This is an old revision of the document!
– by Alex, Nadeesha and Louis –
Choosen example reaction: 45V(p,γ)46Cr
⇒important for 44Ti production rate in core collapse Supernova (Horoi et al. Nucl.Phys.A 718, (2003))
Beam: 45V13+ of 135 MeV (1% enegry spread)
Command: OV 1 1 0 ; {order 1, phase space dim 1 INCLUDING ENERGY, # of parameters 0}
Output:
1.0 | 0.0 | 0.0 | 0.0 | -0.41 |
2.2 | 1.0 | 0.0 | 0.0 | -0.35 |
Explanation:
R11 | R12 | 0.0 | 0.0 | R15 |
R21 | R22 | 0.0 | 0.0 | R25 |
R11 = 1.0 is “Magnification”, i.e. no magnification provided with the dipole.
R12 = 0.0 is “Focusing”, i.e. no focusing is provided by the dipole.
R21 = 2.2 is approximate “Path length”,which is 0.5+0.78+1.0 meters
R22 = 0.0 mean that output angles does not depend on input angles.
R15 = -0.41 is ToF difference due to different initial position.
R25 = -0.35 is ToF difference due to different initial angle.
Reaction summary for 45V+p→γ+46Cr, Ekin(45V)=135 MeV
The maximum γ energy is 8.481 MeV. The minimum γ energy is 7.249 MeV.
The maximum 46Cr energy is 132.634 MeV. The minimum 46Cr energy is 131.402 MeV. The maximum 46Cr angle is 0.13 degrees.
If we assume a normalized emittance of 0.6 π mm mrad provided from ReA3 at 3.0 MeV/u the geometric emittance is 0.6/0.08 = 7.5 π mm mrad.
With the spot size on the target, designed to be ±0.5 mm (1σ), the anglular spread then is ±15 mrad.
Adding the calculated spread from the reaction with the target of 0.13 deg = ±2.26 mrad we get ±17.26 mrad of angular spread.
⇒COSY beam input: SB 0.0005 0.01726 0 0.0005 0.01726 0 0 0.0047 0 0 0 ;
Output for this beam passing the dipole:
The distance between the center of Q7 and the focal plane FP2 is 6.085 m as extracted from the script file.
BQ7 [T] | Xmax[m] | ap [m] | Bρ* [Tm] | L [m] | K |
0.02 | 2.91E-03 | 0.13 | 0.8 | 6.085 | 0.065384615 |
0.01 | 2.27E-03 | 0.13 | 0.8 | 6.085 | 0.032692308 |
0 | 1.62E-03 | 0.13 | 0.8 | 6.085 | 0 |
-0.01 | 1.20E-03 | 0.13 | 0.8 | 6.085 | -0.032692308 |
-0.02 | 9.08E-04 | 0.13 | 0.8 | 6.085 | -0.065384615 |
-0.03 | 6.23E-04 | 0.13 | 0.8 | 6.085 | -0.098076923 |
-0.04 | 9.54E-04 | 0.13 | 0.8 | 6.085 | -0.130769231 |
-0.05 | 1.60E-03 | 0.13 | 0.8 | 6.085 | -0.163461538 |
-0.06 | 2.26E-03 | 0.13 | 0.8 | 6.085 | -0.196153846 |
*Bρ the magnetic rigidity was extracted from COSY by comand CONS(CHIM)
Fit result for parabola Xmax2 = σ11 = a·K2 - 2ab·K + ab2 + c is:
a = 0.000362572706
b = 0.0834414129893
c = 3.506973286e-07
The consistency check for beam size calculation in Q7 shows:
X_calculated = 3.13mm, X_cosy_read_out = 3.16mm at the Q7 exit.
Emittance calculated from fit parameters ε= √(ac) / L2 = 3.05E-7 π m rad = 0.305 π mm mrad.
Start beam emittance= XX · AX= 0.2 π mm mrad, so the emittance grows from the start to the focal point.
This emittance grow is possibly due to the optics aberrations. That is because the input COSY file does a 4th-order-calculation. Also the measured points don't fit the parabola ideally, i.e. the optics is non-linear.
The effective length of Q2 was reduced by 3% to 0.291m with the drift lenghts before and after increased by 0.0045m.
This led to a mass resolution change from 601 to 164 for the standard particle of the script.