– 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:

Explanation:

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, E_kin(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.

*Bρ the magnetic rigidity was extracted from COSY by comand CONS(CHIM)

Fit result for parabola X_max² = 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 445 to 102 for the standard particle of the script.