Mismatched distributions at the PSB injection LIU PSB
Mismatched distributions at the PSB injection LIU PSB injection meeting – CERN – 12/01/2016 Layout Transverse mismatch at injection Single-particle parametric studies Space charge parametric studies Small and large tune spreads Single macro-particles behaviors Vincenzo Forte Thanks to: E. Benedetto, F. Schmidt
Transverse mismatch at injection • For the LHC, the future H- charge-exchange injection foresees a multi-turn scheme from unmodulated chopped beams from Linac 4 in an accelerating bucket (Bdr/dt= 10 Tm/s, V 1=8 k. V V 2=6 k. V in antiphase). • Up to 23 turns (for a target bunch population 3. 42 e 12 p) are necessary to face the requirements for Standard HL-LHC beams (61% chopping factor @ 40 m. A unchopped from Linac 4). • Two schemes, here called on-axis and with painting are foreseen for the multi-turn injection to define the initial emittance, leading to different space charge tune spread. On-axis scheme Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016 Transverse painting scheme
Brightness curves Where we started from… B K L A T P A R . E Y T X E O N T E T H E T D N NE I UP BE CERN PS BOOSTER UPGRADE AND LHC BEAMS EMITTANCE E. Benedetto et al. – IPAC 15 W • Space charge is a serious limit for the brightness of the LHC beams. • The brightness curves (intensity vs. emittance) define the expected performances for the future injection. • After working point optimization a good injection tune could be 4. 43, 4. 6 Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Brightness curves • Simulations with multi-turn injection, foil for the on-axis and the transverse painting solution… What happens for intermediate starting emittances? Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Single-particle parametric studies • Parametric studies are needed to determine the dependence of the final emittances vs. different initial steering conditions and to see if the transverse painting solution is truly needed (complex GFA). • Fixed the KSWs GFA to the on-axis scheme, one could think to inject at a certain fixed (x-y) offset from the COD (x. COD, y. COD)=(-80. 9, 0). • In single-particle (no s. c. ), the evolution after the injection would be the following. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Single-particle parametric studies Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) • The scenario changes with space charge Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) • The solution of the half-sum emittance is almost steady-state after 10 ms. For a wide range of initial conditions. 1. 7 um Standard HL-LHC limit 30 % margin (w. r. t. 1. 7 um) Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) • Space charge diffusion phenomena induce “Gaussian-like” shapes even if the mismatch is large… Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Residuals with Gaussian fits Without s. c. With s. c. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – maximum tune shift after 10 ms from single turn tunes computation • • The tunes behavior suggests the presence of a boundary induced by the Qx-Qy=0 coupling line, even if the lattice does not contain sources of coupling. The space charge itself could drive the coupling: linear coupling due to beam tilting (see G. Franchetti), Montague (E. Metral et al. )… Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (23 turns inj. - I = 3. 42 e 12 p. ) – coupled emittances 23 turns - End of accumulation • The tunes behavior suggests the presence of a boundary induced by the Qx-Qy=0 coupling line. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Average phase advance computation • • The tunes behavior suggests the presence of a boundary induced by the Qx-Qy=0 coupling line, even if the lattice does not contain evident sources of coupling between the two planes, but in reality all machines always have coupling induced by misalignments. The coupling is a source of energy exchange, but does not create issues for low emittance beams. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Single particle close to the resonances in presence of space charge Injecting at (x, y)=(-80. 4, 0) =(-80. 9, 0)+(0. 5, 0) CO OFFSET Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016 10 times more particles instantaneously on the coupling for the extreme tune spread
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Single particle close to the resonances in presence of space charge • Particles with tunes in a “safe-area”, far from the coupling resonance, present linear motion behavior. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Single particle close to the resonances in presence of space charge • Tunes close to the coupling resonance feel its trapping effects. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Single particle close to the resonances in presence of space charge • The coupling is more evident when one picks up a particle which makes a small movement around the coupling. In this case the particle is clearly trapped Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Large tune spread DOUBLE SCATTERING EFFECT (VERTICAL INTEGER + COUPLING) Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Summary and conclusions • • • Basic concepts about the multi-turn injection for the emittance tailoring have been introduced (transverse mismatch techniques). Starting from the results and models presented by E. Benedetto et al. (IPAC 15), the brightness curves have been simulated including the multi-turn injection process. A parametrization matrix of the possible x-y injection misteerings keeping the KSW at constant value has been analyzed in detail (0. 5 mm resolution). • Single particle and multi=particle simulation results have been shown. The capture process with space charge (I=3. 421 e 12, HL-LHC Standard) has been simulated over the parametrization matrix (extensive simulation campaign: 121 jobs launched of 10000 turns each). Good results in terms of capture and HL-LHC target emittance (<1. 7 um) have been achieved (up to 30% margin) arriving to a steady-state condition of the emittances half-sum after 10 ms for a wide range of mismatches. • It is possible to obtain round beam in the wanted emittances. • The space charge diffusion helps the beam profiles to stay reasonably “Gaussian” even for big injection mismatches. • Complicated KSW GFAs are not necessary. Simulations say that in long term it is sufficient a constant mismatch from the COD. • The maximum tune shift is limited by the coupling line. The brightness of the PSB with Linac 4 is influenced by the integer resonances and the coupling. • The integer resonances are a strong limit –> emittance blow-up - known • The coupling resonance is a small limit – as energy exchange, it makes the emittances approach each other but does not represent a concern for small emittance beams. The particles tune spread after 10 ms, averaged over one synch period, shows a negligible component over the coupling line. Particles are trapped and scattered through multiple resonance crossing across the coupling line – linear coupling induced by space charge seems dominant. Larger tune spreads have more particles with average tune on the coupling line. Fix lines (see F. Schmidt and G. Franchetti studies) are clearly visible also in space charge dominated regime. • Each case of particle-resonance interaction should be treated independently to show the nature of the resonance. Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
Appendix
G. Franchetti – space charge lectures – Intensity effects CAS – CERN 2015
G. Franchetti – space charge lectures – Intensity effects CAS – CERN 2015
Frequency response of the transverse positions in one synch period
Parametric studies with space charge (I = 3. 42 e 12 p. ) – Single particle close to the resonances in presence of space charge Nice shapes are evident also with larger tune spread excursions Mismatched distributions at the PSB injection Vincenzo Forte – LIU PSB injection meeting – CERN – 12/01/2016
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