CONCEPT FOR CONTROLLED TRANSVERSE EMITTANCE TRANSFERWITHIN A LINAC ION BEAM

L. Groening, GSI Helmholtzzentrum fur Schwerionenforschung, D-64291 Darmstadt, Germany

Abstract

Generally the two transverse emittances of a linac beamare quite similar in size (round beam). However, injec-tion into subsequent rings often imposes stronger limitsfor the upper allowed value of one of these emittances.Provision of flat linac beams (different transverse emit-tances) thus can considerable inrease the injection effi-ciency into rings. Round-to-flat transformation has beenalready demonstrated for electron beams. It was alsoproposed for angular momentum dominated beams fromElectron-Cyclotron-Resonance sources. We introduce aconcept to extend the transformation to ion beams that un-derwent charge state stripping without requiring their ex-traction from an ECR source. The concept is of specialinterest for beams from low-charge-state / high-particle-current sources. It can be also applied to stripping of H− toproton beams. These proceedings are a compressed versionof [1].

INTRODUCTION

Emittance transfer was proposed for electrons [2]and has been demonstrated experimentally [3]. Rms-emittances are defined through the beam second momentmatrix

C =

< xx > < xx′ > < xy > < xy′ >< x′x > < x′x′ > < x′y > < x′y′ >< yx > < yx′ > < yy > < yy′ >< y′x > < y′x′ > < y′y > < y′y′ >

,

(1)where the full 4d-emittance is defined byǫ2

4d = detC andǫx,y are defined by the corresponding sub phase space de-terminants. If for a given 4d-distribution with vanishinginter-plane correlations moments, the horizontal and verti-cal emittances are equal, they will remain equal and may bejust increased by symplectic transformationsM [4], beingdefined through

MTJM = J (2)

with

J :=

0 1 0 0−1 0 0 00 0 0 10 0 −1 0

. (3)

Drifts, solenoids, quadrupoles, and dipoles are symplec-tic, the later even if they are tilted, that do preserveǫ4d,however. Accordingly, to transfer emittance between thetransverse planes, a non-symplectic transformation must

be applied. This transformation nevertheless should pre-serveǫ4d. A transformation through a fringe field of asolenoid

MSolFringe =

1 0 0 00 1 +K 00 0 1 0

−K 0 0 1

(4)

with

K :=B

2(Bρ), (5)

B as the solenoid on-axis magnetic field strength, and(Bρ)as the beam rigidity is such a transformation.The issue can be addressed also through the concept of theeigen-emittances±Ex and±Ey of a 4d-distribution [5].They solve the complex equation

det (JC − iEI) = 0 (6)

whereI is the identity matrix. The eigen-emittances donot change with symplectic transformations. But they dochange by transformation through a solenoid fringe field.Their product is equal toǫ4d and for vanishing inter-planecoupling moments they are equal to the rms-emittances.

BEAMS FROM AN ECR SOURCE

For beams from an ECR source emittance transfer hasbeen proposed already in [6] assuming a beam second mo-ment matrix (Eq. 1) with nonzero elements just along thetwo diagonals. But generally all coupling moments aredifferent from zero. Extraction of the ions from an ECRsource is through the fringe of the plasma-confining lon-gitudinal magnetic field. Accordingly, the source itselfinhabits intrinsically the non-symplectic transformationwhich changes the eigen-emittances. The fringe createsinter-plane coupling moments as seen in the projections ofthe transverse distribution after extraction (Fig. 1) [7].Hor-izontal and vertical rms-emittance are equal. In the figurescoupling moments are quantified through the correspond-ing α-parameter. The 120◦ symmetry in the inter-planeprojections is due to the non-linear inter-plane couplinghexapolar field inside the ECR source. Along the beamlinefollowing the extraction only symplectic elements are ap-plied, thus preserving the eigen-emittances. This beamlineneeds to remove the inter-plane correlations, i.e. equalizingthe final rms-emittances to these eigen-emittances. For typ-ical beam parameters obtained after the GSI ECR source,a beamline comprising a sequence of two solenoids, two

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x [mm]

x‘ [m

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ε = 125 mm mradβ = 1.60 mα = -6.00

x [mm]

y [m

m]

α = -0.03

x [mm]

y‘ [m

rad]

α = -0.17

y [mm]

x‘ [m

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α = 0.12

s = 0 cm

x‘ [mrad]

y‘ [m

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α = -0.02

y [mm]

y‘ [m

rad]

ε = 125 mm mradβ = 1.60 mα = -6.00

ε4d = 3690 mm2mrad2

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Figure 1: Two dimensional projections of the initial ECRtransverse phase space distribution.

quadrupoles, another solenoid, and two skew-quadrupolescan do this task within reasonable apperture and field lim-its. The total length of this beamline is four meters. Fig-ure 2 shows the distribution at the exit of this beamline. Theinter-plane correlations are zero, final rms-emittances areequal to the eigen-emittances, and their ratio is about 16.

