.98253E-05
0.44, X,Y= 0.268778 34.9990, B= 1.70468 -2.88147E-03 -6.10492E-05
0.48, X,Y= 0.293212 34.9988, B= 1.70434 -3.14508E-03 -7.21607E-05
0.52, X,Y= 0.317646 34.9986, B= 1.70399 -3.40061E-03 -8.31608E-05
0.56, X,Y= 0.342079 34.9983, B= 1.70362 -3.64808E-03 -9.40477E-05
0.60, X,Y= 0.366512 34.9981, B= 1.70325 -3.88753E-03 -1.04829E-04
0.64, X,Y= 0.390946 34.9978, B= 1.70286 -4.11908E-03 -1.15502E-04
0.68, X,Y= 0.415379 34.9975, B= 1.70246 -4.34254E-03 -1.26066E-04
0.72, X,Y= 0.439811 34.9972, B= 1.70205 -4.55811E-03 -1.36520E-04
0.76, X,Y= 0.464244 34.9969, B= 1.70642 3.92014E-03 3.09307E-04
0.80, X,Y= 0.488676 34.9966, B= 1.70607 3.70177E-03 3.02506E-04
0.84, X,Y= 0.513108 34.9962, B= 1.70570 3.48468E-03 2.95684E-04
-----------------------------------------------------------------------
=======================================================================
-----------------------------------------------------------------------
0.88, X,Y= 0.537540 34.9959, B= 1.70531 3.26921E-03 2.88854E-04
0.92, X,Y= 0.561972 34.9955, B= 1.70491 3.05525E-03 2.82015E-04
0.96, X,Y= 0.586403 34.9951, B= 1.70449 2.84290E-03 2.75174E-04
1.00, X,Y= 0.610834 34.9947, B= 1.70406 2.63184E-03 2.68312E-04
1.04, X,Y= 0.635265 34.9942, B= 1.70361 2.42232E-03 2.61438E-04
1.08, X,Y= 0.659695 34.9938, B= 1.70315 2.21437E-03 2.54556E-04
1.12, X,Y= 0.684125 34.9933, B= 1.70268 2.00758E-03 2.47658E-04
1.16, X,Y= 0.708555 34.9928, B= 1.70218 1.80251E-03 2.40749E-04
1.20, X,Y= 0.732985 34.9923, B= 1.70168 1.59870E-03 2.33824E-04
1.24, X,Y= 0.757414 34.9918, B= 1.70115 1.39611E-03 2.26876E-04
1.28, X,Y= 0.781842 34.9913, B= 1.70062 1.19529E-03 2.19934E-04
1.32, X,Y= 0.806271 34.9907, B= 1.70006 9.95510E-04 2.12958E-04
1.36, X,Y= 0.830699 34.9901, B= 1.69950 7.97267E-04 2.05974E-04
1.40, X,Y= 0.855126 34.9896, B= 1.69892 6.00510E-04 1.98986E-04
1.44, X,Y= 0.879553 34.9889, B= 1.69832 4.04906E-04 1.91968E-04
1.48, X,Y= 0.903980 34.9883, B= 1.69771 2.10831E-04 1.84945E-04
1.52, X,Y= 0.928406 34.9877, B= 1.69708 1.78487E-05 1.77893E-04
1.56, X,Y= 0.952832 34.9870, B= 1.69644 -1.73826E-04 1.70824E-04
1.60, X,Y= 0.977257 34.9864, B= 1.69579 -3.63868E-04 1.63752E-04
It is clear that it is not enough to correct the field in the range of
about 0.5 of the TAN(PHI) step (0.86 degrees). It seems reasonable to make
a singularity correction for about 1.5 of the step. But to make this the
magnetic field should be recalculated not for the 17 but for 18 nodes (one
more step over 30 degrees). But this kind of the recalculation can be done only
next weekend... if any good approximation of the field is necessary at less
then 2.7 degrees from the coil plane.
Mikhail 7/13/97
--------------6291754718F4--