Title                  :TRANSPORT
Keywords               :Optics, Quadropoles, Sextapoles, Bending Magnets, EELS
Computer               :DEC VAX 11/730-785
Operating System       :VAXVMS, 
Programming Language   :Fortran IV
Hardware Requirements  :None
Author(s)              :K.L.Brown, F.Rothacker D.C., Carey, Ch. Iselin
Correspondence Address :Stanford linear Accelerator Center, Stanford CA. USA 
                       :Fermi National Accelerator Lab. Batavia, IL. USA
		       : CERN, Geneva, Switzerland

Documentation: 
	
	A 256 page instruction manual on the operation of TRANSPORT is
available from: The Reports Office, Fermi National Accelerator Laboratory, 
P.O. Box 500, Batavia IL 60510, USA (Ref. NAL-91, "Transport Appendix")

The following general information can be used to generate a running version
of TRANSPORT on a VAX system.  Additional code is available from the 
authors for the following computers: IBM (Mainframe), CDC, PDP 10
------------------------------------------------------------------------------

General Information:

      PRODUCT:        TRANSPORT
      VERSION:        VAX/VMS  
      DOCUMENT NAME:  PM0008  
 
      TRANSPORT IS A BEAM LINE OPTICS PROGRAM.
      (REFER TO DOCUMENT PM0008 FOR FURTHER INFORMATION)
      
      TRANSPORT WAS MODIFIED FOR THE VAX ON AUG. 7, 1985
      BY SUSAN SISSELMAN, FERMI NATIONAL LABORATORY
 
      TRANSPORT.DAT MAY BE USED TO TEST TRANSPORT.  
      ASSIGN TRANSPORT.DAT FOR005
 
      NOTE: THIS DATA DOES NOT GENERATE THE RANDON GENERATOR.

Compilation and Linking Procedure on a VAX:
-------------------------------------------


$!	[LIB.TRANSPORT]GENERATE.COM	7 AUG 85
$!
$!
$ WRITE SYS$OUTPUT " Compiling TRANSPORT ..."
$ FORTRAN TRANSPORT.FOR
$ WRITE SYS$OUTPUT " Linking   TRANSPORT ..."
$ LINK TRANSPORT
$ DELETE TRANSPORT.OBJ
$ WRITE SYS$OUTPUT " Linking   TRANSPORT ..."
$ WRITE SYS$OUTPUT " TRANSPORT is now ready for use !"

	
Listing of changes made to this version of TRANSPORT
----------------------------------------------------
 
 3 JAN 86	A. Kreymer
	Modified GENERATE to report progress, bell at end, delete .OBJ file
 
7 JULY 1985
	COPIED CYBER VERSION OF TRNSPRT
 
7 AUG  1985       
     CONVERSIONS MADE IN CHANGING PROGRAM FROM CDC VERSION TO VAX VERSION
 
              CDC                                     VAX
              ---                                     ---
1.   PROGRAM NAME - LINE 1               OMITTED PARENTHESIS WITH DEVICE NAMES  
                                         MADE INTO A COMMENT
2.   SUBROUTINE RDPACK                   READ A CHARACTER IN USING INTEGER DATA
     REORGANIZED                         CONVERTED TO CHARACTER DATA
                                         USING AN INTERNAL READ
3.   RANSET, RANGET, RANST               RESTRUCTURED AND COMBINED
                                         INTO FUNCTION RANNU
4.   RANSET  -  CLOCK                    REPLACED BY:   SECONDS
5.   FUNCTION RANNU                      REPLACED BY:   RAN(ISEED)
     RESTRUCTURED                        ISEED SET TO A LARGE ODD INTEGER


Test Data for Evalutation of Transport Code: TRANSPORT.DAT
----------------------------------------------------------

