We're the first group and anyone who claims otherwise is wrong.

1. We are going to model the reaction P-31(p,γ)S-32 in SECAR

2. The Energy of the incident phosphorus is 31MeV

3. We wrote our code, foolishly putting Isaac in charge. Our (commented) code can be found here (add link later) COSY output shown below

4. Final x and y positions were determined to be x_f=.018 y_f=.009 at dE/E=.05

5. We used http://skisickness.com/2010/04/relativistic-kinematics-calculator/ to determine the recoil energy and angular distribution

5. Our energy spread is ~3.1%, the same as SECAR's 3.1% limit

6. Our opening angle is 7.0 mrad which is under the 25 mrad max of SECAR

7. Our reaction has been performed before at much lower energies. (~1MeV total)

→ 9/12

8. We finding three bibliographical information on the reaction(P-31(p,γ)S-32) our propose to study. 1. (http://www.publish.csiro.au/ph/pdf/PH750155) Total Yield Measurements 2. (http://www.publish.csiro.au/ph/pdf/PH750383) Accurate Branching Ratio Measurements 3. (https://ac.els-cdn.com/0375947469903352/1-s2.0-0375947469903352-main.pdf?_tid=6aa70e34-a7e3-49d4-8a85-e12712e5caa3&acdnat=1536684968_ccf8a340de1e4652e100ac01d110ea64) MECHANISM OF THE REACTION IN THE GIANT DIPOLE RESONANCE REGION

9. Xmax(g)=σ11(1+σ12L/σ11-Lg)+(εL)^2/σ22 We need to know the values of σ11, σ12, and σ22 to find the Emittance value. Changing Qurupole Strangth(g value) for make three equation. and using three eqaution find three unknown parameter(σ11, σ12, and σ22).

10. Extract the distance L for the center of quad Q7 to the focal plan FP2 (0.17005(center of quad)+0.5+2.365+0.5+0.26+0.28+0.26+1.75=6.08505)

11. In emittance script.fox plus 'WRITE 6 'VAMX :' VMAX(RAY(1)) ;' and extract VMAX Value.

12. Using σ11(1,K)=aK^2-2abK+ab^2+c Calculate σ11=2.7*10^-6 σ12=1.72*10^-6 σ22=0.14*10^-6 ε=0.794*10^-6

9-13-18

13. Original mass resolving power of SECAR before sections 3 and 4 is 742.3138003312769 when the order is set to 1. If resolving power is on the order of 1000, then you need to comment out section 3 and 4 in the fox file.

14. We increased the effective length of Q3 by 3% and also changing DL7 and DL8, so that the center of Q3 stays in the same place. This decreases the mass resolution to 602.6032654725383

15. We fit the strength of Q3 using the objective function OBJ:=1/ABS(Mass Resolution) + ABS(ME(1,2)/(XX)) . From this we found that we could recover the original resolving power by reducing the strength of Q3 by 3%. The ray paths are shown below.

16. We are now changing a variety of system parameters to see how much things can be changed before our mass resolution is changed by at least 5%.

BEAM SPOT: X width: <.714286mm >.789414mm (~.04mm tolerance) Y width: <.714286mm >.789414mm (~.04mm tolerance)

BEAM POSITION: X tolerance: -2.346mm/+2.148mm Y tolerance: -0.01166mmmm/+0.01168mm

QUADRUPOLE ALIGNMENT CHANGES: Q3: Z Position change by +/- 1mm (~1mm tolerance) X Position change by +/- .75mm Y Position change by +/- 8.45mm

Roll:

17. Ate Ice-Cream