Compressor Ring. Contents Where do we go? Beam physics limitations Possible Compressor ring choices Conclusions. Valeri Lebedev.

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1 Compressor Ring Valeri Lebedev Fermilab Contents Where do we go? Beam physics limitations Possible Compressor ring choices Conclusions Muon Collider Workshop Newport News, VA Dec. 8-1, 8

2 Where do we go? Tevatron Run II ends in two years FNAL future Energy frontier -> Intensity frontier Project X -> Neutrino factory -> Muon collider Before we build machine We have to anticipate coherent upgrade path Energy choice Initial infrastructure choice Future developments The most general structure for Muon collider proton source Linac -> Synchrotron (?) -> Accumulator ring (?) -> Compressor ring Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8

3 Boundary conditions Linac Beam current 4 ma Pulse length 1 ms Repetition rate = 15 Hz RMS bunch length after compressed < 6 cm Beam is focused on the mercury target of 5 mm radius Rms beam size = mm Beta-function on the target target length (~ cm) Maximize beam power on the target More or about 1 MW is desirable Main beam physics limitations Consistency of beam parameters through entire chain of the planned proton accelerators Beam focusing on the target Longitudinal beam stability Transverse beam stability Particle loss due to non-linear forces of the beam space charge 3 Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8

4 Choices to be considered Present Project-X with injection to Recycler + Compressor ring Linac Recycler Compressor ring Target (8 GeV) (8 GeV, ~3 km) (8 GeV) Project-X linac + Compressor ring with direct H - strip injection Linac Compressor ring Target (8 GeV) (8 GeV) Recycler Alternative Project-X + compressor ring Linac Synchrotron Compressor ring Target ( GeV) (1 GeV, 15 Hz) (1 GeV) Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 4

5 Main beam physics limitations (1) Focusing on the target BETA_X&Y[m] 5 Size_X[cm] Fri Dec 5 :7:45 8 OptiM - MAIN: - C:\Users\Valeri\VAL\Op BETA_X BETA_Y DISP_X DISP_Y Fri Dec 5 14:58:19 8 Beta functions DISP_X&Y[m] OptiM - MAIN: - C:\VAL\Optics\MuonC Ax_bet Ay_bet Ax_disp Ay_disp Rms beam sizes (ε=1 mm mrad ε n95% = 57 mm mrad) 5 Size_Y[cm] Design requirements Beam energy = 8 GeV Rms beam size = mm β* > cm Δp/p ~ ±3% Limitations of the FF chromaticity and the quad gradient result in FF parameters ε 95%n = 57 mm mrad β* = 4 cm β max = m Rms beam size on the vacuum window = 1.3 cm Final focus quads L [cm] G [kg/cm] a [3σ+] [cm] B [kg] qf qd qf Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 5

6 Focusing on the target (continue) Other issues Compensation of focusing chromaticity by sextupoles is limited because of very large beam emittance Beam power deposition on the vacuum window Further decrease => larger S target-to-window => larger β max => larger FF chromaticity Beam envelopes in the target vicinity for Δp/p = -3, -, 3% Using SC quads could reduce FF chromaticity but its usefulness is limited by desire to have large beam size on the vacuum window 1 MW window looks challenging but solvable problem Particle flux: dn/dt= p/s; dn/(dtds)= p/cm /s Beryllium, d=1 mm, R=5. cm (4σ), dp/ds max ~3.5 W/cm => ΔT = 4 K o for edge cooled window Radiation hardness needs to be investigated Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 6

7 Main beam physics limitations () Longitudinal beam stability For continuous beam the dispersion equation is ε ( δω) n ei Z n = 1+ πir p δω + n δ + Δp x = p, df / dx dx = ω ηx iδ 1 η = α γ Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8, δω = ω nω Stability condition depends on particle distribution, f(x) Z n n where = πβησ p δω pc A( y) ei y =, A( y) = iσ p ω ηn δ +, df / dx dx y + x iδ There is no significant difference in stability thresholds for the cases above and below critical energy for particle distribution close to the rectangular one 1.4 σ p f () x n.3 Im(A(y))..1 f () x n 1 b σ exp n n x a σ n n f 1 f f 3 f x/ σ p Re( A( y) ) f 1 f f 3 f 4 7

8 Longitudinal beam stability (continue) Longitudinal impedance has three major contributions Space charge For round beam & vacuum chamber Z( ωn) Z = a i ln n βγ 1.6σ Resistive wall For round beam & vacuum chamber Z( ωn) Zβc = ( 1 i sign( ωn) ) n a πσω n Effect of RF cavities, vacuum chamber discontinues, etc. can be controlled by machine design and dampers (f < 1 MHz) Space charge contribution does not depend on frequency and dominates at high frequency It result very fast momentum spread growth, λ nω η( p p) For high frequencies used n s Zn/n [Hz] 1 qf n Δ / λ >> ω, and the continuous beam theory can be 1 Space charge Resistive wall f [Hz] Copper chamber, f = 1.13 MHz, a = 4.8 cm, E=8 GeV Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 8

