Apr 2009  (revised)

   Use TAO to gauge increase in z axis sigma through TA section 
   of ERL 7.3 lattice, as a function of input vert/horz beam
   size,  and use/lack of radiation simulation in TA section.
        Nominal design emittance = .08e-6 m*Radians (v=h) 
   This has to be increased: A,B norm_emitt= 2e-4, 4e-4 to result 
   in test case desired:  1 mm rms beam size at TA_MAR_BEG
   (Marker at start of Turnaround).

  Use Gaussian XY beam distribution at TA_MAR_BEG  (beta x,y   =28,34 m)  
  and  in all 4 cases below, set starting z emitt =0.0 to isolate
  effect of turnaround;   no magnet errors are included.  To obtain the
  1 mm transverse sigma, normalised a,b emittances of 2,4 10**-4 
  were specified. (~4000 x design value of .08 10**-6)

  TA_MAR_BEG   transverse beam sigma x,y  = .986,  1.05 mm 
  at TA_MAR_END, no synch rad fluctuations or damping, Sig z= 3.98 microns  pix    
  turning on synch rad fluctuation and damping,        Sig z= 3.97 microns  pix     

  TA_MAR_BEG  compare  transverse beam sigma x,y ~= 0, 0 mm
                                 Radiation eff off     Sig z=   .0 microns  pix     
                        with radiation effects on      Sig z=  .22  microns  pix    

   Summary:  1mm sigma initial xy beam results in 4 micron sigma z at
  end of turnaround, with or without radiation effects included; with a
  point xy distribution, even with radiation effects, only a .2 micron
  z-sigma results.


   23 April 2009   Add gaussian quadrupole K1 errors and repeat:
   using sigma  (k err absolute, not relative) = .0002; max=3 sigma 

  "worst" case with 1 mm xy, and rad effects on, shows
  only a ~2% increase 3.97 ->4.05 microns

   Using a larger .001 sigma for k variations, 5 random tries
 only gets up to sigma z = 4.6 microns for worst case.
  5 values were: 4.33  4.10  3.74  4.29  4.6 microns.
   Executable for tao used: is ~sbp/old_exe/tao_24_apr_2009


   24 April 2009   Add bend errors: