BMAD based computer excercises

The program first_turn is used to track a single particle, compute closed orbit and twiss parameters, tunes, chromaticity, etc. Parameters are initialized in the lattice file bmad_ring.lat and on the command line.

g2_tracking is used to propagate a single particle or a distribution of particles. Tracking is initiated at the end of the M5 line or in the ring. Input parameters are set in an initialization file named input.dat as well as the lattice file bmad_g2_tracking.lat

Update USPAS computer with latest bmad

• To check out the distribution type svn co https://accserv.lepp.cornell.edu/svn/trunk/src/g-2
• To update, go to the g-2/ directory and type svn up

Characterize the ring

1. Compute and plot the closed orbit for the magic momentum
   1. Compute and plot the closed orbit for fractional momentum offsets Δp/p = -0.003,-0.002 ... 0.003 Instructions
   2. Use the momentum dependent closed orbit data to determine the dispersion (dx/dp)
   3. Compute the closed orbit for the asymmetric quad voltage corresponding to the start of the quad ramp and compare to the end of scraping orbit. (Vary quad voltages as required in the bmad_ring.lat file)
   4. Determine the dependence of the closed orbit on a radial component of the field.
2. Compute and plot horizontal and vertical β functions and tunes and dispersion (η). Is the dispersion consistent with your earlier calculation?
   1. Compute beta functions and tunes for start of scraping quad voltages
   2. Determine dependence of beta functions and tunes on quad voltage. Plot tune vs voltage. Plot betatron frequency vs voltage
   3. Compute and plot tunes and betatron frequency vs momentum.
3. The beam is focused to a waist to clear the narrow inflector aperture.
   1. Estimate values of horizontal and vertical β required at the inflector to insure that 95% of the particles in an injected distribution with emittance ε= 40 mm-mrad clear the inflector (28mm full width, 56mm full height). Then propagate β around the ring. Compare the mismatched β function with your result from above.
   2. Estimate the value of the dispersion at the inflector to insure that 95% of the particles in an injected distribution with 2% momentum spread clear the aperture. Propagate that value of dispersion around the ring and compare to the closed ring dispersion computed above.

Spin tracking

1. Propagate polarization of a single muon through many turns. The NAFF algorithm is used to compute spin tunes. Keep in mind that in order to evaluate systematics we need to measure spin tune. with ~10 part per billion precision. How many turns do we need to track to achieve that precision? (Use initialization file input_ST.dat) Instructions The polarization on each turn is recorded in the file single_particle_tbt.dat
2. Track a single particle, for however many turns is required to determine spin tune with part per billion precision, with momenta -0.002,-0.001,...,0.002 and plot omega_a vs momentum. Compare the change in omega_a for each momentum to the contribution from average (βXE) along the particle trajectory. Plot the running average of (βXE) and translate to Ce (E-field correction) using BetaCrossE-single-uspas.gnu
3. Track a single on momentum particle with initial vertical displacements -0.035,-0.025,...,0.035 m and determine dependence of omega_a on vertical amplitude. Compare the shift in omega_a for each vertical amplitude to the average (β•B)β contribution.

Track a distribution

1. Create a distribution of 1000 muons with ε_x=ε_y = 40 mm-mrad, Δp/p=0 and 120ns bunch length. Propagate for 400 microseconds. Plot and characterize the fast rotation signal and its fourier transform. (Use initialization file input_FR1.dat)Instructions
2. Create a distribution of 1000 muons with ε_x=ε_y = 40 mm-mrad, Δp/p=0.002. Characterize the fast rotation signal and use FFT to reconstruct the frequency distribution from the FR data. How is the frequency distribution related to the momentum distribution? (Use input_FR2.dat)

Programs

First_turn

• To run the program type ./first_turn and type responses to the prompts. The appropriate response to the first question is bmad_ring.lat
  
• The field map for each of the quad plates (inner, bottom, outer, top and short and long) is defined in quad_combined_curvilinear.bmad
• The voltage on each plate is set in bmad_ring.lat. There are four quads, each consisting of a short and long set of plates. The four plates are labelled grid_field(i)%field_scale with index 3-6 corresponding to inner, bottom, outer, and top plates. The multiplier f sets the voltage for that plate in kV.
• Edit the file to change the multiplier (and plate voltage).
• Turn on a uniform radial field by setting radial_field to some non-zero value.

