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Feature #1600

Analytical form for transfer matrix in transverse coordinates, arbitrary magnetic field

Added by Rogers, Chris about 3 years ago. Updated almost 2 years ago.

Status:
Closed
Priority:
Normal
Assignee:
Start date:
16 December 2014
Due date:
% Done:

100%


Description

attached...

2014-12-16_13.34.24.jpg (1.09 MB) Rogers, Chris, 16 December 2014 13:41

2014-12-16_13.34.41.jpg (1.06 MB) Rogers, Chris, 16 December 2014 13:41

2014-12-16_13.34.51.jpg (1.08 MB) Rogers, Chris, 16 December 2014 13:41

2014-12-16_13.35.00.jpg (1.08 MB) Rogers, Chris, 16 December 2014 13:41

2014-12-16_13.37.17.jpg (1.01 MB) Rogers, Chris, 16 December 2014 13:41

2015-08-27_17.25.44.jpg (1.16 MB) Rogers, Chris, 27 August 2015 17:29

2015-08-27_17.25.52.jpg (1.12 MB) Rogers, Chris, 27 August 2015 17:29

2015-08-27_17.26.05.jpg (1.05 MB) Rogers, Chris, 27 August 2015 17:29

2016-02-25_10.12.27.jpg (1.1 MB) Rogers, Chris, 25 February 2016 10:17

2016-02-25_11.50.14.jpg (1.04 MB) Rogers, Chris, 25 February 2016 11:53

2016-02-25_11.50.30.jpg (1.03 MB) Rogers, Chris, 25 February 2016 11:53

History

#1 Updated by Rogers, Chris almost 3 years ago

  • Status changed from Open to Closed
  • % Done changed from 0 to 100

#2 Updated by Rogers, Chris over 2 years ago

Notes on error propagation through fields; these precede the notes above.

#3 Updated by Rogers, Chris over 2 years ago

Note that in "propagation of errors" note number 2:

  • (page 1) I have used the Einstein summation notation when I do the Taylor series expansion
  • (page 2) D matrix is the matrix with elements <du_i du_j>

#4 Updated by Rogers, Chris almost 2 years ago

I noticed that the 1/pz term for t vs E in 2014-12-16_13.35.00.jpg should be 1/(pz beta^2 gamma ^2). 1/pz is the absolute value, not the derivative.

#5 Updated by Rogers, Chris almost 2 years ago

I note I dropped a factor 1/pz in the bottom left hand square of M_d in http://micewww.pp.rl.ac.uk/attachments/3173/2014-12-16_13.35.00.jpg

So elements m_31, m_32, m_41, m_42 (indexing from 1 through 4).

#6 Updated by Rogers, Chris almost 2 years ago

Also correction to the 0, 1, 2 row in 2016-02-25 10.12.27.jpg ; I am checking everything against numerical derivatives, a few more errors to fix...

#7 Updated by Rogers, Chris almost 2 years ago

Updated equations for px, py

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