9 Main beam physics limitations (3) Transverse beam stability Worst case estimate can be obtained for the case of the bunch with zero revolution frequency spread rpn Z δν cb = i πβγν Z - continuous beam 1/ 4 C δν δν cb L - constant bunch density b At small frequencies impedance is dominated by wall resistivity c( sign( ω) i) Z Z 3 πa πσω - round chamber; Z y π Z 1, Z x π Z 4 - flat chamber Flat copper chamber, f = 1.13 MHz, a = 4.8 cm, ν=5.73, C/L. b =.35 E=8 GeV, N= For short machine, high wall conductivity and large chamber size the transverse instabilities should not be a problem Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 9

10 Main beam physics limitations (4) Compressed beam has very large particle density. That results large longitudinal and transverse fields Both longitudinal and transverse fields drop fast with beam energy Incoherent tune shift due to beam space charge Betatron tune shift is equal to δν rp N p C β Δp x y σ ε β D σ πβ γ L =, =, = +, 3 b x y x, y x x x x y y y ( σ + σ ) σ p s Dispersive contribution to the tune shift can significantly reduce δν Longitudinal field of the bunch For Gaussian bunch enc ln( a /(1.6σ )) s V SC ( s) = πγ σ s s exp σ s ε β Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 1

11 Choice 1 CR with Recycler beam Low longitudinal phase density of the Recycler beam is the main limitation of the beam power Recycler Project-X bunch: N = , ε s =.4 ev s/bunch (53 MHz RF) Only 8 bunches can be coalesced to fit to the required ε L : σ s = 6 cm, σ p =.1%, ε s95 = 6π σ s σ p p / (βc) ~3.3 ev s => 47 kw beam power on target (15 Hz, 1 bunch) What s wrong with Recycler? Large circumference Small acceptance θ x Stainless steel vacuum chamber Can multiple bunches be merged in transverse phase X space Recycler beam emittance: ε n95 = 5 mm mrad FF limit = 57 mm mrad On paper merging ~1 bunches is allowed (57/(*5)) But realistically only 4 bunches can be merged because the small phase space distance between bunches is required 11 Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8

12 Choice CR with direct strip injection from Linac Optics design criteria Small circumference (Space charge, tr. & long instabilities) Large acceptance Large Δp/p => high periodicity Zero dispersion in RF cavities Large slip factor to avoid microwave instability It requires larger RF voltage and horizontal aperture in arcs Mon Dec 8 9:41:55 8 OptiM - MAIN: - C:\VAL\Optics\MuonCollider\Comp BETA_X&Y[m] DISP_X&Y[m] 3 5 BETA_X BETA_Y DISP_X DISP_Y 65.9 Twiss parameters for a quarter of ring circumference Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 1

13 Choice (continue) Main parameters of 8 GeV Compressor ring Circumference 64 m Tunes, ν x / ν y 6.4/5.4 Transition energy 3.9 GeV Dipole field kg Acceptance 1 mm mrad Momentum acceptance ±3% Mon Dec 8 1:5:51 8 OptiM - MAIN: - C:\VAL\Optics\MuonCollider\Comp Size_X[cm] Size_Y[cm] 1 1 Ax_bet Ay_bet Ax_disp Ay_disp 65.9 Beam envelopes for a quarter of ring circumference (ε=1 mm mrad, Δp/p=±3%) Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 13

14 Choice (continue) Beam injection & compression Micro wave instability is the major limitation of the beam power Injection parameters Injection type H - strip Linac current 4 ma Linac rms momentum spread < 1-4 Linac energy sweep ±6 1-4 Filling factor, L b /C.35 Total injection time.9 ms DC beam current 9.4 A Number of particles Harmonic number, h 1 RF voltage 1.5 kv Synchrotron tune (Z n /n) Space charge = (Z n /n) Stability 1 Ω Beam power 1 MW Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 Longitudinal phase space at the end of injection and after compression 14

15 Beam injection & compression (continue) Parameters of compressed bunch Harmonic number, h 1 RF voltage 1 MV/turn Max. bunch long. field ~35 kv/turn Synchrotron tune Rotation time 37 turns RF bucket height, Δp/p.53 Coulomb tune shifts, Δν x / Δν y.7/.15 instability growth rate 1-5 /turn There is not much leverage left to exceed 1MW beam power for 8 GeV proton driver (15 Hz, single bunch) σ s =67 cm s [cm] Δp /p Projections of longitudinal particle distribution to s and p planes after compression Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 15

16 Choice 3 CR with injection from 1 GeV RCS 1 GeV compressor ring allows to exceed 1 MW limit of 8 GeV choice The help comes from Smaller number of particles per bunch (8/1) Reduced effect of space charge fields as 1/γ However to exceed.3 MW power one needs to have the longitudinal phase space density higher than is presently planned for Project-X This choice also implies that the beam leaves longer time in the ring and high frequency RF is used for acceleration High frequency RF and high beam intensity provoke electron multipactoring in the vacuum chamber and, consequently, epinstability. This problem has to be addressed if RCS is preferred for Project X Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 16

17 Conclusions 8 GeV linac is a good asset for muon collider proton driver It is feasible to achieve 1 MW with a single bunch mode at 15 Hz repetition rate in the specialized compressor ring It looks like that other Project X infrastructure hardly can be useful for muon collider Further beam power increase requires larger energy 1 GeV RCS looks as a good alternative If chosen the problems of increased longitudinal phase space density (factor of 4) and ep-instability have to be addressed Compressor ring, Valeri Lebedev, Muon Collider Workshop, Newport News, VA, Dec. 8 1, 8 17

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