 ' CHECK DECK FOR TRANSPORT/360 MATRIX ELEMENTS K L BROWN OCT. 10 1969'         
 0        
 (THIS TEST DECK IS DESIGNED TO CHECK ALL OF THE MATRIX ELEMENTS IN THE )       
(SLAC TRANSPORT/360 PROGRAM.  IT IS NOT INTENDED TO CHECK PROGRAM LOGIC NOR  )  
 (FITTING ROUTINES.  IF THIS CHECK DECK IS VERIFIED, THE MATRIX OUTPUT)         
(TABULATIONS OF A TRANSPORT CALCULATION SHOULD BE CORRECT PROVIDED THAT)        
(NO INSERTS ARE MADE BETWEEN A TYPE CODE 2.0 AND A TYPE CODE 4.0 ELEMENT)       
(IN THE PROGRAM LISTING.       KARL L BROWN OCTOBER 1969)   
 SENTINEL 
 '(1)   DRIFT MATRIX    L= 10 METERS    NORMALIZED UNITS               '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.  299.792458 ; 13. 2. ; 3. 10. ; 13. 4. ;        
13.       1.        ;         
 (IN THE DIMENSIONS CHOSEN FOR THIS PROBLEM, THE R12 MATRIX ELEMENT)  
 (SHOULD EQUAL 10.0 METERS/RADIAN)      
 SENTINEL 
 '(2)  QUADRUPOLE MATRIX    K= 1/2   KL= 30 DEGREES   NORMALIZED UNITS '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
    1. 2. 3. 4. 5. 6. 7.   2997.92458  ;    13. 2.  ;  17. ;
  5.00 1.04719  5.00 0.2    ;    13. 4.   ;       
13.       1.        ;         
 (THE NUMERICAL VALUES OF THE 1ST AND 2ND ORDER QUADRUPOLE MATRIX ELEMENTS)     
 (IN THIS CALCULATION SHOULD AGREE WITH THE QUADRUPOLE MATRIX ELEMENT EQUATIONS)
 (ON PAGES 68 AND 69 OF SLAC  REPORT NO. 75. BY K.L. BROWN.  THE NORMALIZED)    
 (DIMENSIONS USED IN THIS CALCULATION, AS DETERMINED BY THE 15 TYPE)  
 (CODES ENTRIES, ARE AS FOLLOWS@D TRANSVERSE DIMENSIONS X AND Y ARE IN METERS,) 
 (TRANSVERSE ANGLES THETA AND PHI ARE IN RADIANS, AND MOMENTUM DEVIATION)       
 (DELTA P/P IS FRACTIONAL .  THE CENTRAL MOMENTUM IS CHOSEN AS P=BR=100 KG)     
 (METERS FOR THIS CALCULATION.)         
 SENTINEL 
 '(3)  PSI CORRECTION TO INPUT FRINGE FIELD  G/R=0.2  K1=0.7           '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
 16. 5. 0.1 'G/2'  ;   16. 7. 0.7 'K1'  ;         
 2. 30.  ;  4. .00001 10. 0.  ;   13. 4. ;        
13.       1.        ;         
 (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM)        
 (TO THE TRANSVERSE FOCAL LENGTH OF A ROTATED ENTRANCE FACE OF A BENDING)       
 (MAGNET RESULTING FROM THE FINITE EXTENT OF THE FRINGING FIELDS.  THE )        
 (DEFINITION OF PSI AND THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN) 
 (ON PAGES 73 AND 74 OF SLAC 75.  NORMALIZED DIMENSIONS ARE USED AS IN THE)     
 (PRECEDING PROBLEM.  FOR THIS CALCULATION ; BR=10 KG METERS, R=1.0 METERS,)    
 (G/R=0.2 AND K1=0.7  WHERE R=THE RADIUS OF THE CENTRAL ORBIT, G=THE GAP OF THE)
 (MAGNET AND K1 IS AN INTEGRAL OF THE FRINGING FIELD DEFINED ON PAGE 74 OF)     
 (SLAC 75.)         
 SENTINEL 
 '(4)  PSI CORRECTION TO INPUT FRINGE FIELD  G/R=0.2  K1=0.7  K2=3.0   '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458  ;  13. 2.   ; 
  16. 5. 0.1 'G/2'  ;    16. 7. 0.7 'K1'  ;    16. 8. 3.0 'K2'  ;     
 2. 30.  ;  4. .00001 10. 0.  ;   13. 4. ;        
13.       1.        ;         
 (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM)        
 (TO THE TRANSVERSE FOCAL LENGTH OF A ROTATED ENTRANCE FACE OF A BENDING)       
 (MAGNET RESULTING FROM THE FINITE EXTENT OF THE FRINGING FIELDS.  THE )        
 (DEFINITION OF PSI AND THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN) 
 (ON PAGES 73 AND 74 OF SLAC 75.  NORMALIZED DIMENSIONS ARE USED AS IN THE)     
 (PRECEDING PROBLEM.  BR=10 KG METERS, R=1.0 METERS, G/R=0.2, K1=0.7, AND)      
 (K2=3.0  K2 IS DEFINED IN THE TRANSPORT/360 INSTRUCTION MANUAL.)     
 SENTINEL 
 '(5)  PSI CORRECTION TO OUTPUT FRINGE FIELD  G/R=0.2  K1=0.7          '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
 16. 5. 0.1 'G/2' ;    16. 7. 0.7 'K1'  ;         
  4. .00001 10. 0.   ;   2. 30.   ;   13. 4.   ;  
13.       1.        ;         
 (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM TO THE) 
 (TRANSVERSE FOCAL LENGTH OF A ROTATED EXIT FACE OF A BENDING MAGNET RESULTING) 
 (FROM THE FINITE EXTENT OF THE FRINGING FIELDS.  THE DEFINITION OF PSI AND)    
 (THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN ON PAGES 74 AND 75 OF) 
 (SLAC 75.  NORMALIZED DIMENSIONS ARE USED AS IN THE PRECEDING PROBLEM.)        
 (BR=10 KG METERS, R=1.0 METERS, G/R=0.2, AND K1=0.7  )     
 SENTINEL 
 '(6)  PSI CORRECTION TO OUTPUT FRINGE FIELD  G/R=0.2  K1=0.7  K2=3.0  '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458  ;  13. 2.   ; 
  16. 5. 0.1 'G/2'  ;    16. 7. 0.7 'K1'  ;    16. 8. 3.0 'K2'  ;     
  4. .00001 10. 0.   ;   2. 30.   ;   13. 4.   ;  
13.       1.        ;         
 (THIS CALCULATION COMPUTES THE PSI CORRECTION TERM TO THE TRANSVERSE FOCAL)    
 (LENGTH OF A ROTATED EXIT FACE OF A BENDING MAGNET RESULTING FROM THE FINITE)  
 (EXTENT OF THE FRINGING FIELDS.  THE DEFINITION OF PSI AND THE EQUATION FOR )  
 (THE TRANSVERSE FOCAL LENGTH ARE GIVEN ON PAGES 74 AND 75 OF SLAC 75.)         
 (NORMALIZED DIMENSIONS ARE USED AS IN THE PRECEDING PROBLEM.)        
 (BR=10 KG METERS, R=1.0 METERS, G/R=0.2, K1=0.7, AND K2=3.0)         
  SENTINEL
 '(7)  2ND ORDER  INPUT FRINGE FIELD  R(2,1) = 1.0  R=1/2  R1= 2.0     '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7. 299.792458  ;  13. 2.  ;   17. ;      
  16. 5. .05 'G/2'  ;    16. 7. 0.7 'K1'  ;    16. 8. 3.0 'K2'  ;     
  16. 12. 0.5 '1/R1'  ;       
  2. 26.566  ; 4.  .00001  20. 0.5   ;              13. 4.  ;         
13.       1.        ;         
 (THIS CALCULATION IS INTENDED TO CHECK BOTH THE 1ST AND 2ND ORDER)   
 (INPUT FRINGING FIELD MATRIX ELEMENTS OF A BENDING MAGNET AND COMPARE THE)     
 (RESULTS WITH PAGES 71 THROUGH 75 OF SLAC 75.  FOR THIS CALCULATION THE )      
 (FOLLOWING PARAMETERS WERE CHOSEN@D  BR=10 KG METERS, R=1/2 METER, TAN BETA=1/2)         
 (R1=2 METERS.  G/R=0.2,  K1=0.7, AND K2=3.0  NORMALIZED UNITS ARE )  
 (USED FOR THE TRANSVERSE DIMENSIONS.)  
  SENTINEL
 '(8)  2ND ORDER OUTPUT FRINGE FIELD  R(2,1) = 1.0  R=1/2  R2= 2.0     '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7. 299.792458  ;  13. 2.  ;   17. ;      
  16. 5. .05 'G/2'  ;    16. 7. 0.7 'K1'  ;    16. 8. 3.0 'K2'  ;     
  16. 13. 0.5 '1/R2'  ;       
  4.  0.00001 20. 0.5 ;   2.0  26.566  ;  13. 4.  ;         
13.       1.        ;         
 (THIS CALCULATION IS INTENDED TO CHECK BOTH THE 1ST AND 2ND ORDER OUTPUT)      
 (FRINGING FIELD MATRIX ELEMENTS OF A BENDING MAGNET AND COMPARE THE RESULTS)   
 (WITH PAGES 71 THROUGH 75 OF SLAC 75.  FOR THIS CALCULATION THE FOLLOWING)     
 (PARAMETERS WERE CHOSEN@D  BR=10 KG METERS, R=1/2 METER, TAN BETA=1/2,)        
 (R2=2 METERS.  G/R=0.2,  K1=0.7, AND K2=3.0  NORMALIZED UNITS ARE USED FOR)    
 (THE TRANSVERSE DIMENSIONS)  
  SENTINEL
 '(9)  SEXTUPOLE MATRIX  K(S)SQUARED = 10.0  L =0.1 METERS  NORM UNITS '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
                         15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
    1. 2. 3. 4. 5. 6. 7.    2997.92458   ;    13. 2.  ;   17. ;       
  18. 0.1 10. 0.1   ;   13. 4.   ;      
13.       1.        ;         
 (THESE RESULTS SHOULD BE COMPARED WITH THE MATRIX ELEMENTS LISTED ON PAGES)    
 (69 AND 70 OF SLAC 75 FOR THE SEXTUPOLE.  KS SQUARED=10. L=0.1, AND BR=100 KG) 
 (METERS.  NORMALIZED TRANSVERSE UNITS ARE USED.) 
  SENTINEL
 '(10)  ACCELERATOR MATRIX     STANDARD UNITS ARE USED  ( SEE BELOW )  '        
  0       
 15. 1. ' CM'  1.  ;   15. 2. ' MR' 1.  ;   15. 5. ' CM' 1. ;         
 15. 8.  '  M' 1.  ;     15. 11. 'GEV'  1.  ;   15. 6. ' PC'  1.   ;  
-16.  3.  1836.  'MASS'  ;    
 1. 2. 3. 4. 5. 6. 7. 10.   ; 
 11. 10. 0.10 30. 1.00   ;      13. 4.   ;        
 (THE ANALYTICAL EXPRESSIONS FOR THE ACCELERATOR MATRIX ELEMENTS ARE LISTED)    
 (IN THE TRANSPORT/360 MANUAL AS DERIVED BY K.L. BROWN.  THIS CALCULATION)      
 (HAS BEEN MADE IN STANDARD TRANSPORT UNITS@D X,Y IN CMS, THETA AND PHI IN )    
 (MILLIRADIANS AND DELTA P/P IN PERCENT.  THE PARAMETERS CHOSEN FOR THE)        
 (CALCULATION ARE E=10 GEV, DELTA E=0.1 GEV, THE PHASE LAG=30 DEGREES AND)      
 (THE WAVELENGTH = 1 CM.        )       
 SENTINEL 
 '(10)  ACCELERATOR MATRIX     NONZERO MASS FOR PARTICLE  ' 
 1        
16.  'MASS'  ;      
SENTINEL  
 '(11)  SOLENOID MATRIX  K = 1/4  KL = 30 DEGREES   NORMALIZED UNITS   '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
    1. 2. 3. 4. 5. 6. 7.    299.792458   ;  13. 2.  ;       
 17. ;    
 19. 209.44 5.0  ;                 13. 4.  ;      
13.       1.        ;         
(THE ANALYTICAL EXPRESSIONS FOR THE SOLENOID MATRIX ELEMENTS ARE LISTED)        
 (IN THE TRANSPORT/360 INSTRUCTION MANUAL AS DERIVED FROM R H HELMS SLAC )      
 (REPORT NO. 4.  FOR THE SOLENOID K=B/2BR WHERE B IS THE MAGNETIC FIELD IN THE) 
 (SOLENOID AND BR = P = THE PARTICLE MOMENTUM.  FOR THIS CALCULATION THE )      
 (MOMENTUM BR = 10 KG METERS, B = 5 KG ;  FROM WHICH K = 1/4.  KL = 30 DEGREES) 
 (IS CHOSEN FOR EASE OF CHECKING.  NORMALIZED TRANSVERSE UNITS ARE USED FOR THE)
 (CALCULATION.)     
 SENTINEL 
 '(12)  SOLENOID + COORDINATE ROTATION  K = 1/4    KL = 30 DEGREES     '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
    1. 2. 3. 4. 5. 6. 7.    299.792458   ;  13. 2.  ;       
 17. ;    
 19. 209.44 5.0  ;  20. -30.   ;   13. 4.  ;      
13.       1.        ;         
 (IF THE TRANSVERSE COORDINATES ARE ROTATED ABOUT THE Z AXIS OF A SOLENOID BY)  
 (AN ANGLE OF -KL ,  THEN THE X AND Y 1ST ORDER MATRIX ELEMENTS ARE DECOUPLED.) 
 (THUS IN THIS TEST CASE THE MATRIX ELEMENTS R13=R14=R23=R24=R31=R32=R41=R42)   
 (ALL SHOULD BE EQUAL TO ZERO.  THIS PROVIDES A TEST FOR THE SOLENOID MATRIX)   
 (ELEMENTS AS WELL AS THE Z ROTATION MATRIX.)     
 SENTINEL 
 '(13)  N=1/2 BETA=1/4  42.43 DEGREE BEND  NO FRINGE FIELDS  NORM UNITS'        
 0        
 15. 1. ' N' 100.   ;   15. 2. ' R ' 1000.  ;  15. 5. ' N ' 100.  ;   
 15. 8. ' CM' 0.01  ;    15. 11. 'MEV' .001  ;    15. 6.  ' N ' 100.  ;         
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
 17. ;    
  16. 1.  0.250  'BETA'  ;    
   4. 74.05 10. .5   ;        
   13. 4.   ;       
13.       1.        ;         
 (THE N=1/2, 42.4265 DEGREE  BENDING MAGNET IS CHOSEN AS A TEST CASE BECAUSE)   
 (KL = 30 DEGREES IS A CONVENIENT ANGLE.  FRINGING FIELDS ARE LEFT OUT SO THAT) 
 (THE BENDING MAGNET MATRIX ELEMENTS MAY BE INDEPENDENTLY VERIFIED.  BR= 10 KG-)
 (METERS, R = 1 METER AND NORMALIZED TRANSVERSE DIMENSIONS ARE USED.  THE )     
 (RESULTS SHOULD AGREE WITH PAGES 57 - 60 OF SLAC 75.)      
 SENTINEL 
 '(14)  N=1/2 BETA= 0   42.43 DEGREE BEND  NO FRINGE FIELDS  NORM UNITS'        
 0        
 15. 1. ' N' 100.   ;   15. 2. ' R ' 1000.  ;  15. 5. ' N ' 100.  ;   
 15. 8. ' CM' 0.01  ;    15. 11. 'MEV' .001  ;    15. 6.  ' N ' 100.  ;         
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
17. ;                16. 1. 0.00 'BETA'  ;        
   4. 74.05 10. .5   ;        
   13. 4.   ;       
13.       1.        ;         
 (THE BETA=0 CASE IS ADDED TO ALLOW A FURTHER CHECK ON THE BENDING MAGNET)      
 (MATRIX ELEMENTS USING THE N=1/2 THEOREMS LISTED ON PAGES 92 AND 93 OF SLAC 75)
 SENTINEL 
 '(15)  N=1/2 BETA=1/4  30.0  DEGREE BEND  NO FRINGE FIELDS  NORM UNITS'        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM' 0.01  ;    15. 11. 'MEV' .001  ;    15. 6.  ' N ' 100.  ;         
  1. 2. 3. 4. 5. 6. 7.   299.792458  ;    13. 2.  ;         
 17. ;    
  16. 1. .250 'BETA'  ;       
 4. 52.36 10. 0.5 ; 
  13. 4.    ;       
13.       1.        ;         
 (IT IS IMPORTANT TO CHECK THAT ANY GIVEN COMPUTER CALCULATES THE CORRECT)      
 (RESULTS FOR BENDING MAGNETS OF ANGLES LESS THAN 0.2 RADIANS.  THE FOLLOWING)  
 (TWO COMPUTATIONS ARE DESIGNED WITH  THIS IN MIND.  THE FIRST CALCULATION IS ) 
 (A SINGLE STEP 30 DEGREE BENDING MAGNET AND THE SECOND COMPUTATION IS A TEN )  
 (STEP CALCULATION ADDING UP TO 30 DEGREES.  OBVIOUSLY, THE RESULTS OF THE TWO) 
 (CALCULATIONS SHOULD AGREE.  NORMALIZED DIMENSIONS ARE USED AND BR = 10 KG)    
 (METERS.)
 SENTINEL 
 '(16)  N=1/2 BETA=1/4  30.0  DEGREE BEND  10 STEPS  NO FRINGE FIELDS  '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM' 0.01  ;    15. 11. 'MEV' .001  ;    15. 6.  ' N ' 100.  ;         
  1. 2. 3. 4. 5. 6. 7.   299.792458  ;    13. 2.  ;         
 17. ;    
  16.  1.0  0.250  'BETA'  ;  
 9. 10. ;    4. 5.236 10. 0.5 ;   9. 0. ;         
  13. 4.    ;       
13.       1.        ;         
(NOTE THE USE OF THE REPEAT ELEMENT TYPE CODE 9.0 IN SETTING UP THIS PROBLEM )  
 SENTINEL 
 '(17)  N=1/4 BETA=1/4  30.0  DEGREE BEND  NO FRINGE FIELDS  NORM UNITS'        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM' 0.01  ;    15. 11. 'MEV' .001  ;    15. 6.  ' N ' 100.  ;         
  1. 2. 3. 4. 5. 6. 7.   299.792458  ;    13. 2.  ;         
 17. ;    
  16. 1. .250 'BETA'  ;       
  4. 52.36 10. 0.25   ;       
  13. 4.    ;       
13.       1.        ;         
 (THIS CALCULATION IS INCLUDED SO AS TO HAVE A BENDING MAGNET CASE WHERE N )    
 (NEITHER EQUALS ZERO NOR 1/2.  NORMALIZED UNITS ARE USED AND BR = 10 KG METERS)
 SENTINEL 
 '(18)  N=1/2 BETA=1/4  84.85 DEGREE BEND WITH FRINGE FIELDS  NORM UNIT'        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
 17. ;    
  16. 1. .250 'BETA'  ;       
 3.  244.94  ;      
 2.  0.  ;  4.  148.10  10.  .5  ;      
 2.  0.  ;
 3.  244.94  ;      
   13. 4.   ;       
13.       1.        ;         
 (THE FOLLOWING THREE CASES ARE INCLUDED BECAUSE THEY ARE COMPOSITE SYSTEMS)    
 (INCLUDING FRINGING FIELDS, DRIFT DISTANCES AND VARIOUS SECOND-ORDER)
 (CORRECTIONS.  NORMALIZED UNITS ARE USED IN ALL CASES AND BR = 10 KG METERS.)  
 (NOTE THAT, TO INCLUDE THE FRINGING FIELD MATRIX ELEMENTS IN THE CALCULATION)  
 (THE 2. ELEMENTS MUST BE ADDED TO THE PROGRAM LISTING EVEN IF THE ROTATION)    
 (ANGLE OF THE ENTRANCE AND/OR EXIT POLE FACE IS ZERO.  THUS, IN THE FOLLOWING) 
 (CALCULATION, 2. 0. ELEMENTS ARE ADDED BEFORE AND AFTER THE 4.0 BENDING )      
 (MAGNET ENTRY.)    
 SENTINEL 
 '(19)  N=0   90 DEGREE BEND WITH FRINGE FIELDS   NORMALIZED UNITS     '        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7.   299.792458     ;          13. 2.     ;        
 17. ;    
 16. 5. .0333333 'G/2'  ;    16. 7. .46 'K1'  ;    16. 8. 2.75 'K2'  ;
  16. 12. .00358 '1/R1'  ;    16. 13. .00358 '1/R2'  ;      
 3.0 210.598  ;  2.0 27.71 ;  4. 157.08 10. 0.  ;  2. 27.71 ; 3. 210.598  ;     
 13. 4.    ;        
13.       1.        ;         
SENTINEL  
 '(20)  N=1/2 BETA= 0   169.7 DEGREE BEND WITH FRINGE FIELDS  NORM UNIT'        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7. 299.792458  ;    13. 2.  ;    17. ;   
  16. 1. 0. 'BETA'  ;         
 3. 81.65 ;    2. 0.  ; 4. 296.19 10.  0.5  ;  2. 0.  ;     3. 81.65  ;         
  13. 4.   ;        
13.       1.        ;         
 SENTINEL 
 '(21)  N=1/2 BETA=1/4  169.7 DEGREE BEND WITH FRINGE FIELDS  NORM UNIT'        
 0        
 15. 1. ' M ' 100.  ;    15. 2. ' R ' 1000.   ;   15. 5. ' M ' 100.  ;
 15. 8. ' CM'  .01  ;    15. 11.  'MEV' .001   ;    15. 6. ' N '  100.  ;       
 1. 2. 3. 4. 5. 6. 7. 299.792458 ;  13. 2. ;  17. ;         
 16. 1. 0.250 'BETA'  ;       
 3.  81.65  ;       
 2.  0.  ;
 4.  296.19  10.  0.5  ;      
 2.  0.  ;
 3.  81.65  ;       
 13. 4. ; 16. 15. 56.6 ; 3. 0. ; 13. 4. ; 16. 15. -56.6 ; 3. 0. ; 16. 15. 0. ;  
 16. 15. 27.7 ;   3. 0.  ;  13. 4.  ;  16. 15. 0.  ;        
13.       1.        ;         
 (THE 16. 15. ALPHA. TYPE CODE IS USED IN THIS EXAMPLE TO ROTATE TO THE  X AND )
 (Y FOCAL PLANES.  THE X FOCAL PLANE CORRESPONDS TO THE ANGLE FOR WHICH THE)    
 (126 MATRIX ELEMENT = 0  ;  THE Y FOCAL PLANE CORRESPONDS TO THE ANGLE FOR )   
 (WHICH THE 346 MATRIX ELEMENT = 0.      )        
 SENTINEL 
' (22)  TEST OF SECOND ORDER MATRIX ELEMENTS FOR STRONGFOCUS'         
 0        
 15.  ;   
1.0  2.0  5.0  2.0  5.0  0.0  2.0  10.0 ;         
17.0 ;    
4.  2.0  5.0  -500. 'BEND' ;  
13. 4. ;  
( THIS WAS PREVIOUSLY THE A.G.B.M. TEST)
(UNITS ARE RESET TO THEIR DEFAULT VALUE   L=CMS FOR THE BEAM PARAMETERS)        
(THIS IS AN EXAMPLE OF SECOND ORDER MATRIX ELEMENTS FOR A STRONG FOCUSING)      
(BENDING MAGNET. IT IS REPEATED FOR BOTH POLARITIES OF THE MAGNET)    
 SENTINEL 
' (23) TEST FOR OPPOSITE POLARITY '     
 1        
4.  2.0  5.0  500. 'BEND' ;   
 SENTINEL 


