ISSN 1063�7796, Physics of Particles and Nuclei, 2014, Vol. 45, No. 1, pp. 279–282. © Pleiades Publishing, Ltd., 2014.

279

1 SPIN MANIPULATION AT JPARC

The muon (g�2) experiment at JPARC is based ona usage of cold muons from muonium atoms ioniza�tion [1]. The measurement of the spin precession fre�quency will be done in a magnetic trap at the energy350 MeV. Initial cold muons will be accelerated by achain of linear accelerators. A first of them is RFQlinac accelerates muons up to kinetic energy 340 KeV(β ≈ 0.08). This energy is suitable for muon’s spinmanipulations. We propose to install at this point somestructure to work with polarization only, keeping otherbeam parameters unchanged.

Let’s remind the main equations. Spin precessionis described by the well�known BMT�equation:

(1.1)

Introducing particle revolution frequency

we can rewrite (1.1) in the form:

(1.2)

1 The article is published in the original.

Ω–q0

γ��� q '+⎝ ⎠⎛ ⎞B⊥

q0 q '+γ

������������B�+=

+q0

γ 1+��������� q '+⎝ ⎠⎛ ⎞ E V×[ ].

ω0–q0

γ���B⊥

γq0

γ2 1–����������� E V×[ ],+=

Ω ω0– ω q 'B q0 aμ

1

γ2 1–�����������–⎝ ⎠

⎛ ⎞ E V×[ ].+= =

In our case of very cold muon beam moving in electro�static field, we obtain the spin tune:

≅ –1. (1.3)

It means, that an electrostatic field for (γ2 – 1) � 1can bend a particle and does not rotates its spins. Onother hand, it’s seen from (1.2), that a magnetic fieldrotates muon’s spin practically together with particle,due to a smallness of its magnetic anomaly. Hence, asimplest scheme for spin manipulation consists of twoelectrostatic bends and the Siberian snake between,which consists from two solenoids. Siberian snakerotates spin by 180 degree (Fig. 1). When spin manip�

ν ωω0

�����1– aμ γ2 1–( )+

������������������������������= =

Two Examples of In�Flight Spin Flippers1

I. A. Koop, A. V. Otboyev, P. Yu. Shatunov, and Yu. M. ShatunovInstitut of Nuclear Physics SB RAN, Novosibirsk, 630090 Russia

Abstract—In precise experiments with polarized beam it’s very often appear a necessity to change beampolarization on opposite. If such operation does not change other beam parameters, it helps to avoid or min�imize some systematic errors. It is especially important in experiments, where spin dependent effect is smallenough. This paper describes two set of equipments, that make spin flip for extracted beams. In both cases,these devices are absolutely distinct, because they are appropriate for different particles and at differentenergy range. The first of them is intended for future muon (g�2) experiment, which is under preparation nowat JPARC. Here, the muon spin flip will be done by chain of electrostatic and magnetic bends at the kineticenergy 340 keV. A beam matching is provided by a number of short solenoids. The other flipper (or Siberiansnake) will rotate spin of protons or antiprotons, which come from Λ�meson decay with the energy up to40 GeV. This experiment (no. 24) is planed at IHEP, Protvino. In this case, two superconducting helical mag�nets with opposite helicities and magnetic field 4.5 T will be used. To correct beam trajectory, additionaldipole correctors are required.

DOI: 10.1134/S106377961401050X

Siberian snake

+–

+ + +–

r L

Fig. 1. Proposed insertion to flip the spin of muons (red arrow).

280

PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014

KOOP et al.

ulation is not needed, the snake’s solenoid fieldsswitch on the opposite polarities. Two additional coilsat the entrance and at the exit of the manipulator haveto provide a matching this scheme with existing optics.

However, this scheme has one essential defect: theSiberian snake rotates plane of transverse motion anddispersion by 90 degree, so we will have uncompen�sated dispersion at the exit. To solve this problem wesuppose to use combination of electric and magneticfield to bend muon beam. In the case of combined Byand Ex fields the particle’s motion can be written in theform:

(1.4)

Now we shall require, that the bending radius does notdepend on the momentum:

Then we get relations:

that in our case (muons with γ ≈ 1) simplify to:

(1.5)

The dispersion free spin manipulator is shown inthe Fig. 2. Taking into account the spin rotation due tothe anomalous part of muon magnetic moment q'(see (1.2)), the bending angle of the curved sectionshas to be (π/2 – q'/q0).

pc e B Eβ���+⎝ ⎠

⎛ ⎞ r.–=

ddp���� B

p��� E

p2��� 1 p2++⎝ ⎠

⎛ ⎞ 0.=

B Eγ2 1+

βγ2�����������, E– B βγ2

γ2 1+�����������,–= =

2pc eBr, E– β2��B.–= =

Numerically, for example, parameters of the pro�posed insertion for JPARC can be taking as follows:

Wk = 340 keV, r = 30 cm, E = –22.7 kV/cm, Bb = Bsn = 1.866 kGs, Lsn = 22 cm,

Bsol1 = Bsol2 = 1.79 kGs, Lsol1 = Lsol2 = 22 cm, Ltot = 2 m.

