Shift of coherent modes for bunches interacting with an electron cloud
description
Transcript of Shift of coherent modes for bunches interacting with an electron cloud
Shift of coherent modes for bunches interacting with an electron cloud
H. Bartosik, Y. Papaphilippou, G.Rumolo
Introduction• Studying the electron cloud instability for a set of parameters similar to
SPS nominal optics• Mode analysis for the two cases of
– varying the electron cloud density – varying the proton bunch intensity
• Proton bunch intensity determines electron oscillation frequency “pinch” • Strength of kick on the bunch particles and tune-spread is determined by
electron cloud density• Simulation aspects
– Simulations for bending magnets– Only small number of turns (250) analyzed since wake field is strongly
depending on bunch transverse dimensions (emittance blow-up, …)– Small initial kick in vertical plane– Nonlinear longitudinal bucket
Identifying instability threshold• Increasing coherent oscillation amplitude is associated with exponential emittance
growth• Possible definition of threshold: smallest value of electron cloud density for which the
emittance after investigated number of turns is bigger than threshold value (arbitrary!!)– Threshold considered here: emittance growth by ~5% after 512 turns – Instability threshold identified by scanning electron cloud density ρ
• Two regimes when scanning electron cloud density– Exponential emittance growth for electron density above but close to threshold– “Incoherent” effects far beyond instability threshold
• Spectral analysis of the first 250 turns mode diagram– Electron cloud induces positive coherent tune shift (focusing force)– Instability threshold previously identified from emittance growth corresponds
to electron density where unstable mode starts appearing
Threshold identified by emittance growth
Mode analysis for constant Nb
Incoherent regime
Nb=1.3e11 p/b
Mode analysis for constant ρ=4e11/m3
– Observed coherent mode is stays constant with increasign bunch intensity Nb
– Bunch intensity defines rise-time– No obvious transition between stable and
unstable motion (threshold ~1.6e11 p/b)
ρ=4e11/m3
Mode analysis for constant ρ=8e11/m3
– Mode structure seems defined by the electron cloud density (see scan of ρ)
– At the onset of instability (~0.7e11 p/b) unstable mode appears
– Coherent modes are almost not shifting with intensity
– Mode diagram becomes fuzzy for high bunch intensities as emittance is blown up rapidly
Instability too violent within the first 250 turns …
ρ=8e11/m3
• Topology of mode diagram very similar for different Qs– Unstable mode between instability threshold and “incoherent regime” – Unstable mode at onset of instability about 1Qs shifted above stable
mode– No indication for “mode coupling”– Onset of instability is shifted towards higher ρ with increasing Qs
Comparison for different values of Qs
Nb=1.3e11 p/b Nb=1.3e11 p/b
• Electron cloud density at which unstable mode starts appearing seems not very dependent on bunch intensity– However unstable mode quickly increases in amplitude for hicher bunch
intensity while it takes longer to become dominant for lower intensity– At the point where unstable mode appears, it is shifted about 1Qs above
the zero mode• To be studied in more detail in future simulations …
Comparison for different Nb
Instability too violent within the first 250 turns …
Nb=2.5e11 p/b Nb=1.3e11 p/b
Summary• Scanning ρ reveals expected positive tune shift due to electron
cloud plus a mode structure – ECI can be identified with mode appearing in mode diagram– For very high ρ, coherent motion seems damped (due to tunespread)
and mode diagram becomes fuzzy – incoherent emittance growth … • When scanning the bunch intensity Nb
– Mode structure seems defined by value of ρ – Only small variation of tunes and modes as function of intensity
• When unstable mode appears, it seems to be shifted by ~1Qs• The electron cloud density for which mode appears depends on Qs
but not (so much) on bunch intensity• No indication for mode coupling …
Interesting…