Example of Computed Output using the Above TEST DATA
----------------------------------------------------
1
0"CHECK DECK FOR TRANSPORT/360 MATRIX ELEMENTS K L BROWN OCT. 10 1969             "
0    0
         (THIS TEST DECK IS DESIGNED TO CHECK ALL OF THE MATRIX ELEMENTS IN THE   )   
         (SLAC TRANSPORT/360 PROGRAM. IT IS NOT INTENDED TO CHECK PROGRAM LOGIC NOR   )   
         (FITTING ROUTINES. IF THIS CHECK DECK IS VERIFIED, THE MATRIX OUTPUT )   
         (TABULATIONS OF A TRANSPORT CALCULATION SHOULD BE CORRECT PROVIDED THAT  )   
         (NO INSERTS ARE MADE BETWEEN A TYPE CODE 2.0 AND A TYPE CODE 4.0 ELEMENT )   
         (IN THE PROGRAM LISTING. KARL L BROWN OCTOBER 1969   )   
0SENTINEL
0    0 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
     1 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1CHECK DECK FOR TRANSPORT/360 MATRIX ELEMENTS K L BROWN OCT. 10 1969             

0*LENGTH*          0.00000 M   
1
0"(1) DRIFT MATRIX L= 10 METERS NORMALIZED UNITS                                  "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
     3.0                       10.00000;
    13.                         4.00000;
    13.                         1.00000;
         (IN THE DIMENSIONS CHOSEN FOR THIS PROBLEM, THE R12 MATRIX ELEMENT   )   
         (SHOULD EQUAL 10.0 METERS/RADIAN )   
0SENTINEL
0   10 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    37 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(1) DRIFT MATRIX L= 10 METERS NORMALIZED UNITS                                  

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *DRIFT*         3.                10.00000 M   
     10.000 M   
 *TRANSFORM 1*                
              1.00000  10.00000   0.00000   0.00000   0.00000   0.00000
              0.00000   1.00000   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   1.00000  10.00000   0.00000   0.00000
              0.00000   0.00000   0.00000   1.00000   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
                                                                           0.000  30.067 M   
                                                                           0.000   3.000 R       0.998
                                                                           0.000  50.160 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.997
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*         10.00000 M   
1
0"(2) QUADRUPOLE MATRIX K= 1/2 KL= 30 DEGREES NORMALIZED UNITS                    "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000  2997.92432;
    13.                         2.00000;
    17.                         2.00000     2.00000;
     5.00                       1.04719     5.00000     0.20000;
    13.                         4.00000;
    13.                         1.00000;
         (THE NUMERICAL VALUES OF THE 1ST AND 2ND ORDER QUADRUPOLE MATRIX ELEMENTS)   
         (IN THIS CALCULATION SHOULD AGREE WITH THE QUADRUPOLE MATRIX ELEMENT EQUATIONS   )   
         (ON PAGES 68 AND 69 OF SLAC REPORT NO. 75. BY K.L. BROWN. THE NORMALIZED )   
         (DIMENSIONS USED IN THIS CALCULATION, AS DETERMINED BY THE 15 TYPE   )   
         (CODES ENTRIES, ARE AS FOLLOWS@D TRANSVERSE DIMENSIONS X AND Y ARE IN METERS,)   
         (TRANSVERSE ANGLES THETA AND PHI ARE IN RADIANS, AND MOMENTUM DEVIATION  )   
         (DELTA P/P IS FRACTIONAL . THE CENTRAL MOMENTUM IS CHOSEN AS P=BR=100 KG )   
         (METERS FOR THIS CALCULATION.)   
0SENTINEL
0   11 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    42 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(2) QUADRUPOLE MATRIX K= 1/2 KL= 30 DEGREES NORMALIZED UNITS                    

 *BEAM*          1.              2997.92432 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *QUAD*          5.                 1.04719 M         5.00000 KG        0.20000 M    (    4.00003 M   )
      1.047 M   
 *TRANSFORM 1*                
              0.86603   0.99999   0.00000   0.00000   0.00000   0.00000
             -0.25000   0.86603   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   1.14024   1.09570   0.00000   0.00000
              0.00000   0.00000   0.27392   1.14024   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  0.000E+00
   1 12  0.000E+00   1 22  0.000E+00
   1 13  0.000E+00   1 23  0.000E+00   1 33  0.000E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44  0.000E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  1.309E-01   1 26  4.655E-02   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  0.000E+00
 
   2 11  0.000E+00
   2 12  0.000E+00   2 22  0.000E+00
   2 13  0.000E+00   2 23  0.000E+00   2 33  0.000E+00
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44  0.000E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  2.384E-01   2 26  1.309E-01   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66  0.000E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  0.000E+00   3 23  0.000E+00   3 33  0.000E+00
   3 14  0.000E+00   3 24  0.000E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -1.434E-01   3 46 -4.917E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  0.000E+00   4 23  0.000E+00   4 33  0.000E+00
   4 14  0.000E+00   4 24  0.000E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36 -2.862E-01   4 46 -1.434E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -1.132E-02
   5 12  1.250E-01   5 22 -4.783E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.264E-02
   5 14  0.000E+00   5 24  0.000E+00   5 34 -1.501E-01   5 44 -5.741E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26  0.000E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                           0.000   4.039 M   
                                                                           0.000   5.069 R       0.768
                                                                           0.000   8.361 M       0.000  0.000
                                                                           0.000  11.096 R       0.000  0.000  0.831
                                                                         -18.906  22.243 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          1.04719 M   
1
0"(3) PSI CORRECTION TO INPUT FRINGE FIELD G/R=0.2 K1=0.7                         "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    16.00           "G/2 "      5.00000     0.10000;
    16.00           "K1  "      7.00000     0.70000;
     2.0                       30.00000;
     4.000                      0.00001    10.00000      0.00000;
    13.                         4.00000;
    13.                         1.00000;
         (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM   )   
         (TO THE TRANSVERSE FOCAL LENGTH OF A ROTATED ENTRANCE FACE OF A BENDING  )   
         (MAGNET RESULTING FROM THE FINITE EXTENT OF THE FRINGING FIELDS. THE )   
         (DEFINITION OF PSI AND THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN)   
         (ON PAGES 73 AND 74 OF SLAC 75. NORMALIZED DIMENSIONS ARE USED AS IN THE )   
         (PRECEDING PROBLEM. FOR THIS CALCULATION ; BR=10 KG METERS, R=1.0 METERS,)   
         (G/R=0.2 AND K1=0.7 WHERE R=THE RADIUS OF THE CENTRAL ORBIT, G=THE GAP OF THE)   
         (MAGNET AND K1 IS AN INTEGRAL OF THE FRINGING FIELD DEFINED ON PAGE 74 OF)   
         (SLAC 75.)   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    47 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(3) PSI CORRECTION TO INPUT FRINGE FIELD G/R=0.2 K1=0.7                         

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 * G/2 *        16.     "G/2 "      5.    0.10000E+00
 * K1 *         16.     "K1  "      7.    0.70000E+00
 *ROTAT*         2.                30.00000 DEG 
      0.000 M   
 *BEND*          4.                 0.00001 M        10.00000 KG        0.00000      (     1.000 M   ,   0.001 DEG )
      0.000 M   
 *TRANSFORM 1*                
              1.00001   0.00001   0.00000   0.00000   0.00000   0.00000
              0.57734   1.00000   0.00000   0.00000   0.00000   0.00001
              0.00000   0.00000   1.00000   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.33308   1.00000   0.00000   0.00000
             -0.00001   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
                                                                           0.000   2.000 M   
                                                                           0.000   3.215 R       0.359
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.174 R       0.000  0.000 -0.257
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(4) PSI CORRECTION TO INPUT FRINGE FIELD G/R=0.2 K1=0.7 K2=3.0                  "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    16.00           "G/2 "      5.00000     0.10000;
    16.00           "K1  "      7.00000     0.70000;
    16.00           "K2  "      8.00000     3.00000;
     2.0                       30.00000;
     4.000                      0.00001    10.00000      0.00000;
    13.                         4.00000;
    13.                         1.00000;
         (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM   )   
         (TO THE TRANSVERSE FOCAL LENGTH OF A ROTATED ENTRANCE FACE OF A BENDING  )   
         (MAGNET RESULTING FROM THE FINITE EXTENT OF THE FRINGING FIELDS. THE )   
         (DEFINITION OF PSI AND THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN)   
         (ON PAGES 73 AND 74 OF SLAC 75. NORMALIZED DIMENSIONS ARE USED AS IN THE )   
         (PRECEDING PROBLEM. BR=10 KG METERS, R=1.0 METERS, G/R=0.2, K1=0.7, AND  )   
         (K2=3.0 K2 IS DEFINED IN THE TRANSPORT/360 INSTRUCTION MANUAL.   )   
0SENTINEL
0   14 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    50 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(4) PSI CORRECTION TO INPUT FRINGE FIELD G/R=0.2 K1=0.7 K2=3.0                  

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 * G/2 *        16.     "G/2 "      5.    0.10000E+00
 * K1 *         16.     "K1  "      7.    0.70000E+00
 * K2 *         16.     "K2  "      8.    0.30000E+01
 *ROTAT*         2.                30.00000 DEG 
      0.000 M   
 *BEND*          4.                 0.00001 M        10.00000 KG        0.00000      (     1.000 M   ,   0.001 DEG )
      0.000 M   
 *TRANSFORM 1*                
              1.00001   0.00001   0.00000   0.00000   0.00000   0.00000
              0.57734   1.00000   0.00000   0.00000   0.00000   0.00001
              0.00000   0.00000   1.00000   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.38847   1.00000   0.00000   0.00000
             -0.00001   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
                                                                           0.000   2.000 M   
                                                                           0.000   3.215 R       0.359
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.236 R       0.000  0.000 -0.297
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(5) PSI CORRECTION TO OUTPUT FRINGE FIELD G/R=0.2 K1=0.7                        "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    16.00           "G/2 "      5.00000     0.10000;
    16.00           "K1  "      7.00000     0.70000;
     4.000                      0.00001    10.00000      0.00000;
     2.0                       30.00000;
    13.                         4.00000;
    13.                         1.00000;
         (THE PURPOSE OF THIS CALCULATION IS TO COMPUTE THE PSI CORRECTION TERM TO THE)   
         (TRANSVERSE FOCAL LENGTH OF A ROTATED EXIT FACE OF A BENDING MAGNET RESULTING)   
         (FROM THE FINITE EXTENT OF THE FRINGING FIELDS. THE DEFINITION OF PSI AND)   
         (THE EQUATION FOR THE TRANSVERSE FOCAL LENGTH ARE GIVEN ON PAGES 74 AND 75 OF)   
         (SLAC 75. NORMALIZED DIMENSIONS ARE USED AS IN THE PRECEDING PROBLEM.)   
         (BR=10 KG METERS, R=1.0 METERS, G/R=0.2, AND K1=0.7  )   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    47 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(5) PSI CORRECTION TO OUTPUT FRINGE FIELD G/R=0.2 K1=0.7                        

