Suppression of coherent betatron oscillations in muon g2

Suppression of coherent betatron oscillations in muon (g-2) experiment I. A. Koop, A. V. Otboev, E. A. Perevedentsev, P. Yu. Shatunov, Yu. M. Shatunov Budker Institute of Nuclear Physics, Novosibirsk, Russia

Muon g-2 ring at BNL g-2

Scheme and parameters Injection: p → π+ → μ+ + ν ν e+ μ+ R = 7. 112 m B = 1. 45 T ΔB/B ≤ 10 -6 E-quads Kicker 100 k. V 24 counters Nμ (t = 0) ~ 5000 τ = γτ0 ≈ 6. 5· 10 -5 sec Eμ = 3. 096 Ge. V (“magic” energy ) electrostatic focusing!

Data Fourier analysis fg-2 ≈229 k. Hz f. CBO≈466 k. Hz g-2

Muons phase space portrait after kicker Nμ = 10000 βx·Δx' ≈ 0. 8 cm Δx' g-2

CBO cure: betatron phases mixing by nonlinear fields x’ x g-2

Octupole in the ring Injection Coil length: 200 cm Center 6 6 cm Octupole Kiker Quad g-2

Muons phase space portrait after 30 turns (octupole “on”) x' y' x y' g-2

CBO “damping” gradient (Gauss/cm 3) 0. 00 0. 15 0. 40 0. 85 turns g-2

Beam sizes gradient (Gauss/cm 3) gradient (G/cm 3) 0. 00 0. 15 0. 40 0. 85 g-2

Muon population census Nμ gradient (G/cm 3) 0. 00 0. 15 0. 40 0. 85 turns g-2

A(t) vs. Δx(0) gradient = 0. 85 (Gauss/cm 3) Δx(0) turns g-2

Scraping gradient = 0. 85 (Gauss/cm 3) Nμ Δx(0) turns g-2

Octupole coil and parameters of generator 2. 5 k. A I(t) injection 1. 25 μsec 16× 2 m 2. 5 k. A 1 μF 1. 3 k. V 1. 0 J 10 μsec + - 6 cm Coil length Current Capacitor Voltage Energy Half period + g-2

Conclusion Pulse octupole is able to minimize the CBO to a stochastic level during 30 turns before data tacking Beam size modulations caused by an injection mismatching are suppressed No more special beam scraping Octupole coil construction doesn’t require big efforts as well and the power supply source Fall out magnetic field from the octupole will be not essential for NMR probe measurements Simulation with real muon distributions is needed