Weis, T

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Particle Accelerators, 1992, Vols. 37-38, pp. 81-86Reprints available directly from the publisherPhotocopying permitted by license only© 1992 Gordon and Breach Science Publishers, S.A.Printed in the United KingdomEMITTANCE DEGRADATION OF INTENSE ANDPARTIALLY SPACE CHARGE NEUTRALIZEDION BEAMStT. WEISInstitut fur Angewandte Physik der Johann Wolfgang Goethe Universitiit,Postfach 111932, D-6000 Frankfurt am Main, Germany.(Received 3 December 1990)Severe transverse emittance growth of intense low-energy ion beams in magnetic transport lines has beenobserved at different laboratories in the case of a partially space charge neutralized beam. This isunfavorable since magnetic systems are the commonly used transfer lines for the transport of high-perveance beams, as are required for heavy ion inertial fusion drivers.Rearrangement of the transverse charge density of the ion beam towards a uniform distribution is aknown mechanism which leads to initial emittance increase at the front end of a transport system. In thepresence of space-charge-compensating electrons, the rearrangement of charge density affects ions andelectrons as well, and the finite electron temperature, together with beam envelope and residual-gaspressure variations along the beam line, is believed to cause continuous emittance increase.Calculations using the tracking code PARMILA TRANSPORT, including the influence of compensatingbackground electrons, have been carried out. First results will be reported and compared to experimentalresults obtained using a 1O-keV, 1.S-mA He + beam in a magnetic transfer line.1 INTRODUCTIONEspecially at ion source extraction energies the HIBALL scenario! requires high-current (high-perveance) beams. They cannot be transported in low-energy beamtransport lines (LEBTs) without an appropriate reduction of space-charge forces bymeans of space-charge neutralization, and it is strongly recommended that specialattention is placed on the low-energy injector part to keep the overall emittancegrowth low.A positive-ion bearD passing through residual gas ionizes the neutral gas atoms.The produced electrons accumulate in the beam region, thus lowering the actingspace charge forces significantly. The positive residual-gas ions (also created by chargeexchange) are expelled from the beam. Several attempts have been made by differentauthors to calculate the distribution of compensating electrons and residual gas ionsin the beam plasma by solving the Poisson equation containing the densities of beamions, compensating electrons and residual gas ions using one-dimensional fluidequations for cold plasmas2 ,3,4 or kinetic equations for the residual gas ion behavior. 5Although the agreement has been excellent in specific cases, general predictions arenot reliable and the aid of supporting measurements is still necessary.t Work supported by BMFT under contract no. 06 OF 1861.8182 T. WEIS(1)2 EMITTANCE DEGRADATION OF INTENSE BEAMSSources of transverse rms emittance growth in high current LEBT lines have beenclearly identified6 , 7 , namely, nonlinear external focusing forces, and nonlinear internalspace-charge fields of the beam itself causing a redistribution of the ion-beamtransverse density towards a homogeneous one, thus minimizing the internal fieldenergy of the ions in their own space-charge field. For a constant or periodic focusingof a round beam, the increase of the transverse emittance along the beam path z isgoverned by the following equation:6d 2 d w- ~- Erms = -K<r ) -,- ,dz dz Wowhere K is the generalized beam perveance, <r2 ) the square of the rms beam size,and (W - Wu)/wo a normalized dimensionless parameter, which relates the nonlinearfield energy to different initial beam profiles. The redistribution of the beam densitydistribution causes an energy transfer to transverse kinetic energy, thus increasingthe rms emittance. This process is adiabatic (constant total energy) in the case of anunneutralized beam and occurs once, if only linear external fields exist.At first sight this looks quite favorable for a compensated beam because K and<r2 ) in Equation (1) are drastically reduced. Compensated beam transport