Feature #1600
Analytical form for transfer matrix in transverse coordinates, arbitrary magnetic field
Start date:
16 December 2014
Due date:
% Done:
100%
Estimated time:
Description
attached...
Files
Updated by Rogers, Chris over 8 years ago
- Status changed from Open to Closed
- % Done changed from 0 to 100
Updated by Rogers, Chris about 8 years ago
- File 2015-08-27_17.25.44.jpg 2015-08-27_17.25.44.jpg added
- File 2015-08-27_17.25.52.jpg 2015-08-27_17.25.52.jpg added
- File 2015-08-27_17.26.05.jpg 2015-08-27_17.26.05.jpg added
Notes on error propagation through fields; these precede the notes above.
Updated by Rogers, Chris about 8 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>
Updated by Rogers, Chris over 7 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.
Updated by Rogers, Chris over 7 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).
Updated by Rogers, Chris over 7 years ago
- File 2016-02-25_10.12.27.jpg 2016-02-25_10.12.27.jpg added
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...
Updated by Rogers, Chris over 7 years ago
- File 2016-02-25_11.50.14.jpg 2016-02-25_11.50.14.jpg added
- File 2016-02-25_11.50.30.jpg 2016-02-25_11.50.30.jpg added
Updated equations for px, py