FASTION ( by end 2007) A code to study the fast ion instability in a transport line

1. FASTION (by end 2007) • A code to studythe fast ioninstability in a transportline • Multi-bunchcode, ions and electronsaremacro-particles • Ions of an arbitrarynumber of speciesarecreated at eachbunchpassage and propagatedthroughthetrain • Line ismade of a sequence of FODO cells, twokicks per FODO cell. • Electromagneticinteraction: theionsarekickedbythepassingbunches and thebunchmacro-particlesfeeltheeffect of theionfield F O D O Bunch n+1 Bunch n y s x ion electron Cell j Kick 2 Kick 1

2. FASTION  Output files • Thecodetransportsthebunchtrainthroughtheline, generatestheions at eachinteraction and propagatesthem • Ion distributions in x and y arestored at an arbitrary time step (forinstance, at thebeginning) • Thephasespacecoordinates of 4 sampleionsarestored at thesame time step as above • Snap-shots of thebunchbybunchcentroids and emittancesaresaved at each time step • Time evolution of thebeamcentroids and emittances (averagedoveronethird of thetrain) arestored 1 2 ...... Nb/3 ...... 2Nb/3 ...... Nb Head Tail I II III

3. Requiredinputfile • All the essential parametersarepassedthrough a simple inputfile (Nel, Nion, Nbunch to bespecified in thesource) • 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. CO (or N2) and H2O A roughmodel of accelerationalongtheline was includedassuming a linear rampbetweentheinputvalues s

4. FASTION (2008) • Wewanted to studythe fast ioninstability in the Main Linac(including a morecomplicatedopticsmodel + correctacceleration) • Anotherinputfileisrequired,twiss.dat • Itgivesenergy and betafunctionsalongthe • Main Linac (at specifiedslocations) • Ion generation and kicksoccur at each of these • points, assuming a meanenergybetweenthe • givenpoint and thenextone.

5. FASTION (2008-2009) • Somefeaturesare still neededfor a morerealisticsimulation of the Main Linac and forextendingtheuse of FASTION.... • For the MAIN LINAC, theeffect of fieldionizationhas to betakenintoaccount • as thebeamsizeshrinks, thepeakelectricfield of thebeamcanexceed a thresholdvalueforfieldionization (~10 GV/m) and all thevolumesweptbythebeamissuddenlycompletelyionized • onlythefirstbunchcanfullyionizethesweptvolume, followingbunchescanonlyionizethemolecules of rest gas that diffuse intothatvolumebetweenbunches • themodel has beenincluded in the FASTION code and the ML simulationshavebeendone (will bediscussed in a dedicatedtalk and in a PAC paper) • Plan to study fast ioninstabilityforthedrivebeam(with Miriam). Somenewingredients come intoplay • as thebeamisdecelerated, itsemittancegrows (additional inputfileemit.dat) • duringdeceleration a large energyspreadisgeneratedacrossthebunch (differencebetweencolumn 3 of Twiss.dat and beamenergy.dat, whichrefer to theenergy of thecentralslice and averagedoverthebeam, respectively) • understandtheavailableinputs (seenextslides)

6. FASTION forthedrivebeam • File Twiss.dat • Legendaseemsnotconsistentwiththecolumns.... # 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: Quadrupolstrenght

7. FASTION forthedrivebeam • File Twiss.dat • Morereasonable to assumecolumns 4 and 8 respectivelyforbx and by. Whataboutcolumns 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: Quadrupolstrenght

8. FASTION forthedrivebeam • File emit.dat • Theemittanceincreasedoesnotseem to occuruniformlyalongthedecelerator, thereforefor a correctmodelingthis has to betakenintoaccount (in a similarfashion as geometricemittancereductionistakenintoaccountduringacceleration/deceleration). FASTION has beenalreadyadapted to readtheemit.datfile in input.

9. FASTION forthedrivebeam • File beamenergy.dat • Thebeamenergyevolutionalongthelinecanbeobtainedfromcolumn 3 of Twiss.dat (likeforthe Main Linac) as well as fromanotherinputfilebeamenergy.dat. HoweverfromTwiss.datonegetstheenergy of thecentralslice and frombeamenergy.datonegetsthebeammeanenergy. • Thereis a hugeenergyspreadacrossthebeam, whichshouldbeincluded in thesimulationforcorrectmodeling ? Withwhichdistribution ? Withwhichwidth ?

10. FASTION forthedrivebeam • Parameters usedforthesimulation.... • Follows a list of thenumbersneeded to run FASTION (from Miriam)....