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 * G/2 *        16.     "G/2 "      5.    0.10000E+00
 * K1 *         16.     "K1  "      7.    0.70000E+00
 *BEND*          4.                 0.00001 M        10.00000 KG        0.00000      (     1.000 M   ,   0.001 DEG )
      0.000 M   
 *ROTAT*         2.                30.00000 DEG 
      0.000 M   
 *TRANSFORM 1*                
              1.00000   0.00001   0.00000   0.00000   0.00000   0.00000
              0.57734   1.00001   0.00000   0.00000   0.00000   0.00001
              0.00000   0.00000   1.00000   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.33308   1.00000   0.00000   0.00000
             -0.00001   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
                                                                           0.000   2.000 M   
                                                                           0.000   3.215 R       0.359
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.174 R       0.000  0.000 -0.257
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(6) PSI CORRECTION TO OUTPUT FRINGE FIELD G/R=0.2 K1=0.7 K2=3.0                 "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    16.00           "G/2 "      5.00000     0.10000;
    16.00           "K1  "      7.00000     0.70000;
    16.00           "K2  "      8.00000     3.00000;
     4.000                      0.00001    10.00000      0.00000;
     2.0                       30.00000;
    13.                         4.00000;
    13.                         1.00000;
         (THIS CALCULATION COMPUTES THE PSI CORRECTION TERM TO THE TRANSVERSE FOCAL   )   
         (LENGTH OF A ROTATED EXIT FACE OF A BENDING MAGNET RESULTING FROM THE FINITE )   
         (EXTENT OF THE FRINGING FIELDS. THE DEFINITION OF PSI AND THE EQUATION FOR   )   
         (THE TRANSVERSE FOCAL LENGTH ARE GIVEN ON PAGES 74 AND 75 OF SLAC 75.)   
         (NORMALIZED DIMENSIONS ARE USED AS IN THE PRECEDING PROBLEM. )   
         (BR=10 KG METERS, R=1.0 METERS, G/R=0.2, K1=0.7, AND K2=3.0  )   
0SENTINEL
0   14 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    50 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(6) PSI CORRECTION TO OUTPUT FRINGE FIELD G/R=0.2 K1=0.7 K2=3.0                 

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 * G/2 *        16.     "G/2 "      5.    0.10000E+00
 * K1 *         16.     "K1  "      7.    0.70000E+00
 * K2 *         16.     "K2  "      8.    0.30000E+01
 *BEND*          4.                 0.00001 M        10.00000 KG        0.00000      (     1.000 M   ,   0.001 DEG )
      0.000 M   
 *ROTAT*         2.                30.00000 DEG 
      0.000 M   
 *TRANSFORM 1*                
              1.00000   0.00001   0.00000   0.00000   0.00000   0.00000
              0.57734   1.00001   0.00000   0.00000   0.00000   0.00001
              0.00000   0.00000   1.00000   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.38847   1.00000   0.00000   0.00000
             -0.00001   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
                                                                           0.000   2.000 M   
                                                                           0.000   3.215 R       0.359
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.236 R       0.000  0.000 -0.297
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(7) 2ND ORDER INPUT FRINGE FIELD R(2,1) = 1.0 R=1/2 R1= 2.0                     "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "G/2 "      5.00000     0.05000;
    16.00           "K1  "      7.00000     0.70000;
    16.00           "K2  "      8.00000     3.00000;
    16.00           "1/R1"     12.00000     0.50000;
     2.0                       26.56600;
     4.000                      0.00001    20.00000      0.50000;
    13.                         4.00000;
    13.                         1.00000;
         (THIS CALCULATION IS INTENDED TO CHECK BOTH THE 1ST AND 2ND ORDER)   
         (INPUT FRINGING FIELD MATRIX ELEMENTS OF A BENDING MAGNET AND COMPARE THE)   
         (RESULTS WITH PAGES 71 THROUGH 75 OF SLAC 75. FOR THIS CALCULATION THE   )   
0NEXT COMMENT TRUNCATED TO 116 CHARS.
         (FOLLOWING PARAMETERS WERE CHOSEN@D BR=10 KG METERS, R=1/2 METER, TAN BETA=1/2 (R1=2 METERS. G/R=0.2, K1=0.7, AND K2=)
         (USED FOR THE TRANSVERSE DIMENSIONS. )   
0SENTINEL
0   16 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    56 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(7) 2ND ORDER INPUT FRINGE FIELD R(2,1) = 1.0 R=1/2 R1= 2.0                     

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 * G/2 *        16.     "G/2 "      5.    0.50000E-01
 * K1 *         16.     "K1  "      7.    0.70000E+00
 * K2 *         16.     "K2  "      8.    0.30000E+01
 * 1/R1 *       16.     "1/R1"     12.    0.50000E+00
 *ROTAT*         2.                26.56600 DEG       2.00000 M   
      0.000 M   
 *BEND*          4.                 0.00001 M        20.00000 KG        0.50000      (     0.500 M   ,   0.001 DEG )
      0.000 M   
 *TRANSFORM 1*                
              1.00001   0.00001   0.00000   0.00000   0.00000   0.00000
              1.00002   1.00000   0.00000   0.00000   0.00000   0.00002
              0.00000   0.00000   0.99999   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.65233   1.00000   0.00000   0.00000
             -0.00002   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -2.500E-01
   1 12  2.500E-05   1 22  5.000E-11
   1 13  0.000E+00   1 23  0.000E+00   1 33  1.250E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -5.000E-06   1 44 -5.000E-11
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16 -1.000E-05   1 26  6.667E-16   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -1.000E-10
 
   2 11 -3.012E-01
   2 12  5.000E-01   2 22 -1.000E-05
   2 13  0.000E+00   2 23  0.000E+00   2 33  1.801E+00
   2 14  0.000E+00   2 24  0.000E+00   2 34 -5.000E-01   2 44 -1.000E-05
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16 -1.000E+00   2 26 -1.000E-10   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -2.000E-05
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  5.000E-01   3 23 -2.500E-05   3 33  0.000E+00
   3 14  1.500E-05   3 24  1.000E-10   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  1.000E-05   3 46  0.000E+00   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  6.025E-01   4 23 -2.500E+00   4 33  0.000E+00
   4 14 -5.000E-01   4 24  0.000E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.000E+00   4 46  1.000E-10   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  6.366E-11
   5 12 -1.000E-05   5 22 -5.000E-06
   5 13  0.000E+00   5 23  0.000E+00   5 33 -2.713E-05
   5 14  0.000E+00   5 24  0.000E+00   5 34  6.523E-06   5 44 -5.000E-06
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26 -1.000E-10   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                          19.001  28.391 M   
                                                                          27.615  44.522 R       0.917
                                                                           0.000   5.657 M       0.000  0.000
                                                                           0.000  42.002 R       0.000  0.000  0.037
                                                                          -0.001   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(8) 2ND ORDER OUTPUT FRINGE FIELD R(2,1) = 1.0 R=1/2 R2= 2.0                    "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "G/2 "      5.00000     0.05000;
    16.00           "K1  "      7.00000     0.70000;
    16.00           "K2  "      8.00000     3.00000;
    16.00           "1/R2"     13.00000     0.50000;
     4.000                      0.00001    20.00000      0.50000;
     2.0                       26.56600;
    13.                         4.00000;
    13.                         1.00000;
         (THIS CALCULATION IS INTENDED TO CHECK BOTH THE 1ST AND 2ND ORDER OUTPUT )   
         (FRINGING FIELD MATRIX ELEMENTS OF A BENDING MAGNET AND COMPARE THE RESULTS  )   
         (WITH PAGES 71 THROUGH 75 OF SLAC 75. FOR THIS CALCULATION THE FOLLOWING )   
         (PARAMETERS WERE CHOSEN@D BR=10 KG METERS, R=1/2 METER, TAN BETA=1/2,)   
         (R2=2 METERS. G/R=0.2, K1=0.7, AND K2=3.0 NORMALIZED UNITS ARE USED FOR  )   
         (THE TRANSVERSE DIMENSIONS   )   
0SENTINEL
0   16 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    56 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(8) 2ND ORDER OUTPUT FRINGE FIELD R(2,1) = 1.0 R=1/2 R2= 2.0                    

 *BEAM*          1.               299.79248 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 * G/2 *        16.     "G/2 "      5.    0.50000E-01
 * K1 *         16.     "K1  "      7.    0.70000E+00
 * K2 *         16.     "K2  "      8.    0.30000E+01
 * 1/R2 *       16.     "1/R2"     13.    0.50000E+00
 *BEND*          4.                 0.00001 M        20.00000 KG        0.50000      (     0.500 M   ,   0.001 DEG )
      0.000 M   
 *ROTAT*         2.                26.56600 DEG       2.00000 M   
      0.000 M   
 *TRANSFORM 1*                
              1.00000   0.00001   0.00000   0.00000   0.00000   0.00000
              1.00002   1.00001   0.00000   0.00000   0.00000   0.00002
              0.00000   0.00000   1.00000   0.00001   0.00000   0.00000
              0.00000   0.00000  -0.65233   0.99999   0.00000   0.00000
             -0.00002   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  2.500E-01
   1 12  2.500E-05   1 22  7.500E-11
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.250E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -2.500E-05   1 44 -1.750E-10
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  3.500E-10   1 26  1.167E-15   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -1.000E-10
 
   2 11 -5.512E-01
   2 12 -5.000E-01   2 22 -1.500E-05
   2 13  0.000E+00   2 23  0.000E+00   2 33  5.119E-02
   2 14  0.000E+00   2 24  0.000E+00   2 34  5.000E-01   2 44 -5.000E-06
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16 -1.000E+00   2 26 -1.000E-05   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -2.000E-05
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -5.000E-01   3 23 -5.000E-06   3 33  0.000E+00
   3 14  1.500E-05   3 24  5.000E-11   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  5.000E-11   3 46 -5.000E-16   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  3.103E+00   4 23  2.500E+00   4 33  0.000E+00
   4 14  5.001E-01   4 24  3.000E-05   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.000E+00   4 46  1.000E-05   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  0.000E+00
   5 12  3.333E-11   5 22 -5.000E-06
   5 13  0.000E+00   5 23  0.000E+00   5 33  0.000E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34  1.000E-10   5 44 -5.000E-06
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26 -1.000E-10   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                         -19.000  28.391 M   
                                                                          -1.387  18.141 R      -0.064
                                                                           0.000   5.657 M       0.000  0.000
                                                                           0.000  48.550 R       0.000  0.000 -0.400
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.00001 M   
1
0"(9) SEXTUPOLE MATRIX K(S)SQUARED = 10.0 L =0.1 METERS NORM UNITS                "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000  2997.92432;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    18.00                       0.10000    10.00000     0.10000;
    13.                         4.00000;
    13.                         1.00000;
         (THESE RESULTS SHOULD BE COMPARED WITH THE MATRIX ELEMENTS LISTED ON PAGES   )   
         (69 AND 70 OF SLAC 75 FOR THE SEXTUPOLE. KS SQUARED=10. L=0.1, AND BR=100 KG )   
         (METERS. NORMALIZED TRANSVERSE UNITS ARE USED.   )   
0SENTINEL
0   11 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    42 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(9) SEXTUPOLE MATRIX K(S)SQUARED = 10.0 L =0.1 METERS NORM UNITS                

 *BEAM*          1.              2997.92432 MEV 
      0.000 M                                                              0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *SEXT*         18.                 0.10000 M        10.00000 KG        0.10000 M   
      0.100 M   
 *TRANSFORM 1*                
              1.00000   0.10000   0.00000   0.00000   0.00000   0.00000
              0.00000   1.00000   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   1.00000   0.10000   0.00000   0.00000
              0.00000   0.00000   0.00000   1.00000   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -5.000E-02
   1 12 -3.333E-03   1 22 -8.333E-05
   1 13  0.000E+00   1 23  0.000E+00   1 33  5.000E-02
   1 14  0.000E+00   1 24  0.000E+00   1 34  3.333E-03   1 44  8.333E-05
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  0.000E+00   1 26  0.000E+00   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  0.000E+00
 
   2 11 -1.000E+00
   2 12 -1.000E-01   2 22 -3.333E-03
   2 13  0.000E+00   2 23  0.000E+00   2 33  1.000E+00
   2 14  0.000E+00   2 24  0.000E+00   2 34  1.000E-01   2 44  3.333E-03
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  0.000E+00   2 26  0.000E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66  0.000E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  1.000E-01   3 23  3.333E-03   3 33  0.000E+00
   3 14  3.333E-03   3 24  1.667E-04   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  0.000E+00   3 46  0.000E+00   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  2.000E+00   4 23  1.000E-01   4 33  0.000E+00
   4 14  1.000E-01   4 24  6.667E-03   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  0.000E+00   4 46  0.000E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  0.000E+00
   5 12  0.000E+00   5 22 -5.000E-02
   5 13  0.000E+00   5 23  0.000E+00   5 33  0.000E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34  0.000E+00   5 44 -5.000E-02
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26  0.000E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                           0.601   2.336 M   
                                                                          12.053  23.609 R       0.512
                                                                           0.000   4.110 M       0.000  0.000
                                                                           0.000  16.836 R       0.000  0.000  0.222
                                                                          -1.700   6.287 M       0.000 -0.001  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*          0.10000 M   
1
0"(10) ACCELERATOR MATRIX STANDARD UNITS ARE USED ( SEE BELOW )                   "
0    0
    15.                         1.00000   "CM  "        1.00000 ;
    15.                         2.00000   "MR  "        1.00000 ;
    15.                         5.00000   "CM  "        1.00000 ;
    15.                         8.00000   "M   "        1.00000 ;
    15.                        11.00000   "GEV "        1.00000 ;
    15.                         6.00000   "PC  "        1.00000 ;
   -16.             "MASS"      3.00000  1836.00000;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000    10.00000;
    11.                        10.00000     0.10000    30.00000     1.00000;
    13.                         4.00000;
         (THE ANALYTICAL EXPRESSIONS FOR THE ACCELERATOR MATRIX ELEMENTS ARE LISTED   )   
         (IN THE TRANSPORT/360 MANUAL AS DERIVED BY K.L. BROWN. THIS CALCULATION  )   
         (HAS BEEN MADE IN STANDARD TRANSPORT UNITS@D X,Y IN CMS, THETA AND PHI IN    )   
         (MILLIRADIANS AND DELTA P/P IN PERCENT. THE PARAMETERS CHOSEN FOR THE)   
         (CALCULATION ARE E=10 GEV, DELTA E=0.1 GEV, THE PHASE LAG=30 DEGREES AND )   
         (THE WAVELENGTH = 1 CM.  )   
0SENTINEL
0   10 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    43 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(10) ACCELERATOR MATRIX STANDARD UNITS ARE USED ( SEE BELOW )                   

