1. Comparing Original MAGIC Sim Polar Vs Cylindrical Coordinates at Alpha = 1.65

Original magic geometry with the superconducting magnetic field Dr. Craig Donaldson 21-09-2015 1. Comparing original MAGIC sim Polar Vs Cylindrical coordinates at Alpha = 1.65 The cylindrical coordinate system is needed in order to import a magnetic field. So I need to be sure the magic sim is still the same as before and geometry acts the same. So here is the comparison between the two simulations. Polar coordinated: (R,Theta,Z) , Cylindrical coordinates: (Z,R,Theta) Pz

Alpha:

Here polar coordinates is plotted in RED, cylindrical coordinates in BLUE Pz (%) Alpha (%) Radius (%) Alpha Polar 8.50 11.24 55 1.66 Cylindrical 8.50 11.24 55 1.66 2. Comparing original MAGIC sim Polar Vs Cylindrical coordinates at Alpha = 1.2 The alpha value is set at 1.2 here. Still comparing Polar vs Cylindrical coordinates Pz

Pz (%) Alpha (%) Radius (%) Alpha Polar 14.1 22.82 94 1.2 Cylindrical 14.1 22.82 94 1.2 3. Comparing cylindical MAGIC sim old coil VS imported magnetic field at Alpha = 1.2 In this section I will compare the old magic magnetic field setup VS the magnetic field imported from text file from the superconducting magnet.

Fig. Comparison of superconducting vs original magnetic field 3. Comparing solenoids VS superconducting field at Alpha = 1.2 The alpha value is set at 1.2 here and we are comparing the original magnetic field vs the superconducting magnetic field Pz

Pz (%) Alpha (%) Radius (%) Alpha Solenoid 14.27 23.52 1.2 Superconducting 92.40 117.06 2.315

Trajectories of Solenoid vs Superconducting simulations Region 1 Solenoid

Superconducting Region 2 Solenoid

Superconducting Region 3 Solenoid

Superconducting 4. Change the cathode-anode spacing The alpha value is set at 1.2 here and we are comparing the original magnetic field vs the superconducting magnetic field

Real gap Change gap Pz Alpha How much is Reflecting 3.5 -1 N/A N/A 7.7% 4.5 0 89.6% 114% No 5.5 +1 44.64% 64.47% No 6.5 +2 N/A N/A 7.7% 7.5 +3 N/A N/A 23%

Here is the Pz plot to compare cathode-anode gap of 0mm and +1mm 5. Change the position of the superconducting magnetic field Shifting the position of the magnetic field will increase/decrease the negative magnetic field the electron beam travels through and shifts the positon of the cusp. This is based from the previous simulation with the cathode-anode gap +1mm.

Shift Z Pz (%)  (%) Ave.  +7 mm 87.35 110.38 2.404 +4 mm 56.09 76.91 1.718 +2 mm 50.43 70.72 1.611 0 44.64 64.47 1.5 -2 mm 38.15 58.32 1.406 -4 mm 32.47 51.84 1.297 -7 mm 23.65 41.66 1.147 -8 mm 20.22 38.43 1.098 -9 mm 18.30 35.17 1.052 -10 mm 16.00 32.00 1.00 -11 mm 13.80 21.12 0.985 -12 mm 11.88 26.73 0.898 -13 mm 10.14 24.20 0.843 -14 mm 9.42 24.57 0.794 6. Change the whole anode radius This change is based on the solenoid position -7mm result. I use this result because the average alpha is 1.2 roughly.

What I am doing is is moving the anode nose up or down in radius. The entire anode moves

Anode R change Pz (%) Alpha (%) R (%) Alpha +0.5 mm 66.53 92.03 130.8 1.751 +0.25 mm 25.62 43.09 98.70 1.159 0 23.65 41.66 1.147 -0.25 mm 22.41 40.25 100 1.138 -0.5 mm 21.48 38.48 102.07 1.131 -0.75 mm 20.68 36.76 105.76 1.124 -1.0 mm 20.43 35.29 109.40 1.122

7. Change the anode nose radius

Based on the anode = 0 result. Anode R change Pz (%) Alpha (%) R (%) Alpha +1.5 mm 24.99 43.46 1.167 +1.0 mm 24.91 43.71 1.165 +0.5 24.61 43.28 1.158 0 mm 23.65 41.66 1.147 -0.5 mm 22.44 40.19 1.123 -1.0 mm 21.13 37.48 1.123 -1.5 mm 20.23 35.72 1.123 The anode nose -1.5mm gives the best result. Use this for future optimisations Based on the anode = -1.0 result. Anode R change Pz (%) Alpha (%) R (%) Alpha +1.5 mm +1.0 mm +0.5 0 mm 20.43 35.29 109.40 1.122 -0.5 mm 26.43 44.21 1.208 -1.0 mm 38.11 58.61 1.374 -1.5 mm 64.22 85.71 1.813

6. Change the top focusing electrode This change is based on the solenoid position -7mm result. I use this result because the average alpha is 1.2 roughly.

What I am doing is changing the geometry of the top focusing electrode. R1 = 7.4mm is the original value.

R1 change Pz (%) Alpha (%) R (%) Alpha 7.6 mm 24.67 41.09 117.67 1.178 7.5 mm 21.12 37.22 113.25 1.137 7.4 mm 23.65 41.66 1.147 7.3 mm 24.31 42.84 98.51 1.153 7.2 mm 26.68 46.02 97.27 1.176

8. Change the emitted voltage 9. Change the emitted current

10. Compare different magnetic field profiles Here I change the negative magnetic field at the cathode to see if the electron beam will improve. The B-field is shown in the graph below.

Bz min = 3.5mT Bz min = 3.75mT Bz min = 4.0mT Shift Z Pz (%)  (%) Ave.  Pz (%)  (%) Ave.  Pz (%)  (%) Ave.  +7 mm 87.35 110.38 2.404 +4 mm 56.09 76.91 1.718 +2 mm 50.43 70.72 1.611 0 44.64 64.47 1.5 50.66 70.38 1.671 70.68 88.77 2.154 -2 mm 38.15 58.32 1.406 43.88 63.25 1.540 58.51 76.85 1.879 -4 mm 32.47 51.84 1.297 37.29 57.27 1.415 48.84 67.23 1.688 -6 mm 23.65 41.66 1.147 30.97 49.62 1.302 39.38 57.62 1.503 -8 mm 20.22 38.43 1.098 24.60 42.53 1.188 24.60 48.96 1.348 -9 mm 18.30 35.17 1.052 -10 mm 16.00 32.00 1.00 18.76 35.50 1.076 23.99 40.96 1.206 -11 mm 13.80 21.12 0.985 -12 mm 11.88 26.73 0.898 13.62 28.42 0.966 17.39 33.01 1.076 -13 mm 10.14 24.20 0.843 -14 mm 9.42 24.57 0.794 9.69 23.51 0.847 12.17 25.95 0.948