# Bunch length modulation in storage rings C. Biscari LNF – INFN - Frascati Workshop on “Frontiers of short bunches in storage rings” – Frascati – 7-8 Nov.

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Bunch length modulation in storage rings C. Biscari LNF – INFN - Frascati Workshop on “Frontiers of short bunches in storage rings” – Frascati – 7-8 Nov 2005

CTF3 stretcher - compressor Bunch length (mm) measurements (2004) R 56 = - 0.1 R 56 = 0R 56 = 0.1 R 56 = 0.2 R 56 = 0.3R 56 = 0.4 R 56 = 0.5 Bunch length manipulation routinely done in linear systems: linacs, fels, ctf3,…. By using dispersion in dipoles and correlation in the longitudinal phase plane introduced by rf acceleration

In storage rings Even if particles follow different paths according to the different energy, their oscillations around the synchronous one are usually within the natural bunch dimensions Large dispersion in dipoles and large rf cavity voltage derivative can force the oscillations to grow and lead to correlation in longitudinal phase plane

Longitudinal plane oscillations in a ring with one rf cavity* Drift functions: *A. Piwinski, “Synchrotron Oscillations in High-Energy Synchrotrons,” NIM 72, pp. 79-81 (1969). Described by the vector Rf cavity lens One-turn matrix Momentum compaction Sections with dipoles

One turn longitudinal matrix – one cavity in the ring Longitudinal Twiss functions Phase advance determined by  c L and rf Bunch length can be modulated Energy spread constant along the ring and defined by rf and phase advance

Longitudinal emittance and energy spread* Energy spread defined by eigen values of matrix M, considering radiation damping and energy emission Emittance diverges for  = 0, 180° (Q s = 0, 0.5)  E/E ll *A.W. Chao, “Evaluation of Beam Distribution Parameters in an Electron Storage Ring”, Journal of Applied Physics 50: 595-598, 1979

The idea of squeezing the bunch longitudinally in a limited part of the ring came to Frascati when working in Superfactories studies (A. Hofmann had proposed a similar experiment in LEP) Short bunches at IP + high currents per bunch Low energy: microwave instability dominates the longitudinal bunch dimensions Strong rf focusing

Longitudinal phase space RF input RF center RF output IP Bunch length Energy spread High rf voltage + high momentum compaction: High synchrotron tune Ellipse rotates always in the same direction From RF to IP Strong rf focusing – monotonic R 1 * *A. Gallo, P. Raimondi, M.Zobov,“The Strong RF Focusing: a Possible Approach to Get Short Bunches at the IP”, e-Print Archive:physics/0404020. Proceedings of the 31th ICFA BD workshop, SLAC 2003 From IP to RF

Evolution of Strong rf focusing – non monotonic R 1 * High rf voltage + high derivative of R 1 (s): Low synchrotron tune Ellipse rotates on both directions dR 1 /ds > 0 dR 1 /ds < 0 Bunch length Energy spread * C. Biscari - Bunch length modulation in highly dispersive storage rings", PRST–AB, Vol. 8, 091001 (2005)

Reference ring – DA  NE like rf cavity Monotonic R 1 (s)Non Monotonic R 1 (s) cLcL C = 100 m E = 0.51 GeV f rf = 1.3 GHz V max = 10 MV

Longitudinal phase advance as a function of V for different  c Minimum  L as a function of  c L for different V Phase advance and minimum beta

Behavior of  L (s) along the ring Monotonic R 1 (s) Opposite the cavity Non Monotonic R 1 (s) Near the cavity  c = 0.001  c = 0.01  c = 0.02  c = 0.03 - - - V = 3MV V = 7.5 MV

Two minima appear in  L (s) if the cavity position is not in the point where R’ 1 (s) changes sign

The energy spread and the emittance increase with the modulation in  L Bunch length in the reference ring for two values of V