 *BEAM*          1.                10.00000 GEV 
      0.000 M                                                              0.000   2.000 CM  
                                                                           0.000   3.000 MR      0.000
                                                                           0.000   4.000 CM      0.000  0.000
                                                                           0.000   5.000 MR      0.000  0.000  0.000
                                                                           0.000   6.000 CM      0.000  0.000  0.000  0.000
                                                                           0.000   7.000 PC      0.000  0.000  0.000  0.000  0.000
 *ACC*          11.                10.00000 M         0.10000     (   10.08660) GEV      30.00000           1.00000
     10.000 M   
 *TRANSFORM 1*                
              1.00000   0.99569   0.00000   0.00000   0.00000   0.00000
              0.00000   0.99141   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   1.00000   0.99569   0.00000   0.00000
              0.00000   0.00000   0.00000   0.99141   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   3.11462   0.99141
0*LENGTH*         10.00000 M   
1
0"(10) ACCELERATOR MATRIX NONZERO MASS FOR PARTICLE                               "
0    1
    15.                         1.00000   "CM  "        1.00000 ;
    15.                         2.00000   "MR  "        1.00000 ;
    15.                         5.00000   "CM  "        1.00000 ;
    15.                         8.00000   "M   "        1.00000 ;
    15.                        11.00000   "GEV "        1.00000 ;
    15.                         6.00000   "PC  "        1.00000 ;
 *  16.00           "MASS"      3.00000  1836.00000;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000    10.00000;
    11.                        10.00000     0.10000    30.00000     1.00000;
    13.                         4.00000;
0SENTINEL
0   10 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    41 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(10) ACCELERATOR MATRIX NONZERO MASS FOR PARTICLE                               

 *P MASS*       16.     "MASS"      3.    0.18360E+04
 *BEAM*          1.                10.00000 GEV 
      0.000 M                                                              0.000   2.000 CM  
                                                                           0.000   3.000 MR      0.000
                                                                           0.000   4.000 CM      0.000  0.000
                                                                           0.000   5.000 MR      0.000  0.000  0.000
                                                                           0.000   6.000 CM      0.000  0.000  0.000  0.000
                                                                           0.000   7.000 PC      0.000  0.000  0.000  0.000  0.000
 *ACC*          11.                10.00000 M         0.10000     (   10.08698) GEV      30.00000           1.00000
     10.000 M   
 *TRANSFORM 1*                
              1.06932   1.01856   0.00000   0.00000   0.00000   0.00000
              0.13962   1.06010   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   1.06932   1.01856   0.00000   0.00000
              0.00000   0.00000   0.13962   1.06010   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.27208   0.08610
              0.00000   0.00000   0.00000   0.00000   3.12795   0.99130
0*LENGTH*         10.00000 M   
1
0"(11) SOLENOID MATRIX K = 1/4 KL = 30 DEGREES NORMALIZED UNITS                   "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    19.00                     209.43999     5.00000;
    13.                         4.00000;
    13.                         1.00000;
         (THE ANALYTICAL EXPRESSIONS FOR THE SOLENOID MATRIX ELEMENTS ARE LISTED  )   
         (IN THE TRANSPORT/360 INSTRUCTION MANUAL AS DERIVED FROM R H HELMS SLAC  )   
         (REPORT NO. 4. FOR THE SOLENOID K=B/2BR WHERE B IS THE MAGNETIC FIELD IN THE )   
         (SOLENOID AND BR = P = THE PARTICLE MOMENTUM. FOR THIS CALCULATION THE   )   
         (MOMENTUM BR = 10 KG METERS, B = 5 KG ; FROM WHICH K = 1/4. KL = 30 DEGREES  )   
         (IS CHOSEN FOR EASE OF CHECKING. NORMALIZED TRANSVERSE UNITS ARE USED FOR THE)   
         (CALCULATION.)   
0SENTINEL
0   12 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    45 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(11) SOLENOID MATRIX K = 1/4 KL = 30 DEGREES NORMALIZED UNITS                   

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *SOLO*         19.               209.44000 CM        5.00000 KG  
    209.440 CM  
 *TRANSFORM 1*                
              0.75000   1.73205   0.43301   1.00000   0.00000   0.00000
             -0.10825   0.75000  -0.06250   0.43301   0.00000   0.00000
             -0.43301  -1.00000   0.75000   1.73205   0.00000   0.00000
              0.06250  -0.43301  -0.10825   0.75000   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  0.000E+00
   1 12  0.000E+00   1 22  0.000E+00
   1 13  0.000E+00   1 23  0.000E+00   1 33  0.000E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44  0.000E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  4.535E-01   1 26  6.849E-01   1 36 -2.618E-01   1 46 -8.138E-01   1 56  0.000E+00   1 66  0.000E+00
 
   2 11  0.000E+00
   2 12  0.000E+00   2 22  0.000E+00
   2 13  0.000E+00   2 23  0.000E+00   2 33  0.000E+00
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44  0.000E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.737E-01   2 26  4.535E-01   2 36  1.759E-01   2 46 -2.618E-01   2 56  0.000E+00   2 66  0.000E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  0.000E+00   3 23  0.000E+00   3 33  0.000E+00
   3 14  0.000E+00   3 24  0.000E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  2.618E-01   3 26  8.138E-01   3 36  4.535E-01   3 46  6.849E-01   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  0.000E+00   4 23  0.000E+00   4 33  0.000E+00
   4 14  0.000E+00   4 24  0.000E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16 -1.759E-01   4 26  2.618E-01   4 36  1.737E-01   4 46  4.535E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  0.000E+00
   5 12  0.000E+00   5 22 -1.047E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33  0.000E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34  0.000E+00   5 44 -1.047E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26  0.000E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                           0.000  34.197 M   
                                                                           0.000  14.651 R       0.796
                                                                           0.000  33.690 M      -0.412  0.053
                                                                           0.000  18.105 R      -0.667 -0.263  0.922
                                                                         -35.605  39.805 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*        209.44000 CM  
1
0"(12) SOLENOID + COORDINATE ROTATION K = 1/4 KL = 30 DEGREES                     "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    19.00                     209.43999     5.00000;
    20.0                      -30.00000;
    13.                         4.00000;
    13.                         1.00000;
         (IF THE TRANSVERSE COORDINATES ARE ROTATED ABOUT THE Z AXIS OF A SOLENOID BY )   
         (AN ANGLE OF -KL , THEN THE X AND Y 1ST ORDER MATRIX ELEMENTS ARE DECOUPLED. )   
         (THUS IN THIS TEST CASE THE MATRIX ELEMENTS R13=R14=R23=R24=R31=R32=R41=R42  )   
         (ALL SHOULD BE EQUAL TO ZERO. THIS PROVIDES A TEST FOR THE SOLENOID MATRIX   )   
         (ELEMENTS AS WELL AS THE Z ROTATION MATRIX.  )   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    47 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(12) SOLENOID + COORDINATE ROTATION K = 1/4 KL = 30 DEGREES                     

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *SOLO*         19.               209.44000 CM        5.00000 KG  
    209.440 CM  
 *Z RO*         20.               -30.00000 DEG
    209.440 CM  
 *TRANSFORM 1*                
              0.86602   2.00000   0.00000   0.00000   0.00000   0.00000
             -0.12500   0.86602   0.00000   0.00000   0.00000   0.00000
              0.00000   0.00000   0.86602   2.00000   0.00000   0.00000
              0.00000   0.00000  -0.12500   0.86602   0.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   1.00000   0.00000
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  0.000E+00
   1 12  0.000E+00   1 22  0.000E+00
   1 13  0.000E+00   1 23  0.000E+00   1 33  0.000E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44  0.000E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  2.618E-01   1 26  1.862E-01   1 36 -4.535E-01   1 46 -1.047E+00   1 56  0.000E+00   1 66  0.000E+00
 
   2 11  0.000E+00
   2 12  0.000E+00   2 22  0.000E+00
   2 13  0.000E+00   2 23  0.000E+00   2 33  0.000E+00
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44  0.000E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  2.384E-01   2 26  2.618E-01   2 36  6.545E-02   2 46 -4.535E-01   2 56  0.000E+00   2 66  0.000E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  0.000E+00   3 23  0.000E+00   3 33  0.000E+00
   3 14  0.000E+00   3 24  0.000E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  4.535E-01   3 26  1.047E+00   3 36  2.618E-01   3 46  1.862E-01   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  0.000E+00   4 23  0.000E+00   4 33  0.000E+00
   4 14  0.000E+00   4 24  0.000E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16 -6.545E-02   4 26  4.535E-01   4 36  2.384E-01   4 46  2.618E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  0.000E+00
   5 12  0.000E+00   5 22 -1.047E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33  0.000E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34  0.000E+00   5 44 -1.047E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  0.000E+00   5 26  0.000E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  0.000E+00
 
                                                                           0.000  39.652 M   
                                                                           0.000  17.419 R       0.879
                                                                           0.000  27.058 M      -0.208  0.111
                                                                           0.000  15.460 R      -0.631 -0.312  0.846
                                                                         -35.605  39.805 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
0*LENGTH*        209.44000 CM  
1
0"(13) N=1/2 BETA=1/4 42.43 DEGREE BEND NO FRINGE FIELDS NORM UNITS               "
0    0
    15.                         1.00000   "N   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "N   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     4.000                     74.05000    10.00000      0.50000;
    13.                         4.00000;
    13.                         1.00000;
         (THE N=1/2, 42.4265 DEGREE BENDING MAGNET IS CHOSEN AS A TEST CASE BECAUSE   )   
         (KL = 30 DEGREES IS A CONVENIENT ANGLE. FRINGING FIELDS ARE LEFT OUT SO THAT )   
         (THE BENDING MAGNET MATRIX ELEMENTS MAY BE INDEPENDENTLY VERIFIED. BR= 10 KG-)   
         (METERS, R = 1 METER AND NORMALIZED TRANSVERSE DIMENSIONS ARE USED. THE  )   
         (RESULTS SHOULD AGREE WITH PAGES 57 - 60 OF SLAC 75. )   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    49 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(13) N=1/2 BETA=1/4 42.43 DEGREE BEND NO FRINGE FIELDS NORM UNITS               

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 N   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 N       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 N       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *BEND*          4.                74.05000 CM       10.00000 KG        0.50000      (   100.000 CM  ,  42.428 DEG )
     74.050 CM  
 *TRANSFORM 1*                
              0.86602   0.70712   0.00000   0.00000   0.00000   0.26796
             -0.35356   0.86602   0.00000   0.00000   0.00000   0.70712
              0.00000   0.00000   0.86602   0.70712   0.00000   0.00000
              0.00000   0.00000  -0.35356   0.86602   0.00000   0.00000
             -0.70712  -0.26796   0.00000   0.00000   1.00000  -0.06675
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -6.101E-02
   1 12  6.440E-01   1 22  1.220E-01
   1 13  0.000E+00   1 23  0.000E+00   1 33 -2.992E-03
   1 14  0.000E+00   1 24  0.000E+00   1 34  3.158E-02   1 44 -1.280E-01
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  3.749E-01   1 26  1.592E-01   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -2.379E-01
 
   2 11  1.610E-01
   2 12  1.220E-01   2 22 -3.220E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -1.579E-02
   2 14  0.000E+00   2 24  0.000E+00   2 34  1.220E-01   2 44 -3.220E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  4.003E-01   2 26 -1.131E-01   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -7.374E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -1.220E-01   3 23 -6.316E-02   3 33  0.000E+00
   3 14  6.440E-01   3 24  2.440E-01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  1.131E-01   3 46  9.340E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  1.579E-02   4 23  5.984E-03   4 33  0.000E+00
   4 14 -1.280E-01   4 24 -3.158E-02   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  3.384E-01   4 46  1.251E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -2.245E-04
   5 12 -1.310E-01   5 22 -3.698E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.557E-02
   5 14  0.000E+00   5 24  0.000E+00   5 34  1.190E-01   5 44 -3.057E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -3.202E-02   5 26 -2.801E-01   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.814E-03
 
                                                                         -14.050  18.969 N   
                                                                         -46.687  53.231 R       0.918
                                                                           0.000  10.080 N       0.000  0.000
                                                                           0.000  11.472 R       0.000  0.000  0.386
                                                                         -11.311  14.802 N       0.054  0.206  0.000  0.000
                                                                           0.000   7.000 N       0.099  0.093  0.000  0.000 -0.032
0*LENGTH*         74.05000 CM  
1
0"(14) N=1/2 BETA= 0 42.43 DEGREE BEND NO FRINGE FIELDS NORM UNITS                "
0    0
    15.                         1.00000   "N   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "N   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.00000;
     4.000                     74.05000    10.00000      0.50000;
    13.                         4.00000;
    13.                         1.00000;
         (THE BETA=0 CASE IS ADDED TO ALLOW A FURTHER CHECK ON THE BENDING MAGNET )   
         (MATRIX ELEMENTS USING THE N=1/2 THEOREMS LISTED ON PAGES 92 AND 93 OF SLAC 75   )   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    49 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(14) N=1/2 BETA= 0 42.43 DEGREE BEND NO FRINGE FIELDS NORM UNITS                