Output: Twiss parameters and closed orbit are written to the file beta_eta_x_y.dat

Instructions

1. Create a working directory. < mkdir a_name >
2. Go down to that directory < cd a_name >
3. Copy the lattice file bmad_ring.lat to the directory < cp <PATH>/g-2/documentation/uspas/bmad_ring.lat . >
4. Create soft links to all reference files
   • <PATH>/g-2/softlink_lnx holds the list of files that the programs read with the appropriate path. You will have to set <PATH> depending on your local environment.
   • If you are at Cornell CLASSE, then create the soft links by typing /home/dlr/development9_linux/g-2/softlink_lnx
   • At Fermilab type <PATH> g-2/softlink_gm2
5. To run the program first_turn type < ./first_turn >
6. Here are a couple of examples
   1. In this example we set intial values of twiss parameters to those of the closed ring and the trajectory to the closed orbit

      -bash-4.2$ ./first_turn
       Lattice file name ? (default= bmad.)bmad_ring.lat 
       lat_file = bmad_ring.lat                                                                                                                               
       lat_file = bmad_ring.lat                                                                                                                               
      [INFO] bmad_parser:
          Parsing lattice file(s). This might take a minute or so...
      [INFO] bmad_parser:
          Created new digested file
       Fractional momentum offset ? 0.001
       Fractional momentum offset =   1.0000E-03
      [WARNING] twiss_from_mat6:
          1-TURN MATRIX MARGINALLY SYMPLECTIC WITH SYMPLECTIC ERROR OF:     0.0286
                           Q_x         Q_y      beta_x      beta_y     alpha_x     alpha_y       eta_x
      Closed ring:      0.9505      0.3157      7.6251     22.1736      0.0382     -0.0156      7.9358
       Initialize twiss ,(or use closed ring values ) (y/n)  ? n
       Closed orbit:  9.8786E-03 -2.9061E-04 -2.4785E-03 -9.5512E-07  0.0000E+00  1.0000E-03
       Initialize orbit, (or use closed orbit values) (y/n) ? n
      [WARNING] twiss_from_mat6:
          1-TURN MATRIX MARGINALLY SYMPLECTIC WITH SYMPLECTIC ERROR OF:     0.0338
      [WARNING] twiss_from_mat6:
          1-TURN MATRIX MARGINALLY SYMPLECTIC WITH SYMPLECTIC ERROR OF:     0.0323
       The length is      44.6790
      -bash-4.2$ 
      

   2. Here is a sample session where we set intial values of twiss parameters to: betax=2, betay=10, alphax=0, alphay=0 and and the start of the trajectory to x=0.. px=.,y=0,py=0

      -bash-4.2$ ./first_turn
       Lattice file name ? (default= bmad.)bmad_ring.lat
       lat_file = bmad_ring.lat                                                                                                                               
       lat_file = bmad_ring.lat                                                                                                                               
       Fractional momentum offset ? 0.001
       Fractional momentum offset =   1.0000E-03
      [WARNING] twiss_from_mat6:
          1-TURN MATRIX MARGINALLY SYMPLECTIC WITH SYMPLECTIC ERROR OF:     0.0286
                           Q_x         Q_y      beta_x      beta_y     alpha_x     alpha_y       eta_x
      Closed ring:      0.9505      0.3157      7.6251     22.1736      0.0382     -0.0156      7.9358
       Initialize twiss ,(or use closed ring values ) (y/n)  ? y
      Type betax, betay, alphax, alphay, etax (separate values with comma)
      2. 10. 0. 0. 0.
       Closed orbit:  9.8786E-03 -2.9061E-04 -2.4785E-03 -9.5512E-07  0.0000E+00  1.0000E-03
       Initialize orbit, (or use closed orbit values) (y/n) ? y
      x, px, y,py (separate values with comma)
      0. 0. 0. 0.
      Initial coordinates =   0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00  0.0000E+00  1.0000E-03
       The length is      44.6790
      

   g2_tracking

   Inputs to g2_tracking include:
   • the lattice field bmad_g2_tracking.lat that defines the geometry and fields of the injection channel, inflector, kickers, ring, quads, fields, collimators, etc.
     
