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

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

Feb 22, 2024 208 likes •454 views

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

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SLIDE 1
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SLIDE 2

TwissOptics Class

Joschua Dilly

TwissOptics Class 2

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SLIDE 3

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

TwissOptics Class 3

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SLIDE 4

The TwissOptics Class

TwissOptics Class 4

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SLIDE 5

New class for TwissOptics

  • Based around tfs pandas
  • Analytical calculations for optic parameters
  • Plotting of results
  • Calculates response matrix analytically

TwissOptics Class 5

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SLIDE 6

Implemented Analytical Functions

  • Resonance Driving Terms (general formula)
  • Linear Dispersion
  • Linear Chromaticity
  • Chromatic Beating

TwissOptics Class 6

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SLIDE 7

Resonance Driving Terms

TwissOptics Class 7

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SLIDE 8

Resonance Driving Terms

  • Two octupoles active (K3L = 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

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SLIDE 9

TwissOptics Class 9

5000 10000 15000 20000 25000

Longitudinal location [m]

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

|f1120|

1e4

Resonance Driving Term '|f1120|'

Analytical MADX-PTC 5000 10000 15000 20000 25000

Longitudinal location [m]

3 2 1 1 2 3 4

|f1120|

1e 4

Resonance Driving Term '|f1120|' - Error

error

|F1120|

  • Relative RMS: 0.0130547%
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SLIDE 10

TwissOptics Class 10

5000 10000 15000 20000 25000

Longitudinal location [m]

300 350 400 450 500 550 600

|f0040|

Resonance Driving Term '|f0040|'

Analytical MADX-PTC 5000 10000 15000 20000 25000

Longitudinal location [m]

1.0 0.5 0.0 0.5 1.0

|f0040|

1e 2

Resonance Driving Term '|f0040|' - Error

error

|F0040|

  • Relative RMS: 0.993668%
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SLIDE 11

Linear Dispersion

TwissOptics Class 11

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SLIDE 12

Linear Dispersion

  • 4 skew Quadrupoles active (K1SL = 0)
  • 2572 Dipoles active (K0L = 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

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SLIDE 13

TwissOptics Class 13

5000 10000 15000 20000 25000

Longitudinal location [m]

3 2 1 1 2 3

DX[m]

Linear Dispersion DX

Analytical MADX 5000 10000 15000 20000 25000

Longitudinal location [m]

0.08 0.06 0.04 0.02 0.00 0.02 0.04 0.06

DX[m]

Linear Dispersion DX - Error

error

Dispersion X-Plane

  • Relative RMS: 0.154571%
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SLIDE 14

TwissOptics Class 14

5000 10000 15000 20000 25000

Longitudinal location [m]

1 1 2 3 4 5 6

DY[m]

1e 3

Linear Dispersion DY

Analytical MADX 5000 10000 15000 20000 25000

Longitudinal location [m]

1.0 0.8 0.6 0.4 0.2 0.0 0.2

DY[m]

1e 2

Linear Dispersion DY - Error

error

Dispersion Y-Plane

  • Relative RMS: 0.0185216%
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SLIDE 15

Coupling

TwissOptics Class 15

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SLIDE 16

Coupling

  • 8 skew Quadrupoles active (K1SL = 0)
  • Timing:

Time to calculate coupling in TwissOptics: 0.142169s

TwissOptics Class 16

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SLIDE 17

TwissOptics Class 17

5000 10000 15000 20000 25000

Longitudinal location [m]

5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50

|F1001|

1e 3

Coupling Term '|F1001|' - TwissOptics

Analytical 5000 10000 15000 20000 25000

Longitudinal location [m]

0.2 0.4 0.6 0.8 1.0

|F1010|

1e 3

Coupling Term '|F1010|' - TwissOptics

Analytical

Coupling Terms

  • No MADX comparison yet
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SLIDE 18

Chromatic Beating

TwissOptics Class 18

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SLIDE 19

Chromatic Beating

  • 2360 Quadrupoles active (K1L = 0)
  • 344 Sextupoles active (K2L = 0)
  • 0 skew Sextupoles active (K2SL = 0)
  • Timing:

Calculating Chromatic Beating Time needed: 3.251451 Pk2Pk chromatic beating DBEATX: 39.9491 Pk2Pk chromatic beating DBEATY: 20.9073

TwissOptics Class 19

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SLIDE 20

TwissOptics Class 20

5000 10000 15000 20000 25000

Longitudinal location [m]

20 15 10 5 5 10 15 20

1/

x, y x, y/ x, y IP2 IP3 IP1 IP6 IP7 IP4 IP5 IP8 IP2 IP3 IP1 IP6 IP7 IP4 IP5 IP8

Chromatic Beating

DBEATX DBEATY

Chromatic Beating

  • No MADX comparison yet
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SLIDE 21

Conclusion

TwissOptics Class 21

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SLIDE 22

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

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SLIDE 23

To do

TwissOptics Class 23

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SLIDE 24

To do

  • MADX comparison: Coupling, Chromatic Beating
  • Implement phase-advance calculation ( 90% done)
  • Depends on δK1 instead of K1: 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