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 N   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 N       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 N       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.00000E+00
 *BEND*          4.                74.05000 CM       10.00000 KG        0.50000      (   100.000 CM  ,  42.428 DEG )
     74.050 CM  
 *TRANSFORM 1*                
              0.86602   0.70712   0.00000   0.00000   0.00000   0.26796
             -0.35356   0.86602   0.00000   0.00000   0.00000   0.70712
              0.00000   0.00000   0.86602   0.70712   0.00000   0.00000
              0.00000   0.00000  -0.35356   0.86602   0.00000   0.00000
             -0.70712  -0.26796   0.00000   0.00000   1.00000  -0.06675
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  2.992E-03
   1 12  6.755E-01   1 22  1.280E-01
   1 13  0.000E+00   1 23  0.000E+00   1 33 -6.699E-02
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44 -1.340E-01
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  3.808E-01   1 26  1.619E-01   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -2.375E-01
 
   2 11  3.220E-01
   2 12  2.440E-01   2 22 -2.904E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -1.768E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44 -3.536E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  4.305E-01   2 26 -9.534E-02   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -7.347E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -2.500E-01   3 23 -9.474E-02   3 33  0.000E+00
   3 14  6.124E-01   3 24  2.321E-01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  1.073E-01   3 46  9.073E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13 -3.062E-01   4 23 -1.160E-01   4 33  0.000E+00
   4 14 -2.500E-01   4 24 -9.474E-02   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  3.082E-01   4 46  1.073E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -1.646E-02
   5 12 -1.370E-01   5 22 -3.707E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33  6.734E-04
   5 14  0.000E+00   5 24  0.000E+00   5 34  1.250E-01   5 44 -3.048E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -3.290E-02   5 26 -2.804E-01   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.849E-03
 
                                                                         -14.897  19.125 N   
                                                                         -48.993  53.436 R       0.922
                                                                           0.000   9.926 N       0.000  0.000
                                                                           0.000  11.204 R       0.000  0.000  0.310
                                                                         -11.103  14.803 N       0.052  0.206  0.000  0.000
                                                                           0.000   7.000 N       0.098  0.093  0.000  0.000 -0.032
0*LENGTH*         74.05000 CM  
1
0"(15) N=1/2 BETA=1/4 30.0 DEGREE BEND NO FRINGE FIELDS NORM UNITS                "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     4.000                     52.36000    10.00000      0.50000;
    13.                         4.00000;
    13.                         1.00000;
         (IT IS IMPORTANT TO CHECK THAT ANY GIVEN COMPUTER CALCULATES THE CORRECT )   
         (RESULTS FOR BENDING MAGNETS OF ANGLES LESS THAN 0.2 RADIANS. THE FOLLOWING  )   
         (TWO COMPUTATIONS ARE DESIGNED WITH THIS IN MIND. THE FIRST CALCULATION IS   )   
         (A SINGLE STEP 30 DEGREE BENDING MAGNET AND THE SECOND COMPUTATION IS A TEN  )   
         (STEP CALCULATION ADDING UP TO 30 DEGREES. OBVIOUSLY, THE RESULTS OF THE TWO )   
         (CALCULATIONS SHOULD AGREE. NORMALIZED DIMENSIONS ARE USED AND BR = 10 KG)   
         (METERS. )   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    49 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(15) N=1/2 BETA=1/4 30.0 DEGREE BEND NO FRINGE FIELDS NORM UNITS                

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *BEND*          4.                52.36000 CM       10.00000 KG        0.50000      (   100.000 CM  ,  30.000 DEG )
     52.360 CM  
 *TRANSFORM 1*                
              0.93224   0.51172   0.00000   0.00000   0.00000   0.13552
             -0.25586   0.93224   0.00000   0.00000   0.00000   0.51172
              0.00000   0.00000   0.93224   0.51172   0.00000   0.00000
              0.00000   0.00000  -0.25586   0.93224   0.00000   0.00000
             -0.51172  -0.13552   0.00000   0.00000   1.00000  -0.02376
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -3.235E-02
   1 12  4.886E-01   1 22  6.470E-02
   1 13  0.000E+00   1 23  0.000E+00   1 33 -7.652E-04
   1 14  0.000E+00   1 24  0.000E+00   1 34  1.156E-02   1 44 -6.623E-02
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  1.964E-01   1 26  5.803E-02   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -1.278E-01
 
   2 11  1.222E-01
   2 12  6.470E-02   2 22 -2.443E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -5.779E-03
   2 14  0.000E+00   2 24  0.000E+00   2 34  6.470E-02   2 44 -2.443E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  2.731E-01   2 26 -6.241E-02   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -5.230E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -6.470E-02   3 23 -2.312E-02   3 33  0.000E+00
   3 14  4.886E-01   3 24  1.294E-01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  6.241E-02   3 46  3.443E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  5.779E-03   4 23  1.530E-03   4 33  0.000E+00
   4 14 -6.623E-02   4 24 -1.156E-02   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  2.502E-01   4 46  6.547E-02   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -4.033E-05
   5 12 -6.699E-02   5 22 -2.617E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33 -5.739E-03
   5 14  0.000E+00   5 24  0.000E+00   5 34  6.393E-02   5 44 -2.384E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -1.164E-02   5 26 -1.386E-01   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -3.242E-04
 
                                                                          -7.480  10.445 M   
                                                                         -33.539  37.914 R       0.898
                                                                           0.000   7.276 M       0.000  0.000
                                                                           0.000   8.808 R       0.000  0.000  0.304
                                                                          -8.424  11.389 M       0.081  0.203  0.000  0.000
                                                                           0.000   7.000 N       0.091  0.094  0.000  0.000 -0.015
0*LENGTH*         52.36000 CM  
1
0"(16) N=1/2 BETA=1/4 30.0 DEGREE BEND 10 STEPS NO FRINGE FIELDS                  "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     9.                        10.00000;
     4.000                      5.23600    10.00000      0.50000;
     9.                         0.00000;
    13.                         4.00000;
    13.                         1.00000;
         (NOTE THE USE OF THE REPEAT ELEMENT TYPE CODE 9.0 IN SETTING UP THIS PROBLEM )   
0SENTINEL
0   15 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    53 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(16) N=1/2 BETA=1/4 30.0 DEGREE BEND 10 STEPS NO FRINGE FIELDS                  

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
      5.236 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     10.472 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     15.708 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     20.944 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     26.180 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     31.416 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     36.652 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     41.888 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     47.124 CM  
 *BEND*          4.                 5.23600 CM       10.00000 KG        0.50000      (   100.000 CM  ,   3.000 DEG )
     52.360 CM  
 *TRANSFORM 1*                
              0.93224   0.51172   0.00000   0.00000   0.00000   0.13552
             -0.25586   0.93224   0.00000   0.00000   0.00000   0.51172
              0.00000   0.00000   0.93224   0.51172   0.00000   0.00000
              0.00000   0.00000  -0.25586   0.93224   0.00000   0.00000
             -0.51172  -0.13552   0.00000   0.00000   1.00000  -0.02376
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -3.235E-02
   1 12  4.886E-01   1 22  6.470E-02
   1 13  0.000E+00   1 23  0.000E+00   1 33 -7.652E-04
   1 14  0.000E+00   1 24  0.000E+00   1 34  1.156E-02   1 44 -6.623E-02
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  1.964E-01   1 26  5.803E-02   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -1.278E-01
 
   2 11  1.222E-01
   2 12  6.470E-02   2 22 -2.443E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -5.779E-03
   2 14  0.000E+00   2 24  0.000E+00   2 34  6.470E-02   2 44 -2.443E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  2.731E-01   2 26 -6.241E-02   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -5.230E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -6.470E-02   3 23 -2.312E-02   3 33  0.000E+00
   3 14  4.886E-01   3 24  1.294E-01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  6.241E-02   3 46  3.443E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  5.779E-03   4 23  1.530E-03   4 33  0.000E+00
   4 14 -6.623E-02   4 24 -1.156E-02   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  2.502E-01   4 46  6.547E-02   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -4.031E-05
   5 12 -6.699E-02   5 22 -2.617E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33 -5.739E-03
   5 14  0.000E+00   5 24  0.000E+00   5 34  6.393E-02   5 44 -2.384E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -1.164E-02   5 26 -1.386E-01   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -3.241E-04
 
                                                                          -7.480  10.445 M   
                                                                         -33.539  37.914 R       0.898
                                                                           0.000   7.276 M       0.000  0.000
                                                                           0.000   8.808 R       0.000  0.000  0.304
                                                                          -8.424  11.389 M       0.081  0.203  0.000  0.000
                                                                           0.000   7.000 N       0.091  0.094  0.000  0.000 -0.015
0*LENGTH*         52.36000 CM  
1
0"(17) N=1/4 BETA=1/4 30.0 DEGREE BEND NO FRINGE FIELDS NORM UNITS                "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     4.000                     52.36000    10.00000      0.25000;
    13.                         4.00000;
    13.                         1.00000;
         (THIS CALCULATION IS INCLUDED SO AS TO HAVE A BENDING MAGNET CASE WHERE N    )   
         (NEITHER EQUALS ZERO NOR 1/2. NORMALIZED UNITS ARE USED AND BR = 10 KG METERS)   
0SENTINEL
0   13 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    49 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(17) N=1/4 BETA=1/4 30.0 DEGREE BEND NO FRINGE FIELDS NORM UNITS                

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *BEND*          4.                52.36000 CM       10.00000 KG        0.25000      (   100.000 CM  ,  30.000 DEG )
     52.360 CM  
 *TRANSFORM 1*                
              0.89894   0.50584   0.00000   0.00000   0.00000   0.13475
             -0.37938   0.89894   0.00000   0.00000   0.00000   0.50584
              0.00000   0.00000   0.96593   0.51764   0.00000   0.00000
              0.00000   0.00000  -0.12941   0.96593   0.00000   0.00000
             -0.50584  -0.13475   0.00000   0.00000   1.00000  -0.02368
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -9.595E-02
   1 12  4.547E-01   1 22  6.056E-02
   1 13  0.000E+00   1 23  0.000E+00   1 33  1.646E-02
   1 14  0.000E+00   1 24  0.000E+00   1 34  1.168E-02   1 44 -6.583E-02
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  2.228E-01   1 26  6.230E-02   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -1.264E-01
 
   2 11 -2.980E-08
   2 12  2.980E-08   2 22 -2.529E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33  6.031E-02
   2 14  0.000E+00   2 24  0.000E+00   2 34  6.583E-02   2 44 -2.412E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  3.838E-01   2 26 -3.311E-02   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -5.117E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  1.151E-03   3 23 -5.759E-03   3 33  0.000E+00
   3 14  5.001E-01   3 24  1.332E-01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  3.235E-02   3 46  2.930E-02   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  1.250E-01   4 23  3.331E-02   4 33  0.000E+00
   4 14 -1.150E-03   4 24  5.759E-03   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.338E-01   4 46  3.541E-02   4 56  0.000E+00   4 66  0.000E+00
 
   5 11  4.305E-03
   5 12 -3.198E-02   5 22 -2.557E-01
   5 13  0.000E+00   5 23  0.000E+00   5 33 -4.394E-03
   5 14  0.000E+00   5 24  0.000E+00   5 34  3.195E-02   5 44 -2.442E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -5.621E-03   5 26 -1.362E-01   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.588E-04
 
                                                                          -7.417  10.420 M   
                                                                         -32.416  37.333 R       0.902
                                                                           0.000   7.246 M       0.000  0.000
                                                                           0.000   6.350 R       0.000  0.000  0.332
                                                                          -8.468  11.446 M       0.090  0.201  0.000  0.000
                                                                           0.000   7.000 N       0.091  0.095  0.000  0.000 -0.014
0*LENGTH*         52.36000 CM  
1
0"(18) N=1/2 BETA=1/4 84.85 DEGREE BEND WITH FRINGE FIELDS NORM UNIT              "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     3.0                      244.93999;
     2.0                        0.00000;
     4.000                    148.10001    10.00000      0.50000;
     2.0                        0.00000;
     3.0                      244.93999;
    13.                         4.00000;
    13.                         1.00000;
         (THE FOLLOWING THREE CASES ARE INCLUDED BECAUSE THEY ARE COMPOSITE SYSTEMS   )   
         (INCLUDING FRINGING FIELDS, DRIFT DISTANCES AND VARIOUS SECOND-ORDER )   
         (CORRECTIONS. NORMALIZED UNITS ARE USED IN ALL CASES AND BR = 10 KG METERS.  )   
         (NOTE THAT, TO INCLUDE THE FRINGING FIELD MATRIX ELEMENTS IN THE CALCULATION )   
         (THE 2. ELEMENTS MUST BE ADDED TO THE PROGRAM LISTING EVEN IF THE ROTATION   )   
         (ANGLE OF THE ENTRANCE AND/OR EXIT POLE FACE IS ZERO. THUS, IN THE FOLLOWING )   
         (CALCULATION, 2. 0. ELEMENTS ARE ADDED BEFORE AND AFTER THE 4.0 BENDING  )   
         (MAGNET ENTRY.   )   
0SENTINEL
0   17 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    57 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(18) N=1/2 BETA=1/4 84.85 DEGREE BEND WITH FRINGE FIELDS NORM UNIT              

