General Particle Tracer GPT Simplified Simulations Counterwound Solenoids

Summary of Elegant Model • Beam characteristics Beam line element – pcentral= 1. 732

Summary of GPT Model • Magnet models – Solenoid • Counter-wound solenoid fieldmap •

Process 1. Find solenoid setting to focus beam at center of quad – All

Counter-Wound Solenoid Fieldmap Extent Solenoid S 1 Only 2 Cells (S 1, S 2,

Solenoid Focused at Quad (Quads Off) 1 Cell 2 Cells S 1=S 2=S 3=S

Solenoid Focused at Quad (Quads On) 1 Cell 2 Cells S 1=S 2=S 3=S

Solenoid Adjusted rinitial=rmiddle (Quads On) 1 Cell Step 2 Adjusted solenoid setting to make

Adjust S 2 and S 3 (Quads On) 2 Cells Step 3 S 1=S

Slides: 9

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General Particle Tracer (GPT) Simplified Simulations: Counter-wound Solenoids A. Hofler July 12, 2017 06/14/2017 1

Summary of Elegant Model • Beam characteristics Beam line element – pcentral= 1. 732 mec ⇒ Solenoid Ek=507. 7 ke. V – Q=0. 65 n. C ⇒ 325 m. A at Permanent Magnet 499 MHz Quadrupole (PMQ)* – �� x, y=7 mm Solenoid – �� =1. 16 ps t Solenoid – �� n(x, y)=1 mm mrad PMQ Solenoid Length (cm) Setting 5 0. 0293 T 0. 6* K 1=-133333 1/m 2 ⇒ -400 T/m* Center location (m) 0. 1860 1. 0029 5 0. 0293 T 1. 8198 5 0. 0293 T 2. 1918 0. 6* K 1=133333 1/m 2 ⇒ 400 T/m* 5 0. 0293 T 3. 0087 3. 8256 *R. K. Li and P. Musumeci, Phys. Rev. Applied 2 024003 (2014) 06/14/2017 2

Summary of GPT Model • Magnet models – Solenoid • Counter-wound solenoid fieldmap • Setpoint in Amps • Long field extent → shift Cell 2 0. 6 m to avoid fieldmap overlap – Quadrupole • Analytical model • no fringe fields • does not remove particles • Horizontally defocussing quad in first cell • Beam characteristics – ϒ=2 – Line of charge • 21 particles • Evenly distributed • 1 mm long in +x direction • (0, 0, 0) to (1, 0, 0) mm • Space charge off Beam line element Length Aperture (cm) Solenoid (S 1) 5 PMQ (Q 1) 0. 6* Attempted Setting 5. 4 0. 025 T ⇒ 2. 66 A 0. 3* 400 T/m* Center location (m) 1. 1 1. 9169 Solenoid (S 2) 5 5. 4 0. 025 T ⇒ 2. 66 A 2. 7338 Solenoid (S 3) 5 5. 4 0. 025 T ⇒ 2. 66 A 3. 7058 PMQ (Q 2) 0. 6* Solenoid (S 4) 5 0. 3* -400 T/m* 5. 4 0. 025 T ⇒ 2. 66 A 4. 5227 5. 3396 *R. K. Li and P. Musumeci, Phys. Rev. Applied 2 024003 (2014) 06/14/2017 3

Process 1. Find solenoid setting to focus beam at center of quad – All solenoids have same setting with quads off 2. With quads on, find a solenoid setting for all solenoids that restores the exit orbit 3. With quads on and focus setting for the outer solenoids, adjust center solenoid setting to restore exit orbit 06/14/2017 4

Counter-Wound Solenoid Fieldmap Extent Solenoid S 1 Only 2 Cells (S 1, S 2, S 3, S 4) 1 Cell (S 1 and S 2) The solenoid is 10. 16 cm long, but the residual field extends ± 45 cm from the center. 06/14/2017 5

Solenoid Focused at Quad (Quads Off) 1 Cell 2 Cells S 1=S 2=S 3=S 4=Sfocus Step 1 Adjusted solenoid S 1 to focus at center of Q 1 Sfocus=0. 025 T 06/14/2017 6

Solenoid Focused at Quad (Quads On) 1 Cell 2 Cells S 1=S 2=S 3=S 4=Sfocus Same solenoid setting as previous slide, Sfocus. Orbit distortion: On-axis beam is displaced after the Quad. 06/14/2017 7

Solenoid Adjusted rinitial=rmiddle (Quads On) 1 Cell Step 2 Adjusted solenoid setting to make rinitial=rmiddle with quad on. Sfocus=0. 025 T SCell 1=0. 99973 Sfocus 1 Cell 2 Cells S 1=S 2=S 3=S 4=SCell 1 06/14/2017 8 Orbit distortion: On-axis beam is displaced after the Quad and is not restored.

Adjust S 2 and S 3 (Quads On) 2 Cells Step 3 S 1=S 4=Sfocus S 2=S 3=�� 1 Sfocus �� 1=0. 9995 Orbit distortion: Onaxis beam is displaced after the Quad and is not restored. Step 3 S 1=S 4=Sfocus S 2=S 3=�� 2 Sfocus �� 2=1. 001249 Adjusted middle solenoid settings (�� ) to make rinitial=rfinal with quad on. 06/14/2017 9