Can Space Charge Stabilize a Bunch Greatly 1 AB APC talk Aug 1 amp 2 2018 Alexey Burov Fermilab Many thanks to T Zolkin and E Metral Problem 2 AB Single bunch in a circular machine Linear optics ID: 766255
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Can Space Charge Stabilize a Bunch Greatly? 1 AB APC talk, Aug 1 & 2, 2018 Alexey Burov Fermilab Many thanks to T. Zolkin and E. Metral
Problem 2 AB Single bunch in a circular machine; Linear optics; Zero chromaticity; Short wake; Space charge (SC); Can SC make bunch transverse coherent oscillations (much) more stable?
What we know 3 AB Threshold wake of the transverse instability (TMCI) may be elevated significantly by SC (Theory) It had to be elevated by the strong SC at CERN SPS Q26 (Theory) This did not happen (CERN observations and macroparticle simulations)
What we do not know 4 AB Threshold wake of the transverse instability (TMCI) may be elevated significantly by SC (Theory) It had to be elevated by the strong SC at CERN SPS Q26 (Theory) This did not happen (CERN observations and macroparticle simulations) What is wrong in the picture?
No SC 5 AB https:// arxiv.org /abs/1806.07521
TMCI, no SC 6 AB TMCI is a single bunch instability at zero chromaticity, having a sharp threshold CERN SPS Q20 Airbag model cm; GHz; ; MOhm/m
TMCI, no SC 7 AB With more rings, the threshold is not that sharp: A low and high intensity thresholds can be introduced. low high
Parameters 8 AB
Thresholds 9 AB The HI TMCI threshold, expressed in terms of dp /p and line density, is very close to the stability threshold of a coasting Gaussian beam, thus confirming Ruth-Wang (1981) microwave stability criterion.
Air-Bag, Square well (ABS) 10 AB M. Blaskiewicz , 1999
ABS model 11 AB Similar long-bunch asymptotic formula was found to be valid for the ABS. With t b =4 s s it is almost identical to the parabolical Gaussian TMCI and Gaussian coasting beam.
Conclusion for no_SC : 12 AB TMCI threshold is close to the coasting beam transverse microwave stability threshold
TMCI with SC: only 2 types are possible 13 AB https://arxiv.org/abs/1711.11110
TMCI with SC: vanishing TMCI 14 AB Coherent tune shift ~ SC tune shift BB impedance model f=1.3GHz sigma_s = 30cm (Quatraro & Rumolo, IPAC’10)
Intrinsic Landau Damping 15 AB SC introduces LD for bunched beams
Stability vs SC for Coasting Beams 16 AB For coasting beams, SC suppresses LD, so wake threshold drops exponentially with SC
Strange theoretical feature of TMCI @ SSC 17 AB According to TMCI @ SSC theory, at dQ sc /Q s >> 1, the threshold condition is Wake* N b ~ dQsc, Thus being independent of the # particles/bunch Nb! Does it contradict to observations? It certainly does.
Contradiction: SPS (2013) 18 AB These measurements reasonably agree with no SC TMCI threshold, but SC was really huge at Q26. They contradict to everything in the TMCI @ SSC theory!
Resolution 19 AB
Convective Instabilities 20 AB
ACI 21 AB
Air-Bag, Square well (ABS) 22 AB
Air-Bag, Square well (ABS) 23 AB
No-Wake Eigenvalues 24 AB
No-Wake Eigensystem 25 AB SSC case q = 20
No-Wake Eigensystem 26 AB Same SSC case
Eigenfunctions, Broadband, No SC AB w = 13 (2 ) No SC Near TMCI At no-SC, Phases run similar to no-wake
Eigenfunctions, Broadband, No SC AB w = 13 (2 ) At no-SC, Modes -2 and -3 are about to couple Near TMCI
AB Strong SC q = 20 w = 13
AB Centroid oscillations, same case q = 20 w = 13
AB Centroid, above the TMCI q = 4 w = 35
AB Cauchy Problem w= 13 , q = 20
AB w= 13 , q = 20
AB w= 13 , q = 20
AB w= 7 , q = 20
Absolute-Convective Instability (ACI) 36 AB
ACI excited by damping 37 AB
ACI excited by damping 38 AB
PS Observations 39 AB E. Metral, HB 2005
SPS Observations 40 AB H. Bartosik, CERN, Thesis , 2013
TMCI with SC: vanishing TMCI 41 AB
42 AB Many thanks!