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Preliminary investigation on SPS space charge effect

Preliminary investigation on SPS space charge effect. 23-02-2011. G. Franchetti Thanks to B. Salvant , H. Bartosik. SPS possible resonances. SPS working point. 3 rd order. 4 th order. Harmonics excited by SPS optics. Harmonics 108. 108 is the periodicity of beta functions (FODO).

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Preliminary investigation on SPS space charge effect

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  1. Preliminary investigation on SPS space charge effect 23-02-2011 G. Franchetti Thanks to B. Salvant, H. Bartosik

  2. SPS possible resonances SPS working point 3rd order 4th order

  3. Harmonics excited by SPS optics Harmonics 108 108 is the periodicity of beta functions (FODO) Harmonics 52 4 Qx = 104 and 2 Qx = 52 The structure resonance of second order is excited harmonic number

  4. Simulation Scan This resonance can be excited by space charge

  5. Self consistent 2D coasting beam Ex/Ex0 Qx0 = 26.13 Is it a second order resonance ? Ey/Ey0 Ex = Ey = 0.072 mm-mrad Peak current 13 A DQx= DQy ~ 0.2 Gaussian distribution truncated at 3 sigma (parameters to be checked ) Qy0

  6. Phase space after 1500 turns 2 islands appears

  7. The excitation of the 2nd order structure resonance might play a role for a high intensity bunched beam Ey/Ey0 (Periodic crossing of a space charge structure resonance…. to be checked) turns

  8. Possible new working point

  9. Low gamma Now the tunes are Qx= 20.088 Qy = 20.221 40 80 The second and forth order resonances are 2 Qx = 40 4 Qx = 80 The 4th order resonance is not excited The second order resonance has harmonics much weaker than for the case of the high Q lattice  roughly a factor 10.

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