Colby, E R

Eylon, S

Fessenden, T J

Garvey, T

Hahn, K

Henestroza, E

CERN Document Server

Particle Accelerators, 1992, Vols. 37-38, pp. 235-240Reprints available directly from the publisherPhotocopying permitted by license only© 1992 Gordon and Breach Science Publishers, S.A.Printed in the United KingdomEMITTANCE VARIATIONS OF VERY COLDOFF-AXIS ION BEAMS DURING TRANSPORTTHROUGH MBE-4tS. EYLON, E. R. COLBY, T. J. FESSENDEN, T. GARVEY, K. HAHN.and E. HENESTROZALawrence Berkeley Laboratory, University of California, Berkeley, CA 94720.(Received 3 December 1990)We have been studying the transverse emittance variations of very low emittance (0.03 mm-mradnormalized K-V)-Cs + beams drifting through the electrostatic quadrupole transport of the MBE-4apparatus at the injection energy of 180 keY. Both experiment and simulation show that these stronglytune-depressed (0" = 7°) beams, when off-axis, interact with image charges and focus field nonlinearitiesto produce a modulated emittance that grows with distance. The modulations appear at frequencies ofapproximately (J2 + 1)0"0 where 0"0 is the undepressed phase advance of the electrostatic focusing lattice.Experimentally, the extent of the emittance variation depends on the amplitude of coherent betatronoscillations induced by injection offsets and by transport alignment errors. At larger emittances andtherefore less tune depression, the modulations and growth are reduced, suggesting that these effects maysaturate with distance in a long transport system. Simulations, verified by experiments, indicate that on-axisbeams exhibit essentially no emittance variation or growth with distance.INTRODUCTIONIn the heavy-ion approach to inertial confinement fusion the transverse emittance ofthe beam will determine how well the beam can be focused on the target. Therefore,an emittance "budget" for any particular scenario is defined by the requirements onemittance at the final focus and by the emittance practically achievable from theinjector. Although the normalized emittance should be conserved for a beam subjectonly to ideal optics, one must envisage some emittance growth from aberrations,nonlinear space-charge effects, alignment errors, transport mismatches, etc. Thesubject of emittance growth in a heavy ion fusion driver is therefore of great concern.In this paper we report on measurements and theory of emittance growth in anelectrostatically focused heavy ion (Cs +) linac, MBE-4. The experiments are ofrelevance to the low energy end of a driver where electrostatic focusing is preferredover magnetic focusing due to the low velocity of the beam (O.OOI7c in MBE-4,typically O.Olc at the low-energy end of a driver).t Work supported by the Director, Office of Basic Energy Research, Office of Basic Energy Sciences,Advanced Energy Projects Division, U.S. Department of Energy under Contract No. DE-AC03-76SF00098.235236 S. EYLON et al.2 EXPERIMENTAL CONFIGURATIONThe MBE-4 apparatus has been adequately described elsewhere 1 and here we givejust a brief summary of the accelerator components relevant to the studies describedin this paper. MBE-4 consists of a 200-keV injector followed by a short matchingsection, which adjusts the beam envelope parameters for injection into the main linacsection. The main linac comprises a 30-period syncopated FODO lattice structure(45.72-cm unit cell length). Following each lattice period is an acceleration gap, withthe exception that every fifth gap is reserved for diagnostic access and vacuumpumping. At the diagnostic ports, the transverse beam parameters, such as size, offset,emittance, etc., can be measured in either plane. Measurements are made using amulti-shot scanning system employing the familiar double-slit technique. Note thatthe parameters of the beam can be measured only at seven discrete locationsthroughout the linac. In a later section we will describe a technique that allows usto infer, from measurements made at the ports, values of the emittance, at locationsintermediate to the diagnostic ports.3 THEORYWe have been modelling the emittance development of drifting beams in MBE-4using a particle-in-cell code (SHIFTXYA)2. This code assumes a 2-D geometry, but withvarying boundary condition in the direction of beam propagation. Thus at placeswhere there are no quadrupoles we replace the boundary condition by free space.The code includes the effect of nonlinear field components in the quadrupoles andthe effects of induced image charges on them. These simulations were performed forthe geometry and parameters of MBE-4, including the matching section, whereenvelope variations are large. Although we preserve the syncopated lattice structurethe quadrupoles are treated as having hard edges. The beam has a nominal S-mAcurrent; 180-keV energy; 0.03 mm-mrad normalized K-V emittance; tune depression(0'0/0') of 10; and 10-mm envelope radius. Focusing is provided by electrostaticquadrupoles of bore radius 27 mm.The principal results of the computations are illustrated in Figures 1 and 2. Figure1 shows that if we include the effects of dodecapole field components and inducedimage charges, then a beam with initial transverse displacements dx and dy from thelinac axis exhibits a continuous variation in emittance with an overall tendency togrowth. It is found that the extent of these oscillations is sensitive to the size anddirection of the initial displacement. If the effects of nonlinear fields are neglected,then even a displaced beam will travel through the linac without emittance growth.The frequency of the oscillations appears to be given by (J2 + 1)0'0' suggesting thesum of the coherent betatron oscillation and plasma frequencies. In contrast, a beamthat propagates on axis shows essentially no change in emittance. The observedemittance growth results from the excitation of coherent beam modes by non-linearforces. The emittance growth is amplitude-modulated by the coherent oscillation ofthe beam. In Figure 2 we observe that if the beam has an increased initial emittanceEMITTANCE VARIATIONS OF ION BEAMS 237dX=dy=O mm0.07,.....,.'