experi-ments at GSI 8 using a periodic structure of magnetic quadrupoles, however, haveshown a severe increase of the rms transverse emittance. Compared to the experimentswith an uncompensated transport, emittance growth occurred even in the low currentregion and could not be explained by rearrangement of the initial beam densitydistribution.Charge density redistribution in the case of a partially compensated beam howevermeans rearrangement of both ions and electrons (and even residual gas ions) towardsa more linear internal self-field of the beam. The more or less thermal behavior ofthe compensating electrons (collisions with each other) and the dynamic equilibriumof heating of the trapped electrons by beam ion collisions and radial and longitudinallosses easily cause broader electron densities in space compared to the ion distribu-tion. Measurements with a transverse electron beam probe indeed have shown thatthere is a region of net negative charge density outside the beam.9 This process isnot adiabatic in the sense that the total energy of the system is not necessarilyconstant. Therefore, rearrangement of the ion beam density distribution for acompensated beam does not necessarily end up in a homogeneous distribution.Variations of residual gas pressure, ion energy or beam radii change the relations ofthe charge distributions of all participating species and cause the beam distributionto react continuously to the varying situations.3 EXPERIMENTAL AND NUMERICAL INVESTIGATIONSWe have set up a small-scale transport experiment in Frankfurt to investigate thebeam behavior of uncompensated and compensated ion beams at ion-sourceEMITTANCE DEGRADATION 83(2)extraction energy.l0 A 1.5-mA He+ beam at 10 keY could be transported with fulltransmission through a short transport line with one solenoid. With the aid of acollimator behind the ion source extraction region an almost constant transversebeam profile' could be obtained. The degree of compensation (80-90%) has beenevaluated with residual gas ion spectrometers 11 at moderate beam sizes in front anddownstream of the solenoid at operating pressures of approximately 10- 5 mbar.Figure 1 summarizes the measured degrees of neutralization near and at beam waistposition behind the magnetic lens. The measured energy of the residual gas ionsexpelled from the beam provide information on the total space charge potential ~qJlbetween beam axis and outer wall and on the beam potential ~qJ2 inside the beam.Measurements at beam waist position showed that the beam potential ~qJ2 is almostunneutralized, whereas the lowering of the total potential ~qJ 1 remains constant andindependent of beam size (Figure 1). The different degrees of compensation f 1 andf 2 are defined via~qJ 1,2(partially compensated)h2=1- ., ~qJl,2(uncompensated)It is worthwhile to mention that the values of f 2 correspond to the degree ofcompensation inside the beam, telling us to what amount the internal space chargeforces are reduced. Th~ overall high values of f l' however, show that even at thewaist position the amount of electrons is approximately the same as anywhere elsein the transport line and that most of the electrons stay outside the beam volume.Solving the Poisson equation with kinetic residual gas ions directly confirms thisresult numerically if the electron temperature is kept constant. Transverse rmsemittance growth has been observed in the case of decreasing compensation obtained20~10~t:E f1=83%"--'en f = 81 % f = 85%.2 1 1""0 0co~Eco:'10 fZ= 43% fZ= 64%~..0f2= 2%-200 10 20 30 40beam path behind the solenoid z (em)FIGURE 1 Beam envelope downstream of the solenoid versus path length. 11 and 12 refer to the differentdefinitions of the degree of compensation (see text).84•Ero 1IE o. ? 0Ina Inlt. _.