Proposal for an experiment on DAFNE: A. Gallo’s talk tomorrow D. Alesini et al: "Proposal of a Bunch Length Modulation Experiment in DAFNE", LNF-05/4(IR), 22/02/2005Proposal of a Bunch Length Modulation Experiment in DAFNELNF-05/4(IR) C. Biscari et al, “Proposal of an Experiment on Bunch Length Modulation in DAFNE”, PAC2005, Knoxville, USA - 2005 Needed: Flexible lattice to tune drift function R 1 O.K. with limits due to dynamic and physical apertures Powerful RF system (high U) Extra cavity – 1.3 GHz, 10 MV

6x6 single particle dynamics in SRFF regime R i : i th element of the ring, including rf cavity D(s) = D’(s) = 0 and the rf cavity effect is neglected In a transfer line: R 56 (s) is modified by the rf cavity and changes along the ring

Bunch lengthening through emittance and dispersion also outside dipoles Transverse and longitudinal plane are coupled:

How much does this effect weight on the bunch longitudinal dimensions? Usually negligible Can appear in isochronous rings* with SRFF the effect can be very large due to Large dispersion, usually associated with large emittance Large energy spread Strong rf cavity In the points where D = D’= 0 => R 51 = R 52 = 0 The lengthening does not appear at the IP. *Y. Shoji: Bunch lengthening by a betatron motion in quasi-isochronous storage rings, PRST–AB, Vol. 8, 094001 (2005)

*Matrix calculations by C. Milardi Terms R 51, R 52, R 55, R 56, along the ring with MADX* DAFNE Now Frf = 368 MHZ - V = 0.3 MV DAFNE for SRFF – non monotonic Frf = 1.3 GHZ - V = 8 MV

Bunch length with transverse contribution ?? Usual conditions SRFF conditions

2 particles: 1  x, 1  p Horizontal phase plane Structure C – 4 MV @1.3GHz D = D’ = 0 D = 2m D’ = 0 D = - 4 m D’ = 0 D = -1 m D’ > 0 D = -2 m D’ >> 0

IP1 (long bunch) ? 500 turns- At Long dipole At rf on short at SLM IP2 (short bunch) Longitudinal phase plane R 51 = R 52 = 0 2 particles: 1  x, 1  p

IP1 (long bunch) 2000 turns At Long dipole At rf on short at SLM IP2 (short bunch) R 51 = R 52 = 0 Longitudinal phase plane 2 particles: 1  x, 1  p

Bunch lengthening* *L. Falbo, D. Alesini Simulation with distributed impedance along the ring in progress DAFNE with SRFF

Possible applications of SRFF Colliders and Light sources Colliders: DA  NE can be used to test the principle Exploiting the regime needs a specially dedicated lattice and optimization of impedance distribution Light sources: Excluding those with field index dipole (large dispersion in dipoles can lead to negative partition numbers)

 1.4 e-03  rad  c = 7.2 e-04  1.7e-02  rad  c = 3.8 e-02 BESSY II – data by G. Wuestefeld High momentum compaction Increasing  c increases emittance in low emittance lattices Exercise

BESSY II - High momentum compaction V (MV) QsQs  p /p (10 -4 ) 1.50.0643.69 27.90.33311.9 32.80.38916.5 36.10.44426.9 E = 0.9 GeV f rf = 500 MHz

lattice calculations by M. Biagini E = 3 GeV, f rf = 1.5 GHz

- - - - Dashed lines – low  c - non monotonic R1 Full lines – high  c PEP II like storage ring

Two cavities in the ring example Synchrotron tune and energy spread depend on the drift distance between the two cavities

Conclusions Talks on different aspects of the same subject by P. Piminov - Dynamic Aperture of the Strong RF Focusing Storage Ring S. Nikitin - Simulation of Touschek Effect for DAFNE with Strong RF Focusing F.Marcellini - Design of a Multi-Cell, HOM Damped SC for the SRFF Experiment at DAFNE A Gallo - The DAFNE Strong RF Focusing Experiment Bunch length modulation can be obtained in storage rings in different regimes with high or low synchrotron tune In any case it is associated to increase of natural energy spread QsHighLow Dynamic aperture Rf acceptance Microwave Instab threshold Needed voltage

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