1. FASTION (by end 2007) A code to study the fast ion instability in a transport line Multi-bunch code, ions and electrons are macro-particles Ions of an arbitrary number of species are created at each bunch passage and propagated through the train Line is made of a sequence of FODO cells, two kicks per FODO cell. Electromagnetic interaction: the ions are kicked by the passing bunches and the bunch macro-particles feel the effect of the ion field ion electron Bunch nBunch n+1 FODO Cell j s x y Kick 2Kick 1

2. FASTION  Output files  The code transports the bunch train through the line, generates the ions at each interaction and propagates them Ion distributions in x and y are stored at an arbitrary time step (for instance, at the beginning) The phase space coordinates of 4 sample ions are stored at the same time step as above Snap-shots of the bunch by bunch centroids and emittances are saved at each time step Time evolution of the beam centroids and emittances (averaged over one third of the train) are stored 12N b /32N b /3NbNb...... IIIIII HeadTail

3. Required input file  All the essential parameters are passed through a simple input file (N el, N ion, N bunch to be specified in the source) Number_of_ion_species: 2 Partial_pressures_[nTorr]: 1. 1. Atomic_masses: 28. 18. Ionization_cross_sections_[MBarn]: 2. 2. Number_of_electrons_per_bunch: 3.7e+9 Bunch_spacing_[ns]: 500.e-3 Normalized_horizontal_emittance_(rms_value)_[nm]: 680. Normalized_vertical_emittance_(rms_value)_[nm]: 10. Bunch_length_(rms_value)_[ns]: 0.12e-3 Initial_relativistic_gamma: 17610.15 Final_relativistic_gamma: 17610.15 Number_of_FODOs: 500 FODO_Length_[m]: 40. Phase_advance_per_cell_[degrees]: 70. s A rough model of acceleration along the line was included assuming a linear ramp between the input values CO (or N 2 ) and H 2 O

4. FASTION (2008) We wanted to study the fast ion instability in the Main Linac (including a more complicated optics model + correct acceleration) ⇒ Another input file is required, twiss.dat ⇒ It gives energy and beta functions along the Main Linac (at specified s locations) ⇒ Ion generation and kicks occur at each of these points, assuming a mean energy between the given point and the next one.

5. FASTION (2008-2009) Some features are still needed for a more realistic simulation of the Main Linac and for extending the use of FASTION.... ⇒ For the MAIN LINAC, the effect of field ionization has to be taken into account as the beam size shrinks, the peak electric field of the beam can exceed a threshold value for field ionization (~10 GV/m) and all the volume swept by the beam is suddenly completely ionized only the first bunch can fully ionize the swept volume, following bunches can only ionize the molecules of rest gas that diffuse into that volume between bunches the model has been included in the FASTION code and the ML simulations have been done (will be discussed in a dedicated talk and in a PAC paper) ⇒ Plan to study fast ion instability for the drive beam (with Miriam). Some new ingredients come into play as the beam is decelerated, its emittance grows (additional input file emit.dat) during deceleration a large energy spread is generated across the bunch (difference between column 3 of Twiss.dat and beamenergy.dat, which refer to the energy of the central slice and averaged over the beam, respectively) understand the available inputs (see next slides)

6. FASTION for the drive beam File Twiss.dat ⇒ Legenda seems not consistent with the columns.... # 1.) Element number # 2.) s: [m] Distance in the beam line: s # 3.) E(s): energy [GeV] (central slice) # 4.) beta_x_m(s) [m] (of central slice) # 5.) alpha_x_m(s) [m] (of cental slice) # 6.) beta_y_m(s) [m] (of central slice) # 7.) alpha_y_m(s) [m] (of cental slice) # 8.) beta_x_i(s) [m] (of average over slices) # 9.) alpha_x_i(s) [m] (of average over slices) # 10.) beta_y_i(s) [m] (of average over slices) # 11.) alpha_y_i(s) [m] (of average over slices) # 12.) ks: Quadrupol strenght

7. FASTION for the drive beam File Twiss.dat ⇒ More reasonable to assume columns 4 and 8 respectively for  x and  y. What about columns 6 and 10 ? # 1.) Element number # 2.) s: [m] Distance in the beam line: s # 3.) E(s): energy [GeV] (central slice) # 4.) beta_x_m(s) [m] (of central slice) # 5.) alpha_x_m(s) [m] (of cental slice) # 6.) beta_y_m(s) [m] (of central slice) # 7.) alpha_y_m(s) [m] (of cental slice) # 8.) beta_x_i(s) [m] (of average over slices) # 9.) alpha_x_i(s) [m] (of average over slices) # 10.) beta_y_i(s) [m] (of average over slices) # 11.) alpha_y_i(s) [m] (of average over slices) # 12.) ks: Quadrupol strenght

8. FASTION for the drive beam File emit.dat ⇒ The emittance increase does not seem to occur uniformly along the decelerator, therefore for a correct modeling this has to be taken into account (in a similar fashion as geometric emittance reduction is taken into account during acceleration/deceleration). FASTION has been already adapted to read the emit.dat file in input.

9. FASTION for the drive beam File beamenergy.dat ⇒ The beam energy evolution along the line can be obtained from column 3 of Twiss.dat (like for the Main Linac) as well as from another input file beamenergy.dat. However from Twiss.dat one gets the energy of the central slice and from beamenergy.dat one gets the beam mean energy. ⇒ There is a huge energy spread across the beam, which should be included in the simulation for correct modeling ? With which distribution ? With which width ?

10. FASTION for the drive beam Parameters used for the simulation.... ⇒ Follows a list of the numbers needed to run FASTION (from Miriam)....