Here we adjust the focusing properties of the insertionto the unit matrix for both transverse modes. One cansee a behavior of two characteristic trajectories in theFig. 3.

So, the proposed in flight spin flipper is satisfied therequirements to reverse spin without optic distortions.

FLIPPER FOR SPASCHARM EXPERIMENT AT IHEP

In principle, the similar task to reverse in�flightspin of protons and antiprotons there is at the experi�ment SPASCHARM, which is under preparation atIHEP (Protvino) [2]. The Fig. 4 presents a scheme ofa transport canal with a number of dipole and quadru�pole magnets and collimators between production anddetector targets.

Since, in this case, the particle energy can achieve40 GeV, the task demands absolutely differentapproach for spin manipulations. Additionally, itrequires not only reverse spin, but also transform thevertical spin to longitudinal one. A general method forhigh energy proton spin rotators has been developedalmost 15 years ago, which it exploits helical magnets[3]. This method was successfully applied at the pro�ton�proton collider RHIC. A simplest rotator, whichcan be used in our case, consists from two helical mag�nets with opposite helicities.

+

+

–

–

snake

⊗B

�B

Fig. 2. Improved dispersion�free bend of muons.

Fig. 3. Two types of trajectories going through insertion.

PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014

TWO EXAMPLES OF IN�FLIGHT SPIN FLIPPERS 281

Magnetic field of helical magnets is presented inthe Fig. 5. To correct beam’s trajectory inside thisinsertion we will use dipole correctors (rectangles ofcorresponding color). Optimal particle trajectorythrough the helical magnets is shown in the Fig. 6.This trajectory corresponds to the unit transfer matrixof our insertion.

The initial polarization of protons and antiprotonswill be vertical. The proposed combination of the

helixes can flip vertical spin (Fig. 7). The same schemecan also flip the longitudinal spin. In both cases, thefinal polarization is not less 97%.

To meet the other requirement (transfer the verticalspin into longitudinal), we should turn off the secondhelix and use dipole correctors to restore particle’sorbit. The results of this measure are shown in theFig. 8 for particle orbit and in the Fig. 9 for spin.

40

20

0

–40

600500300100 2000 400

–20

Bx, By

z, cm

ξ = + ξ = –

By Bx

Fig. 5. Helical magnetic field along the magnet’s axis ofinsertion.

1.0

0.5

0

–1.5

600500300100 2000 400

–1.0

Orbit, cm

z, cm

y

x

1.5

–0.5

Fig. 6. Corrected trajectory in set of helical magnets.

0.5

0

600500300100 2000 400–1.0

Spin

z, cm

1.0

–0.5Sx

SySz

Fig. 7. Vertical spin flip.

–4

600500300100 2000 400

–2

Orbit, cm

z, cm

yx

–1

–3

0

23 k

Gs

23 k

Gs

29 k

Gs

29 k

Gs

Fig. 8. Getting longitudinal polarization.

M80400 6020 100

100

0

100

X, mm

Y, mm

T Texp

K2

K1M1

K4

K3

Q5–6M2Q1–4 M3 M4 M5Q7–8 Q9–12

Fig. 4. Transport channel scheme.

282

PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014

KOOP et al.

At the end, the parameters of proposed helicalinsertion for IHEP are given:

Bmax = 47 kGs, λ = 2.5 m, Lcor = 30 cm, Bcor = 23 kGs, tilt = ±0.1 rad, Ltot = 6.5 m.

ACKNOWLEDGMENTS

The work is supported by the Ministry of Educationand Science of the Russian Federation, grant no.14.518.11.7003.

REFERENCES

1. N. Saito, Spin Physics at J�PARC, in Proc. ofSPIN2012, JINR, 2012.

2. V. Mochalov, Polarized Studies at IHEP, in Proc. ofSPIN2012, JINR, 2012.

3. V. I. Ptitsyn and Yu. M. Shatunov, NIM, Ser. A 398, 126(1997).

0.5

0

600500300100 2000 400

Spin

z, cm

1.0

–0.5

Sx

Sy

Sz

Fig. 9. Corrected orbit in case of one helix used.