TwissOptics Class Joschua Dilly TwissOptics Class 2 The - PowerPoint PPT Presentation

TwissOptics Class Joschua Dilly TwissOptics Class 2

The TwissOptics Class Resonance Driving Terms Linear Dispersion Coupling Chromatic Beating Conclusion To do TwissOptics Class 3

The TwissOptics Class TwissOptics Class 4

New class for TwissOptics • Based around tfs pandas • Analytical calculations for optic parameters • Plotting of results • Calculates response matrix analytically TwissOptics Class 5

Implemented Analytical Functions • Resonance Driving Terms (general formula) • Linear Dispersion • Linear Chromaticity • Chromatic Beating TwissOptics Class 6

Resonance Driving Terms TwissOptics Class 7

Resonance Driving Terms • Two octupoles active ( K 3 L � = 0) • Comparison with MADX-PTC: Time to calculate RDTs in TwissOptics: 0.601843s f4000 relative RMS: 0.000393362 f3100 relative RMS: 0.000601316 f2020 relative RMS: 0.000375948 f2011 relative RMS: 0.000470409 f2002 relative RMS: 0.000188584 f1120 relative RMS: 0.000130547 f0040 relative RMS: 0.00993668 f0031 relative RMS: 0.00442634 TwissOptics Class 8

Resonance Driving Term '|f1120|' Resonance Driving Term '|f1120|' - Error 1e4 1e 4 Analytical error 3.2 4 MADX-PTC 3.0 3 2.8 2 | f 1120| 2.6 | f 1120| 1 2.4 0 2.2 1 2.0 2 1.8 3 1.6 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Longitudinal location [m] Longitudinal location [m] | F 1120 | • Relative RMS: 0.0130547% TwissOptics Class 9

Resonance Driving Term '|f0040|' Resonance Driving Term '|f0040|' - Error 1e 2 Analytical error 600 MADX-PTC 1.0 550 0.5 500 | f 0040| | f 0040| 450 0.0 400 0.5 350 300 1.0 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Longitudinal location [m] Longitudinal location [m] | F 0040 | • Relative RMS: 0.993668% TwissOptics Class 10

Linear Dispersion TwissOptics Class 11

Linear Dispersion • 4 skew Quadrupoles active ( K 1 SL � = 0) • 2572 Dipoles active ( K 0 L � = 0) • Comparison with MADX: Time to calculate linear dispersion in TwissOptics: 0.294876s DX relative RMS: 0.00154571 DY relative RMS: 0.000185216 TwissOptics Class 12

Linear Dispersion DX Linear Dispersion DX - Error 3 Analytical error 0.06 MADX 2 0.04 0.02 1 D X [ m ] D X [ m ] 0.00 0 0.02 1 0.04 0.06 2 0.08 3 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Longitudinal location [m] Longitudinal location [m] Dispersion X-Plane • Relative RMS: 0.154571% TwissOptics Class 13

Linear Dispersion DY Linear Dispersion DY - Error 1e 3 1e 2 Analytical error 6 MADX 0.2 5 0.0 4 0.2 D Y [ m ] D Y [ m ] 3 0.4 2 0.6 1 0.8 0 1 1.0 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Longitudinal location [m] Longitudinal location [m] Dispersion Y-Plane • Relative RMS: 0.0185216% TwissOptics Class 14

Coupling TwissOptics Class 15

Coupling • 8 skew Quadrupoles active ( K 1 SL � = 0) • Timing: Time to calculate coupling in TwissOptics: 0.142169s TwissOptics Class 16

Coupling Term '|F1001|' - TwissOptics Coupling Term '|F1010|' - TwissOptics 1e 3 1e 3 7.50 Analytical Analytical 1.0 7.25 7.00 0.8 6.75 | F 1001| | F 1010| 6.50 0.6 6.25 0.4 6.00 5.75 0.2 5.50 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Longitudinal location [m] Longitudinal location [m] Coupling Terms • No MADX comparison yet TwissOptics Class 17

Chromatic Beating TwissOptics Class 18

Chromatic Beating • 2360 Quadrupoles active ( K 1 L � = 0) • 344 Sextupoles active ( K 2 L � = 0) • 0 skew Sextupoles active ( K 2 SL � = 0) • Timing: Calculating Chromatic Beating Time needed: 3.251451 Pk2Pk chromatic beating DBEATX: 39.9491 Pk2Pk chromatic beating DBEATY: 20.9073 TwissOptics Class 19

Chromatic Beating 20 DBEATX DBEATY 15 10 x , y 5 x , y / 0 x , y 5 1/ 10 15 20 IP1 IP1 IP2 IP2 IP3 IP3 IP4 IP4 IP5 IP5 IP6 IP6 IP7 IP7 IP8 IP8 0 5000 10000 15000 20000 25000 Longitudinal location [m] Chromatic Beating • No MADX comparison yet TwissOptics Class 20

Conclusion TwissOptics Class 21

Conclusion • Analytical Formulas evaluate fast • Results close to MADX where comparison was done • Results seem reasonable, where comparison was not yet done TwissOptics Class 22

To do TwissOptics Class 23

To do • MADX comparison: Coupling, Chromatic Beating • Implement phase-advance calculation ( 90% done) • Depends on δ K 1 instead of K 1: How to implement best? • Implement Response Matrix • Analytical Formulas only for ∆Φ and Dispersion • Can be implemented quickly, as the formulas are similar to already implemented ones • New Class? TwissOptics Class 24