-E 0.06IEE 0.05Q)uc 0.04co~~E 0.03Q)"CQ) 0.02Nco 0.01E ~'- -x0z 0.00-5 0 5 10 15 20 25 30lattice periodFIGURE 1 Simulation of the transverse emittance variations in MBE-4 for both off-axis and on-axisbeams. The off-axis beam is displaced by 3 mm in both transverse planes (x and y).dx=dy=3mm0.07,........'-EI 0.06EE0.05C1.>uc:0.04ro...,...,E 0.03C1.>"'0C1.> 0.02NroE 0.01'-0Z 0.00-5 0 5 10 15 20 25 30lattice periodFIGURE 2 Emittance variations in MBE-4 for off-axis beams that have initial emittances of 0.025 and0.05 mm-mrad.238 S. EYLON et al.(i.e., a decrease in the tune depression) then the emittance oscillations are lesspronounced. We note that an earlier simulation of the drift of space-charge-dominated beams in a continuous electrostatic focusing lattice also revealed thepresence of emittance oscillations3 .4 EXPERIMENTSIt is clear that we cannot experimentally recover the high-frequency behavior of thesimulated emittance oscillations by sampling the value at the sparsely distributeddiagnostic ports. In order to effectively measure at locations upstream and down-stream of the ports, we ha-v.e employed the following technique4 . The zero-currentphase advance per cell ((Jo) is adjusted by varying the strength of the focusingquadrupoles, thus altering the total accumulated phase advance between injectionand a fixed measurement location. This can be considered equivalent to changingthe total number of periods traversed by a beam at the nominal 0'0' The permittedvariation in the quadrupole strength was limited by beam envelope instability(high-voltage end) and by useful quadrupole aperture (low-voltage end). The coherentoscillation was induced by deliberately mis-steering the beam at injection using anelectrostatic dipole.5 RESULTSOf the normalized emittance of the beam the variation with (Jo, as measured afterdrifting 25 lattice periods, is shown in Figure 3 for coherent amplitudes of ±4.5 mm(b)0.07'i:'5 0.06e! 0.05Q)(jc 0.04~..........·s 0.03Q)"0Q) 0.02.~";5 0.01s-oZ0.0060 70 80 90zero-current phase advance (deg.lcell)FIGURE 3 Measured emittance as a function of (Yo at lattice period 25. The maximum beam amplitudedisplacements are (a) 4.5 mm and (b) 1.2 mm.EMITTANCE VARIATIONS OF ION BEAMS 2390.090.08~S 0.07eg 0.06~u 0.05c~...... 0.04Os~"C 0.03~O~-; 0.02Ss.0 0.01Z0.0060 70 80 90zero-current phase advance (deg.lceIl)FIGURE 4 Measured emittance dependence on (Jo at lattice period 25 for beams of initial emittancesdiffering by '" 2 (as measured at (Jo- 71 deg.jcell).and ±1.2 mm. It should be understood that this corresponds to data that mightbe taken between periods 23 and 29 (if the diagnostics could be moved continuouslythrough the linac) and is therefore representative of only a small part of the simulationresult of Figure 1. However, there is good qualitative agreement between thesimulation and the measurement in terms of the amplitude modulation and thefrequency of the oscillations. As in the simulation one can see that the emittancevariation for the reduced offset beam is much smaller than for the beam with a largeoffset. By placing a pair of wire grids, between which there is an electric field, in thepath of the beam, we have been able to degrade the beam emittance. This occurs asthe result of a net transverse impulse being imparted to the particles as they traversethe electric fieldS. In Figure 4 we compare the variation of the measured emittancewith (J 0 for beams of initial emittances (or tune depressions) differing by a factor oftwo. Once again we see that, at least qualitatively, the simulation results are supportedby our experimental results.6 DISCUSSION AND CONCLUSIONSWe have obtained experimental evidence, supported by simulations, that stronglyspace-charge dominated beams propagating off-axis in electrostatic focus channelswill exhibit growth and oscillation in the transverse emittance. Reducing the spacecharge depression reduces the emittance oscillation amplitude. This indicates thatthe growth of the emittance may ultimately saturate. The observed behavior ofoff-axis beams might have consequences for the low-energy end of a driver, as the240 S. EYLON et al.need to minimize emittance growth may necessitate strict machining and alignmenttolerances for the lattice elements. Alternatively, frequency trajectory correction couldbe applied to maintain a well-aligned beam, although such a measure will have itsown cost implications.ACKNOWLEDGEMENTSWe are indebted to L. Smith, A. Faltens and W. M. Fawley for their helpful remarks.REFERENCES1. T. J. Fessenden et al., Proceedings of the 1987 Particle Accelerator Conference, pp. 898-902, IEEE Cat.No. 87CH2387-9 (1987).2. K. Hahn and L. Smith, Lawrence Berkeley Laboratory report LBL-29094 (1990).3. C. Celata, Proceedings of the 1987 Particle Accelerator Conference, pp. 996-1000 (1987).4. This technique was originally suggested to us by Denis Keefe.5. W. M. Fawley and E. P. Lee, Lawrence Berkeley Laboratory report LBL-28686 (1990).

Emittance variations of very cold off-axis ion beams during transport through MBE-4

Abstract

Similar works

Full text

Available Versions

CERN Document Server