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *DRIFT*         3.               244.93997 CM  
    244.940 CM  
 *ROTAT*         2.                 0.00000 DEG 
    244.940 CM  
 *BEND*          4.               148.10001 CM       10.00000 KG        0.50000      (   100.000 CM  ,  84.855 DEG )
    393.040 CM  
 *ROTAT*         2.                 0.00000 DEG 
    393.040 CM  
 *DRIFT*         3.               244.93997 CM  
    637.980 CM  
 *TRANSFORM 1*                
             -0.99999   0.00002   0.00000   0.00000   0.00000   3.99999
             -0.61238  -0.99999   0.00000   0.00000   0.00000   1.22476
              0.00000   0.00000  -0.99999   0.00002   0.00000   0.00000
              0.00000   0.00000  -0.61238  -0.99999   0.00000   0.00000
             -1.22476  -3.99999   0.00000   0.00000   1.00000  -0.51247
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  3.333E-01
   1 12  3.266E+00   1 22  5.333E+00
   1 13  0.000E+00   1 23  0.000E+00   1 33 -9.167E-01
   1 14  0.000E+00   1 24  0.000E+00   1 34 -4.082E+00   1 44 -6.666E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  3.324E+00   1 26  8.677E+00   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -3.980E+00
 
   2 11  2.041E-01
   2 12  1.333E+00   2 22  1.633E+00
   2 13  0.000E+00   2 23  0.000E+00   2 33 -4.083E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -1.667E+00   2 44 -2.041E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  8.996E-01   2 26  1.990E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -1.391E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -8.333E-01   3 23 -4.082E+00   3 33  0.000E+00
   3 14 -4.082E+00   3 24 -1.333E+01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  3.010E+00   3 46  1.255E+01   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13 -2.041E-01   4 23 -6.666E-01   4 33  0.000E+00
   4 14 -1.667E+00   4 24 -4.082E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.142E+00   4 46  4.676E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -4.658E-01
   5 12 -1.990E+00   5 22 -4.339E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.167E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34 -4.676E+00   5 44 -6.275E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  1.621E+00   5 26  1.294E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.891E+00
 
                                                                        -327.033 424.121 M   
                                                                        -110.202 134.836 R       0.988
                                                                           0.000 494.157 M       0.000  0.000
                                                                           0.000 178.705 R       0.000  0.000  0.996
                                                                        -309.147 283.725 M       0.819  0.841  0.000  0.000
                                                                           0.000   7.000 N       0.066  0.064  0.000  0.000 -0.013
0*LENGTH*        637.97998 CM  
1
0"(19) N=0 90 DEGREE BEND WITH FRINGE FIELDS NORMALIZED UNITS                     "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "G/2 "      5.00000     0.03333;
    16.00           "K1  "      7.00000     0.46000;
    16.00           "K2  "      8.00000     2.75000;
    16.00           "1/R1"     12.00000     0.00358;
    16.00           "1/R2"     13.00000     0.00358;
     3.0                      210.59799;
     2.0                       27.71000;
     4.000                    157.08000    10.00000      0.00000;
     2.0                       27.71000;
     3.0                      210.59799;
    13.                         4.00000;
    13.                         1.00000;
0SENTINEL
0   21 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    69 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(19) N=0 90 DEGREE BEND WITH FRINGE FIELDS NORMALIZED UNITS                     

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 * G/2 *        16.     "G/2 "      5.    0.33333E-01
 * K1 *         16.     "K1  "      7.    0.46000E+00
 * K2 *         16.     "K2  "      8.    0.27500E+01
 * 1/R1 *       16.     "1/R1"     12.    0.35800E-02
 * 1/R2 *       16.     "1/R2"     13.    0.35800E-02
 *DRIFT*         3.               210.59799 CM  
    210.598 CM  
 *ROTAT*         2.                27.71000 DEG     279.32959 CM  
    210.598 CM  
 *BEND*          4.               157.08000 CM       10.00000 KG        0.00000      (   100.000 CM  ,  90.000 DEG )
    367.678 CM  
 *ROTAT*         2.                27.71000 DEG     279.32959 CM  
    367.678 CM  
 *DRIFT*         3.               210.59799 CM  
    578.276 CM  
 *TRANSFORM 1*                
             -0.99978   0.00062   0.00000   0.00000   0.00000   4.21212
             -0.72413  -0.99978   0.00000   0.00000   0.00000   1.52524
              0.00000   0.00000  -1.00017  -0.00056   0.00000   0.00000
              0.00000   0.00000  -0.59554  -1.00017   0.00000   0.00000
             -1.52524  -4.21212   0.00000   0.00000   1.00000  -0.57080
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -5.878E-02
   1 12  3.636E-01   1 22  5.021E-01
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.660E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -6.921E+00   1 44 -1.170E+01
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  4.462E+00   1 26  1.087E+01   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -4.318E+00
 
   2 11  6.895E-02
   2 12  3.808E-01   2 22  1.817E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -7.860E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -3.130E+00   2 44 -4.251E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.575E+00   2 26  3.413E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -1.878E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -1.907E+00   3 23 -6.967E+00   3 33  0.000E+00
   3 14 -8.473E+00   3 24 -2.340E+01   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  1.806E+00   3 46  1.042E+01   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13 -2.904E-01   4 23 -8.020E-01   4 33  0.000E+00
   4 14 -3.138E+00   4 24 -6.967E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  6.278E-01   4 46  4.398E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -8.101E-01
   5 12 -3.412E+00   5 22 -5.437E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.274E+00
   5 14  0.000E+00   5 24  0.000E+00   5 34 -4.295E+00   5 44 -5.018E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  2.326E+00   5 26  2.211E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -2.450E+00
 
                                                                        -526.324 581.513 M   
                                                                        -208.980 222.545 R       0.993
                                                                           0.000 522.651 M       0.000  0.000
                                                                           0.000 189.845 R       0.000  0.000  0.980
                                                                        -318.031 277.790 M       0.924  0.946  0.000  0.000
                                                                           0.000   7.000 N       0.051  0.048  0.000  0.000 -0.014
0*LENGTH*        578.27600 CM  
1
0"(20) N=1/2 BETA= 0 169.7 DEGREE BEND WITH FRINGE FIELDS NORM UNIT               "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.00000;
     3.0                       81.65000;
     2.0                        0.00000;
     4.000                    296.19000    10.00000      0.50000;
     2.0                        0.00000;
     3.0                       81.65000;
    13.                         4.00000;
    13.                         1.00000;
0SENTINEL
0   17 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    57 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(20) N=1/2 BETA= 0 169.7 DEGREE BEND WITH FRINGE FIELDS NORM UNIT               

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.00000E+00
 *DRIFT*         3.                81.65000 CM  
     81.650 CM  
 *ROTAT*         2.                 0.00000 DEG 
     81.650 CM  
 *BEND*          4.               296.19000 CM       10.00000 KG        0.50000      (   100.000 CM  , 169.704 DEG )
    377.840 CM  
 *ROTAT*         2.                 0.00000 DEG 
    377.840 CM  
 *DRIFT*         3.                81.65000 CM  
    459.490 CM  
 *TRANSFORM 1*                
             -0.99999   0.00002   0.00000   0.00000   0.00000   3.99999
             -0.61238  -0.99999   0.00000   0.00000   0.00000   1.22476
              0.00000   0.00000  -0.99999   0.00002   0.00000   0.00000
              0.00000   0.00000  -0.61238  -0.99999   0.00000   0.00000
             -1.22476  -3.99999   0.00000   0.00000   1.00000  -3.47429
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  3.750E-01
   1 12  1.225E+00   1 22  2.000E+00
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.625E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -2.041E+00   1 44 -3.333E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  2.064E+00   1 26  9.190E+00   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  2.372E+00
 
   2 11  5.543E-06
   2 12  3.623E-05   2 22  6.124E-01
   2 13  0.000E+00   2 23  0.000E+00   2 33 -6.124E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -1.000E+00   2 44 -1.021E+00
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.033E+00   2 26  3.564E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66  3.843E-01
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -2.500E-01   3 23 -2.041E+00   3 33  0.000E+00
   3 14 -2.041E+00   3 24 -6.667E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -1.064E+00   3 46 -1.025E+00   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  6.124E-01   4 23  2.000E+00   4 33  0.000E+00
   4 14 -1.000E+00   4 24 -2.041E+00   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.921E-01   4 46  4.362E-01   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -8.811E-01
   5 12 -3.564E+00   5 22 -4.595E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -3.437E-01
   5 14  0.000E+00   5 24  0.000E+00   5 34 -4.362E-01   5 44  5.124E-01
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -5.342E-01   5 26 -5.745E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -2.356E+00
 
                                                                          26.407 288.971 M   
                                                                         -10.974  92.509 R       0.945
                                                                           0.000 114.937 M       0.000  0.000
                                                                           0.000  43.939 R       0.000  0.000  0.390
                                                                        -153.005 215.420 M      -0.870 -0.727  0.000  0.000
                                                                           0.000   7.000 N       0.097  0.093  0.000  0.000 -0.113
0*LENGTH*        459.49002 CM  
1
0"(21) N=1/2 BETA=1/4 169.7 DEGREE BEND WITH FRINGE FIELDS NORM UNIT              "
0    0
    15.                         1.00000   "M   "      100.00000 ;
    15.                         2.00000   "R   "     1000.00000 ;
    15.                         5.00000   "M   "      100.00000 ;
    15.                         8.00000   "CM  "        0.01000 ;
    15.                        11.00000   "MEV "        0.00100 ;
    15.                         6.00000   "N   "      100.00000 ;
     1.000000                   2.00000     3.00000     4.00000     5.00000     6.00000     7.00000   299.79248;
    13.                         2.00000;
    17.                         2.00000     2.00000;
    16.00           "BETA"      1.00000     0.25000;
     3.0                       81.65000;
     2.0                        0.00000;
     4.000                    296.19000    10.00000      0.50000;
     2.0                        0.00000;
     3.0                       81.65000;
    13.                         4.00000;
    16.00                      15.00000    56.60000;
     3.0                        0.00000;
    13.                         4.00000;
    16.00                      15.00000   -56.60000;
     3.0                        0.00000;
    16.00                      15.00000     0.00000;
    16.00                      15.00000    27.70000;
     3.0                        0.00000;
    13.                         4.00000;
    16.00                      15.00000     0.00000;
    13.                         1.00000;
         (THE 16. 15. ALPHA. TYPE CODE IS USED IN THIS EXAMPLE TO ROTATE TO THE X AND )   
         (Y FOCAL PLANES. THE X FOCAL PLANE CORRESPONDS TO THE ANGLE FOR WHICH THE)   
         (126 MATRIX ELEMENT = 0 ; THE Y FOCAL PLANE CORRESPONDS TO THE ANGLE FOR )   
         (WHICH THE 346 MATRIX ELEMENT = 0.   )   
0SENTINEL
0   27 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    82 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(21) N=1/2 BETA=1/4 169.7 DEGREE BEND WITH FRINGE FIELDS NORM UNIT              

 *BEAM*          1.               299.79248 MEV 
      0.000 CM                                                             0.000   2.000 M   
                                                                           0.000   3.000 R       0.000
                                                                           0.000   4.000 M       0.000  0.000
                                                                           0.000   5.000 R       0.000  0.000  0.000
                                                                           0.000   6.000 M       0.000  0.000  0.000  0.000
                                                                           0.000   7.000 N       0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *EPS*          16.     "BETA"      1.    0.25000E+00
 *DRIFT*         3.                81.65000 CM  
     81.650 CM  
 *ROTAT*         2.                 0.00000 DEG 
     81.650 CM  
 *BEND*          4.               296.19000 CM       10.00000 KG        0.50000      (   100.000 CM  , 169.704 DEG )
    377.840 CM  
 *ROTAT*         2.                 0.00000 DEG 
    377.840 CM  
 *DRIFT*         3.                81.65000 CM  
    459.490 CM  
 *TRANSFORM 1*                
             -0.99999   0.00002   0.00000   0.00000   0.00000   3.99999
             -0.61238  -0.99999   0.00000   0.00000   0.00000   1.22476
              0.00000   0.00000  -0.99999   0.00002   0.00000   0.00000
              0.00000   0.00000  -0.61238  -0.99999   0.00000   0.00000
             -1.22476  -3.99999   0.00000   0.00000   1.00000  -3.47429
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -4.621E-06
   1 12  1.440E-05   1 22  2.358E-05
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.250E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -8.165E-01   1 44 -1.333E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  1.855E+00   1 26  6.057E+00   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  2.907E-01
 
