Spin States Separation Based on the Longitudinal Stern-Gerlach Effect

Transcription

1 SIN96 Amsterdam S e p t. 9-14, t BNL Spin States Separation Based on the Longitudinal Stern-Gerlach Effect N. Akchurin', M. Conte2, W.W. MacKay3, Y. Onel', R. arodi4, A. enzoq M. usterla' and R. Rossmanith7. sti (1) Department of hysics, University of Iowa, Iowa City, IA 52242, USA. (2) Dipartimento d i Fisica dell'universita d i Genova, INFN Sezione di Genova, Via Dodecaneso 33, Genova, Italy. (3) RHIC roject, Brookhaven National Laboratory, Upton, N Y 11973, USA? (4) I N F N Sezione d i Genova, Via Dodecaneso 33, Genova, Italy. (5) INFN Sezione di Trieste, Via Valerio 2, Trieste, Italy. (6) Dipartimento di Fisica dell'universith d i adova, INFN Sezione di adova, Via Marzolo 8, adova, Italy. (7) D E S Y, Notkestrasse 85, Hamburg 52, Germany. ABSTRACT Repetitive longitudinal impulses of the Stern-Gerlach force are proposed for attaining the separation of the opposite spin states of (anti)proton beams, circulating either in existing collider facilities or in a small ring, conceived just for producing polarized antiprotons at very low energy. After a brief presentation of the theoretical background which supports this proposal, the experimental features are discussed emphasizing in particular the bunch separation within the RF bucket and the feasibility of a high magnetic gradient T E cavity. A polarized particle experiencing a magnetic gradient GIIparallel to its motion direction over a length l ~undergoes, a momentum variation [1],[2] due to the SternGerlach force, of the type: + - =sll -- f y s t - YGIIUIG spin down 27mc2 where p = 1.41 x JT-' is the proton magnetic moment, mc2 = x lo-'' J is the proton rest mass. Since the beam polarization is defined as Figure 1: Schematic of model accelera = Nt - Nl. (2) tor. Nt + Nl where indicates the macroscopic average over the particle distribution in the beam, N t = No. articles Spin Up (parallel to &jng) and Nl = No. articles Spin Down (antiparallel to Zring). Notice that an unpolarized beam has = 0 i.e. N t = N J. 1, consists in rotating spin-up to The experimental procedure, illustrated in Fig. e.g. spin-forward and spin-down to spin-backward making eq. (2) become: *Work performed under t h e a u s p i c e s of t h e U.S. Dept. of Energy.

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4 = N+ - N+ N+ N+ A suitable (system of) TE RF-cavity accelerates spin- + forward particles and deaccelerates spin-backward particles; then the original situation is restored. The dc These two bunches, parted by the TE cavity, are revolving inside a TM stationary bucket pertaining to the RF bunching system of the ring. The corresponding synchrotron oscillations equation is then: OSf(4) = c F ( t ) (4) dt with I i..; V Icml Figure 3: Longitudinal gradient in a splitter cavity. f(4)= s i n 4 and F ( t ) = sin(r,t) This sinusoidal law gives rise to filamentation phenomena (see Fig. 4) which destroy the bunch le-07separation. Nevertheless we are studying the possibility of time tagging those particles whose T phases are so small that the condition s i n is fulfilled. Should the request of having polarized an- -1e-07tiproton become impelling, a small ad hoc ring ~ -9 -i :, * could be devised (see Table I), where wave-form of any shape could be implemented like, for in- Figure 4: Filamentation of split stance, the saw-tooth waveform, i.e. the ap- bunches. 2

5 proximation f(4)= $J can be done. Besides, at these very low energies, longitudinal space charge effects can take place and eq. (4) transforms into: Table 1: Small Ring for Antiproton g = l + l n -,br o = a q2 4momc2 and The phase separation between the two bunches of particles with opposite spin states is then: E A 4 = -t a, Circumference Moment um-spread Kinetic Energy Momentum Velocity /c Revolution eriod Harmonic Number articles/bunch Radio Frequency eak rf Voltage Transition gamma sin(r,t) = (Ad),,,sin(R,t) where N is the number of turns; therefore we have: with Still with an integrated gradient G&G= lo3 T, eq. (6) would yield a separation of 1 radian after 1.5 x lo6 revolutions. References [l] M. Conte, A. enzo and M. usterla, I1 Nuovo Cimento, A108 (1995) 127. [2] N. Akchurin et al., Evolution of the Spin-Splitter Concept, Communication presented (by M. Conte) at ARC95, Trends in Collider Spin hysics, Trieste 5-8 December [3]. Fernandes and R. arodi, Oscar2D User s Guide, INFN/TC-90/04. [4]M. Conte, R. Jagannathan, S.A. Khan and M. usterla, Beam Optics of the Dirac article with Anomalous Magnetic Moment, INFN/AE96/06, IMSc96/03/07 and art. Acc., 56 (1996)