   • and the initialization file named input.dat
   • There are a couple of example initialization files < cp <PATH>/g-2/documentation/uspas/input<>.dat in < cp <PATH>/g-2/documentation/uspas/ include input_ST.dat,input_FR1.dat,and input_FR2.dat You will edit the input file to adjust various parameters. Note that g2_tracking reads an input file named input.dat

     Initialization file input.dat notes

     • Set number of muons and number of turns to track

           ! <nturns> :integer - Number of turns to track                                                                          
          nturns  =1000                                                                                                        
          ! <nmuons> :integer - Number of muons to track                                                                          
          nmuons = 100                                    
       	  

     • Set initial coordinates of a single particle, or the centroid of a distribution.
       Some examples

         !initial_offsets = <x>,<y>,<z>,<px><py><dp>    (x,y,z are in meters, px, and py in rad, dp as fractional momentum offset)
          initial_offsets =  0.  0. 0. 0. 0. 0.   !magic momentum muon on the magic radius
          initial_offsets =  0.001  0. 0. 0. 0. 0.   !magic momentum muon displaced radially outward by 1mm
          initial_offsets =  0.0  0. 0. 0.0 0.001 0.   !magic momentum muon with initial vertical angle of 1mrad
          initial_offsets =  0.0  0. 0. 0.0 0.0 0.001   !muon with 0.1% momentum offset
               

     • Parameters that define a distribution

       ! <tdistr> : Time distribution of the muons, choices are "flat", "gaus", "e821", "e989"                                 
         tdistr    = "gauss"                                                                                                
       ! <tlength> : Width in time of distribution : (doesn't apply to tdistr="e821")                                          
         tlength   = 120.e-9                                                                                              
       ! <tsigma> : standard deviation (width) of time distribution if it is gaussian, (sigma for tdistr="gaus", doesn't apply 
         tsigma    = 70.e-9                                                                                              
       ! <pzdistr> : momentum distribution: "flat", "gaus"                                                                     
         pzdistr   = "gaus"
         
       ! <pz> : cutoff of longitudinal momentum distribution, (fractional energy offset with respect to reference)             
         pz        = 0.0                                                                                                 
       ! <pzsigma> : sigma for pzdistr="gaus"                                                                                  
         pzsigma   = 0.0                                                                                                 
       ! <epsdistr> : emittance distribution at production target: "delta", "flat", "gaus"                                     
         epsdistr  = "gaus"                                                                                                    
       ! <epsx> : horizontal emittance at inflector assuming no losses in injection channel (m-rad)                            
         epsx      = 16.6e-6                                                                                            
       ! <epsy> : vertical emittance at inflector assuming no losses in injection channel (m-rad)                              
         epsy      = 16.6e-6              
       	

     • Set the time bin width

         !<time_bin_width>: real - if non-zero, save moments vs time at end of each turn in bins of width = time_bin             
             time_bin_width = 10.e-9                                                                                                  
         

   Output:

   • A subdirectory with name corresponding to the date and time is created for each run and output files are written to that directory
     • Spin tunes (and cycltron tune) are in spin_tunes.dat
     • The running average of (β•B)β (along with phase space coordinates, etc.) are written to BetaCrossE_turn.dat
     • Turn by turn coordinates of single particles are written to single_particle_tbt.dat
     • Element by element coordinates of single particles are written to single_particle_by_element.dat
     • Turn by turn (and element by element) moments of a distribution are written to Beam_moments_tbt.dat (Beam_moments_by_element.dat

     • Instructions (spin tracking)

       1. Create a working directory. < mkdir a_name >
       2. Go down to that directory < cd a_name >
       3. Copy the lattice file bmad_g2_tracking.lat to the directory < cp < cp <PATH>/g-2/documentation/uspas/bmad_g2_tracking.lat . >
       4. Copy the appropriate input file from <PATH>/g-2/documentation/uspas/ to input.dat in your working directory < cp <PATH>/g-2/documentation/uspas/input_ST.dat input.dat >
       5. Create soft links to all reference files by typing < <PATH>/g-2/softlink_uspas >
       6. To run the program g2_tracking type < ./g2_tracking >
       7. The relevant data files spin_tunes.dat and BetaCrossE_turn.dat will appear in the subdirectory yyyymmdd_hhmmss

     • Instructions (fast rotation)

       1. Create a working directory. < mkdir a_name >
       2. Go down to that directory < cd a_name >
       3. Copy the lattice file bmad_g2_tracking.lat to the directory < cp <PATH>/g-2/documentation/uspas/bmad_g2_tracking.lat . >
       4. Copy the appropriate input file from <PATH>/g-2/documentation/uspas/ to input.dat in your working directory < cp <PATH>/g-2/documentation/uspas/input_FR1.dat input.dat >
       5. Create soft links to all reference files by typing < <PATH>/g-2/softlink_uspas >
       6. To run the program g2_tracking type < ./g2_tracking >
       7. The time binned data is written to Time_Dep_Moments_at_END.dat. The file contains the number of muon hits in an imaginary detector plane in each time bin along with the moments of the distribution. This is the fast rotation data.