BEAMS TO BE STRIPPED

Beams from sources different from an ECR, pre-accelerated to some MeV/u along a linac, do generallyhave similar rms-emittances, zero inter-plane correlations,and thus their eigen-emittances are equal to the rms-emittances. The required solenoid fringe field to vary theeigen-emittances cannot be provided in a straight forwardway, since any entrance fringe intrisically causes an exitfringe field. Both fringe effects just cancel out, making theoveral transformation symplectic again. This cancellationcan be bypassed through placing a charge state strippingfoil between both fringes as displayed in Fig. 3. Such asolenoidal stripper is proposed to be integrated into the ex-isting charge state stripping & separating beam line of theGSI UNILAC [8]. Simulations have been done using anH+

3 beam stripped to a proton beam in a 20µg/cm2 car-bon foil placed between to pancake coils. Figure 4 showsthe transverse distribution at the beginning of the beamline.Its rms- and eigen-emittances are equal to each other andare equal in each plane.

Figure 5 shows the beamline itself together with thecorresponding beam envelopes and rms-emittances. Theentrance fringe creates inter-plane correlations which in

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x [mm]

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α = 0.11

x [mm]

y‘ [m

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α = -0.10

y [mm]

x‘ [m

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α = 0.02

s = 391 cm

x‘ [mrad]

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α = 0.27

y [mm]

y‘ [m

rad]

ε = 17 mm mradβ = 0.15 mα = 0.30

ε4d = 3690 mm2mrad2

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Figure 2: Two dimensional projections of the final ECRtransverse phase space distribution.

Figure 3: Conceptual layout of an ion stripper set-upproviding a non-symplectic transformation for transverseemittance transfer. The stripping foil is placed between twopancake coils, i.e. inside a region with a longitudinal mag-netic field of few Tesla in strength.

turn increase both transverse rms-emittances. After thenon-symplectic entrance fringe the horizontal and verti-cal eigen-emittances are different. Since the exit fringe ispassed by the beam with reduced rigidity w.r.t. the entrancefringe, there is no cancellation of the two non-symplecticfringes. The exit fringe separates the two eigen-emittanceseven more. Along the subsequent vertical four-bend chi-cane the rms-emittances and correlations are preserved un-til the entrance to the skewed quadrupole triplet (verticalrms-emittance growth is due to dispersion). The skewed

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α = 0.00

x [mm]

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α = 0.00

y [mm]

x‘ [m

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α = 0.00

s = 0 cm

x‘ [mrad]

y‘ [m

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α = 0.00

y [mm]

y‘ [m

rad]

ε = 1.20 mm mradβ = 6.50 mα = 1.00

ε4d = 1.44 mm2mrad2

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Figure 4: Two dimensional projections of the initial UNI-LAC transverse phase space distribution.

triplet removes all inter-plane correlations and another reg-ular quadrupole provides matching to the following beam

Figure 5: From top to bottom: horizontal beam envelope,vertical beam envelope, horizontal rms-emittance, and ver-tical rms-emittance along the proposed emittance transfersection along the UNILAC.

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y [mm]

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s = 1079 cm

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y‘ [m

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ε = 2.71 mm mradβ = 8.47 mα = -1.01

ε4d = 1.51 mm2mrad2

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Figure 6: Two dimensional projections of the final UNI-LAC transverse phase space distribution.

transport section. Figure 6 displays the distribution at theexit of this quadrupole. The final rms-emittance ratio is 4.8.The rms-emittance values are equal to the eigen-emittancesbehind the exit fringe, being the last non-symplectic ele-ment of the beamline.

The solenoidal stripper is of special interest for beamsfrom low-charge-state high-particle-current sources. Itwastentativley applied to heavy ions. First simulations indi-cated horizontal emittance reduction of about 40% for in-tense beams of238U27+ stripped to238U73+ based on theexisting foil stripping section at the GSI UNILAC. Furtheroptimization of the layout for an emittance transfer sectionfor intense beams of heavy ions is needed.

REFERENCES

[1] L. Groening, PRST-AB14, 064201 (2011).

[2] R. Brinkmann et. al., PRST-AB4, 053501 (2001).

[3] D. Edwards et al., Proc. XX Linac Conf., p. 122, (2000).

[4] K.L. Brown et al. SLAC-Rep. No. slac-pub-4679, (1989).

[5] B.E. Carlsten et al., PRST-AB14, 050706, (2011).

[6] P. Bertrand et al., Proc. 10th EPAC Conf., p. 1687, (2006).

[7] P. Spadtke et al., Proc. 1st IPAC Conf., p. 4029, (2010).

[8] W. Barth et al., Proc. XXIV Linac Conf., p. 175, (2008).

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