   2 11  2.772E-06
   2 12  1.812E-05   2 22  7.222E-06
   2 13  0.000E+00   2 23  0.000E+00   2 33 -6.124E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -1.000E+00   2 44 -4.082E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.161E+00   2 26  1.855E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -1.097E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  5.000E-01   3 23 -8.165E-01   3 33  0.000E+00
   3 14 -8.165E-01   3 24 -2.667E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -8.546E-01   3 46  2.108E+00   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  6.124E-01   4 23  2.000E+00   4 33  0.000E+00
   4 14 -1.000E+00   4 24 -8.165E-01   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  6.406E-02   4 46  2.145E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -2.937E-01
   5 12 -1.855E+00   5 22 -3.029E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -9.311E-01
   5 14  0.000E+00   5 24  0.000E+00   5 34 -2.145E+00   5 44 -1.054E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -1.781E-01   5 26 -4.582E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.943E+00
 
 *FOTILT*       16.                15.    0.56600E+02
 *DRIFT*         3.                 0.00000 CM  
    459.490 CM  
 *TRANSFORM 1*                
             -0.99999   0.00002   0.00000   0.00000   0.00000   3.99999
             -0.61238  -0.99999   0.00000   0.00000   0.00000   1.22476
              0.00000   0.00000  -0.99999   0.00002   0.00000   0.00000
              0.00000   0.00000  -0.61238  -0.99999   0.00000   0.00000
             -1.22476  -3.99999   0.00000   0.00000   1.00000  -3.47429
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  9.287E-01
   1 12  1.517E+00   1 22 -1.114E-05
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.250E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -8.165E-01   1 44 -1.333E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16 -3.718E+00   1 26 -9.110E-03   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  7.720E+00
 
   2 11  2.772E-06
   2 12  1.812E-05   2 22  7.222E-06
   2 13  0.000E+00   2 23  0.000E+00   2 33 -6.124E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -1.000E+00   2 44 -4.082E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.161E+00   2 26  1.855E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -1.097E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  1.429E+00   3 23 -8.166E-01   3 33  0.000E+00
   3 14  7.000E-01   3 24 -2.667E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -4.569E+00   3 46 -3.958E+00   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  6.124E-01   4 23  2.000E+00   4 33  0.000E+00
   4 14 -1.000E+00   4 24 -8.165E-01   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  6.406E-02   4 46  2.145E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -2.937E-01
   5 12 -1.855E+00   5 22 -3.029E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -9.311E-01
   5 14  0.000E+00   5 24  0.000E+00   5 34 -2.145E+00   5 44 -1.054E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -1.781E-01   5 26 -4.582E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.943E+00
 
 *FOTILT*       16.                15.   -0.56600E+02
 *DRIFT*         3.                 0.00000 CM  
    459.490 CM  
 *FOTILT*       16.                15.    0.00000E+00
 *FOTILT*       16.                15.    0.27700E+02
 *DRIFT*         3.                 0.00000 CM  
    459.490 CM  
 *TRANSFORM 1*                
             -0.99999   0.00002   0.00000   0.00000   0.00000   3.99999
             -0.61238  -0.99999   0.00000   0.00000   0.00000   1.22476
              0.00000   0.00000  -0.99999   0.00002   0.00000   0.00000
              0.00000   0.00000  -0.61238  -0.99999   0.00000   0.00000
             -1.22476  -3.99999   0.00000   0.00000   1.00000  -3.47429
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  3.215E-01
   1 12  5.250E-01   1 22  1.156E-05
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.250E+00
   1 14  0.000E+00   1 24  0.000E+00   1 34 -8.165E-01   1 44 -1.333E+00
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16 -7.438E-02   1 26  3.957E+00   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66  2.863E+00
 
   2 11  2.772E-06
   2 12  1.812E-05   2 22  7.222E-06
   2 13  0.000E+00   2 23  0.000E+00   2 33 -6.124E-01
   2 14  0.000E+00   2 24  0.000E+00   2 34 -1.000E+00   2 44 -4.082E-01
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.161E+00   2 26  1.855E+00   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -1.097E+00
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  8.215E-01   3 23 -8.166E-01   3 33  0.000E+00
   3 14 -2.915E-01   3 24 -2.667E+00   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -2.141E+00   3 46  7.915E-03   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  6.124E-01   4 23  2.000E+00   4 33  0.000E+00
   4 14 -1.000E+00   4 24 -8.165E-01   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  6.406E-02   4 46  2.145E+00   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -2.937E-01
   5 12 -1.855E+00   5 22 -3.029E+00
   5 13  0.000E+00   5 23  0.000E+00   5 33 -9.311E-01
   5 14  0.000E+00   5 24  0.000E+00   5 34 -2.145E+00   5 44 -1.054E+00
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -1.781E-01   5 26 -4.582E+00   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.943E+00
 
 *FOTILT*       16.                15.    0.00000E+00
                                                                          88.228 224.390 M   
                                                                         -73.741  91.872 R      -0.496
                                                                           0.000  73.186 M       0.000  0.000
                                                                           0.000  80.763 R       0.000  0.000  0.040
                                                                        -164.903 182.927 M      -0.789  0.474  0.000  0.000
                                                                           0.000   7.000 N       0.125  0.093  0.000  0.000 -0.133
0*LENGTH*        459.49002 CM  
1
0"(22) TEST OF SECOND ORDER MATRIX ELEMENTS FOR STRONGFOCUS                       "
0    0
    15.                         0.00000   "    "        0.00000 ;
     1.000000                   2.00000     5.00000     2.00000     5.00000     0.00000     2.00000    10.00000;
    17.                         2.00000     2.00000;
     4.000          "BEND"      2.00000     5.00000   -500.00000;
    13.                         4.00000;
         (THIS WAS PREVIOUSLY THE A.G.B.M. TEST   )   
         (UNITS ARE RESET TO THEIR DEFAULT VALUE L=CMS FOR THE BEAM PARAMETERS)   
         (THIS IS AN EXAMPLE OF SECOND ORDER MATRIX ELEMENTS FOR A STRONG FOCUSING)   
         (BENDING MAGNET. IT IS REPEATED FOR BOTH POLARITIES OF THE MAGNET)   
0SENTINEL
0    5 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    22 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(22) TEST OF SECOND ORDER MATRIX ELEMENTS FOR STRONGFOCUS                       

 *BEAM*          1.                10.00000 GEV 
      0.000 M                                                              0.000   2.000 CM  
                                                                           0.000   5.000 MR      0.000
                                                                           0.000   2.000 CM      0.000  0.000
                                                                           0.000   5.000 MR      0.000  0.000  0.000
                                                                           0.000   0.000 CM      0.000  0.000  0.000  0.000
                                                                           0.000   2.000 PC      0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *BEND*          4.     "BEND"      2.00000 M         5.00000 KG     -500.00000      (    66.713 M   ,   1.718 DEG )
      2.000 M   
 *TRANSFORM 1*                
              0.78318   0.18533   0.00000   0.00000   0.00000   0.02887
             -2.08619   0.78318   0.00000   0.00000   0.00000   0.27780
              0.00000   0.00000   1.23323   0.21532   0.00000   0.00000
              0.00000   0.00000   2.41899   1.23323   0.00000   0.00000
             -0.02778  -0.00289   0.00000   0.00000   1.00000  -0.00029
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11 -5.907E-05
   1 12  1.775E-05   1 22  9.223E-07
   1 13  0.000E+00   1 23  0.000E+00   1 33  1.622E-05
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44 -1.444E-06
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16  2.089E-03   1 26  1.439E-04   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -2.778E-04
 
   2 11 -2.670E-04
   2 12 -5.549E-05   2 22 -1.790E-05
   2 13  0.000E+00   2 23  0.000E+00   2 33  1.560E-04
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44 -1.389E-05
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16  1.924E-02   2 26  2.081E-03   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -2.563E-03
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13  6.720E-05   3 23  6.984E-06   3 33  0.000E+00
   3 14  3.426E-05   3 24  3.560E-06   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36 -2.418E-03   3 46 -1.563E-04   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13  3.849E-04   4 23  4.000E-05   4 33  0.000E+00
   4 14  6.720E-05   4 24  6.984E-06   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36 -2.595E-02   4 46 -2.418E-03   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -1.538E-04
   5 12  1.930E-04   5 22 -8.630E-05
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.842E-04
   5 14  0.000E+00   5 24  0.000E+00   5 34 -2.604E-04   5 44 -1.164E-04
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16  1.958E-05   5 26 -2.684E-05   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66  1.255E-07
 
0*LENGTH*          2.00000 M   
1
0"(23) TEST FOR OPPOSITE POLARITY                                                 "
0    1
    15.                         0.00000   "    "        0.00000 ;
     1.000000                   2.00000     5.00000     2.00000     5.00000     0.00000     2.00000    10.00000;
    17.                         2.00000     2.00000;
 *   4.000          "BEND"      2.00000     5.00000    500.00000;
    13.                         4.00000;
0SENTINEL
0    5 ELEMENTS USED OUT OF A MAXIMUM ALLOWABLE 3129
    20 NUMBERS USED OUT OF A MAXIMUM ALLOWABLE 13160
1(23) TEST FOR OPPOSITE POLARITY                                                 

 *BEAM*          1.                10.00000 GEV 
      0.000 M                                                              0.000   2.000 CM  
                                                                           0.000   5.000 MR      0.000
                                                                           0.000   2.000 CM      0.000  0.000
                                                                           0.000   5.000 MR      0.000  0.000  0.000
                                                                           0.000   0.000 CM      0.000  0.000  0.000  0.000
                                                                           0.000   2.000 PC      0.000  0.000  0.000  0.000  0.000
 *2ND ORDER*    17.                     GAUSSIAN DISTRIBUTION    2.    2.
 *BEND*          4.     "BEND"      2.00000 M         5.00000 KG      500.00000      (    66.713 M   ,   1.718 DEG )
      2.000 M   
 *TRANSFORM 1*                
              1.23275   0.21529   0.00000   0.00000   0.00000   0.03112
              2.41380   1.23275   0.00000   0.00000   0.00000   0.32271
              0.00000   0.00000   0.78360   0.18535   0.00000   0.00000
              0.00000   0.00000  -2.08234   0.78360   0.00000   0.00000
             -0.03227  -0.00311   0.00000   0.00000   1.00000  -0.00031
              0.00000   0.00000   0.00000   0.00000   0.00000   1.00000
0*2ND ORDER TRANSFORM*
   1 11  7.662E-05
   1 12  4.480E-05   1 22  2.160E-06
   1 13  0.000E+00   1 23  0.000E+00   1 33 -1.748E-05
   1 14  0.000E+00   1 24  0.000E+00   1 34  0.000E+00   1 44 -1.556E-06
   1 15  0.000E+00   1 25  0.000E+00   1 35  0.000E+00   1 45  0.000E+00   1 55  0.000E+00
   1 16 -2.408E-03   1 26 -1.556E-04   1 36  0.000E+00   1 46  0.000E+00   1 56  0.000E+00   1 66 -3.227E-04
 
   2 11  4.188E-04
   2 12  8.076E-05   2 22 -1.112E-05
   2 13  0.000E+00   2 23  0.000E+00   2 33 -1.813E-04
   2 14  0.000E+00   2 24  0.000E+00   2 34  0.000E+00   2 44 -1.614E-05
   2 15  0.000E+00   2 25  0.000E+00   2 35  0.000E+00   2 45  0.000E+00   2 55  0.000E+00
   2 16 -2.589E-02   2 26 -2.418E-03   2 36  0.000E+00   2 46  0.000E+00   2 56  0.000E+00   2 66 -3.462E-03
 
   3 11  0.000E+00
   3 12  0.000E+00   3 22  0.000E+00
   3 13 -6.720E-05   3 23 -6.480E-06   3 33  0.000E+00
   3 14  2.529E-05   3 24  2.438E-06   3 34  0.000E+00   3 44  0.000E+00
   3 15  0.000E+00   3 25  0.000E+00   3 35  0.000E+00   3 45  0.000E+00   3 55  0.000E+00
   3 16  0.000E+00   3 26  0.000E+00   3 36  2.082E-03   3 46  1.434E-04   3 56  0.000E+00   3 66  0.000E+00
 
   4 11  0.000E+00
   4 12  0.000E+00   4 22  0.000E+00
   4 13 -2.841E-04   4 23 -2.739E-05   4 33  0.000E+00
   4 14 -6.720E-05   4 24 -6.480E-06   4 34  0.000E+00   4 44  0.000E+00
   4 15  0.000E+00   4 25  0.000E+00   4 35  0.000E+00   4 45  0.000E+00   4 55  0.000E+00
   4 16  0.000E+00   4 26  0.000E+00   4 36  1.921E-02   4 46  2.082E-03   4 56  0.000E+00   4 66  0.000E+00
 
   5 11 -1.840E-04
   5 12 -2.604E-04   5 22 -1.164E-04
   5 13  0.000E+00   5 23  0.000E+00   5 33 -1.536E-04
   5 14  0.000E+00   5 24  0.000E+00   5 34  1.930E-04   5 44 -8.630E-05
   5 15  0.000E+00   5 25  0.000E+00   5 35  0.000E+00   5 45  0.000E+00   5 55  0.000E+00
   5 16 -2.564E-05   5 26 -3.359E-05   5 36  0.000E+00   5 46  0.000E+00   5 56  0.000E+00   5 66 -1.443E-07
 
0*LENGTH*          2.00000 M