•1.S•T. WEIS•• •derived from Parrnilasimulations withbackground electronsFIGURE 2 Ratio of final and initial transverse emittance versus decompensating electrode voltages.by biasing cylindrical electrodes in the beam line to positive and negative potentials(Figure 2).Numerical simulations with the GSI version of PARMILA TRANSPORT, including thecoupling of both transverse planes and the consideration of the spherical aberrationproperties of the lens, were totally inconsistent with the experimental results. In thesecalculations the reduction of the acting space-charge forces is considered only by thevariation of the ion current in the space-charge routine of the code.Based on the numerical solution of the Poisson equation using kinetic residual gasion behavior (Figure 3), the PARMILA code has been extended in a first step to allowfor the creation of compensating background electrons. The electron distribution ne(r)is created with Gaussian shape (line 3 in Figure 3) and adapted to the second momentof the ion distribution <r2 )ne(r) == neO * exp( - ar2/2<r2 »). (3)The factor a used in Equation (3) has been evaluated to be a == 1.33 to give anacceptable agreement with the calculated electron distribution (line 2 in Figure 3).The numerical results obtained for various degrees of neutralization explain qualitat-ively as well as quantitatively the experimental results. The numerical derivedevolution of the rms emittance along the beam path shows a slight increase duringthe initial drift, then an enhanced increase in the lens due to the large lens aberrations,followed by a decrease of the emittance beyond the lens.4 CONCLUSIONExperimental as well as numerical studies have shown that space charge neutraliza-tion is necessary to keep the emittance degradation small in a system with large lensEMITTANCE DEGRADATION 851::2 leO -------- 15ICI.) I~~ Oe8 f ~ 12;>(1) I ........--OIJ , ~~ Oe6 f ct$ 9ct$ e.-c...t:= f ~0 r le5 rnA He+~(1)~ I ~Oe4 0 6(1) 10 keY 0.-Ne.-c S~ct$e Oe2 ct$ 3(1)~.D0~0.00 10 20 30 40 SOradial distance r (mm)FIGURE 3 Calculated normalized charge densities for the ions (line 1), the electrons (line 2 (calculated)and 3 (adapted Gaussian shape)) and beam potential (line 4) versus distance r from the axis.aberrations. This is due to the reduced beam radii in the aberrative elements. Theexperimental, theoretical and numerical studies, however, also indicate that, after aninitial density redistribution, uncompensated beam transport in the absence ofnonlinearities caused by the focusing system is the only way to avoid further emittancedegradation.Electrostatic focusing seems to be a way out, but the limited current capability ofsuch "full perveance" systems restricts the transportable current in one channel tounacceptable values with respect to inertial confinement fusion requirements. Space-charge-neutralized transport is therefore the right track to follow, and the task forthe future is keeping the emittance growth caused by the neutralization process aslow as possible. To do this the following recommendations can be made: degrees ofcompensation as high as possible to achieve small remaining beam perveances(Equation (1)); strong focusing to keep the mean beam radii small (Equation (1)); andavoidance of large envelope variations or large beam-tube cross sections, whichshould be adapted as closely as possible to the actual beam radius.The measurements will be repeated using a new transport line with low-aberrationsolenoids. The obtained experimental results will be used to extend the PARMILA codeto a more sophisticated consideration of background electrons. An optimization ofthe compensated beam transport with respect to low emittance increase is one of ourmajor goals.ACKNOWLEDGMENTSThe author expresses his great appreciations to all members of the "Frankfurtneutralization group."86 T. WEISREFERENCES1. HIBALL II, Kernforschungszentrum Karlsruhe, Report KfK 3840 (1985).2. E. B. Hooper et al., Phys. Fluids 22, 2334 (1979).3. D. S. Lemons et al., J. Appl. Phys. 57, 4962 (1985).4. M. Reiser et al., SPIE 873, Microwave and Particle Beam Sources and Propagation 172 (1988).5. A. 1. T. Holmes, Phys. Rev. A 19,389 (1979).6. I. Hofmann et al., Part. Ace. 21, 69 (1987).7. T. Wangler et al., IEEE Trans. Nucl. Sci. NS-32, 2196 (1985).8. J. Klabunde et aI., Proc. 1986 Lin. Ace. Conf., SLAC-Report 303,296 (1986).9. P. Gross et al., Proc. 1990 Europ. Part Ace. Con!, Editions Frontieres, Gif-sur-Yvette, France 806(1990).10. T. Weis et al., ibid. 809 (1990).11. T. Weis et al., this conference.

Emittance degradation of intense and partially space charge neutralized ion beams

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