Results are presented of the simulation of low&#8211;energy ion dynamics with three different codes: KOBRA, IGUN and CPO. To share work between different codes one needs to be confident that they agree. For test cases, good agreement was found between the codes and analytical solutions. Where possible, results have been compared to experimental data from the CERN Laser Ion Source. These simulations are in general agreement with the data of the real beam line. c The following article has been submitted to Review of Scientific Instruments. After it is published, it will be found at http://ojps.aip.org/rsio/

Hanke, K

Heising, S

Probert, G

Scrivens, R

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN/PS 2001-061Comparison of Simulation Codes for the Beam Dynamicsof Low-Energy IonsK. Hanke, S. Heising, G. Probert, R. ScrivensAbstractResults are presented of the simulation of low–energy ion dynamics with three differentcodes: KOBRA, IGUN and CPO. To share work between different codes one needs to beconfident that they agree. For test cases, good agreement was found between the codes andanalytical solutions. Where possible, results have been compared to experimental data fromthe CERN Laser Ion Source. These simulations are in general agreement with the data ofthe real beam line.c© The following article has been submitted to Review of Scientific Instruments. After itis published, it will be found at http://ojps.aip.org/rsio/.Presented at ICIS2001, Oakland, California, USA3-7 September 2001Geneva, SwitzerlandOctober 20011 IntroductionSimulation of the extraction and low-energy transport of ions is a complex problem. Inthe case of the CERN Laser Ions Source (LIS) the beam is space-charge dominated and consistsof a variety of charge states. To simulate the transport of beams through electrostatic fields, onestarts from a set of measured beam parameters at the entry of the beam line. The result of thetracking depends then on the precision of the measurement, the field solver and the integrationroutine for the equation of motion of the particles.The simulation of particle transport in the space-charge domain can be shared betweendifferent codes if they have been cross-checked against each other. At CERN, the three codesKOBRA, IGUN and CPO are available. We have cross-checked these codes against each otherwith simple examples and have compared the results with experimental data available from theCERN LIS. The input beam distribution was identical for all codes. The codes were comparedusing two tests:1. Expansion of a space-charge dominated beam in a drift region without external fields;2. Transport of particles in the electrostatic field of a Gridded Electrostatic Lens (GEL) [1]as used on the CERN LIS (see later description).2 Simulation Codes2.1 KOBRAKOBRA3-INP [2] is a three-dimensional program for the simulation of steady state prob-lems. The program contains a Vlasov solver, which finds the solution of the Poisson equationand of the particle distribution function via the space-charge map which is then included infurther iterations of the Poisson equation.2.2 IGUNIGUN [3] is a 2D ray-tracing simulation code that is designed for the simulation of ionextraction and transportation in electrostatic and magneto-static systems. The code is based onan electron ray-tracing code (EGUN) with additional modelling of the compensation of the ionspace-charge by electrons in a plasma.2.3 CPOCharged Particle Optics (CPO)[4] is a three-dimensional code that uses the surface chargemethod. In contrast to the other codes, the electrical fields are determined by charges depositedonto surface elements of the conductors within the volume. A comparison of finite elementmethods and the surface charge method is given in [5, 6].3 Space Charge ExpansionThe first example used to cross-check the codes is the space-charge expansion of a beamwith given parameters going through a drift space. For this study, a uniform beam of Ta20+ions was generated with 30 mm initial diameter and zero emittance (‘pencil beam’). The initialkinetic energy was set according to an extraction voltage of 60 kV. The drift length was 10 cmand two beam currents of 60 mA and 120 mA were simulated.The three simulation codes give the output beam parameters shown in Table 1. Notethat IGUN provides only two–dimensional results (r, r ′) and that the emittances calculated byIGUN are significantly lower compared to other codes. KOBRA and IGUN agree to within 1%and CPO to within 2% to the approximate analytical solution of the radius. We are thereforeconvinced that space–charge is treated correctly in the three codes.1Table 1: Output beam parameters for space charge expansion computed with the three codes.KOBRA IGUN CPO60 mA 120 mA 60 mA 120 mA 60 mA 120 mAr [mm] 17.5 a 19.6 b 17.3 19.6 17.2 19.2a) Analytical value is 17.4 mAb) Analytical value is 19.6 mAFigure 1: Gridded electrostatic lens LEBT. All dimensions in mm.4 Simulation of LEBTWe will now consider beam transport through an electrostatic focusing element as used inlow-energy beam transport (LEBT) lines. The input beam parameters are in general accessibleto measurements and therefore known within the measurement precision. The electrostatic fieldis computed by the field solver of the codes. This is also a possible source of discrepancybetween codes.The gridded electrostatic lens LEBT used on the CERN LIS was chosen as an example.It consists of three long (40 mm) electrodes at variable potential separated by grids at groundpotential. The complete GEL set-up is shown in Fig. 1. It is used to match the beam from theextraction system to the acceptance of the subsequent Radio-Frequency Quadrupole (RFQ).As a test case to verify the correct beam transfer in the three codes, we have consideredone single GEL element at V = 30 kV. The geometry used was a 30 mm drift, one GEL elementand a 30 mm exit drift region. The GEL element consists of a grid at ground potential, a drift of18 mm, the 40 mm long electrode at 30 kV, a second drift of 18 mm and a second grid at groundpotential. Ta20+ ions at a kinetic energy corresponding to 110 kV extraction were transported.Space-charge effects were suppressed for this test case.4.1 Potential on Beam AxisThe field solvers of the three different codes were compared. The potential map for thegiven geometry and potentials was computed, and the potential along the z axis was plotted2z / mm0 20 40 60 80 100 120U / kV051015202530Potential Comparison at r=15IGUNKOBRACPOz / mm0 20 40 60 80 100 120U / kV051015202530Potential Comparison at r=0IGUNKOBRACPOFigure 2: Potential at rx,y = ± 15 mm (upper plot) and rx = ry = 0 mm (lower plot) ascomputed by the three codes. No discrepancy is visible.for the three cases (rx =15 mm, ry =0 mm), (rx =0 mm, ry =15 mm) and (rx = 0 mm,ry = 0 mm). The resulting plots are shown in Fig. 2. The difference plot is shown in Fig. 3,where the largest deviation is below 50 V. Therefore it is concluded that the calculation of thepotential map is done correctly in all three codes.4.2 Transport of Test Rays through GELSingle test rays were traced through the potential map. The test rays started at 5 mm,10 mm and 15 mm from the axis in x- and y-direction. A plot of the trajectories is shown inFig. 4, where the rays overlap perfectly.4.3 Beam Transport through GELFinally we transported a typical LIS beam with a current of 74 mA through the three-cellGEL as shown in Fig. 1. The parameters for the initial distribution are taken from a measurementat the entry plane of the GEL. The emittance at 50 mm after the exit grid as well as the currentinto a Faraday cup with two input apertures was obtained. The double-aperture cup has two3z / mm30 40 50 60 70 80 90 100U / V-100-80-60-40-20020406080100rel. Potential Comparison at r=15IGUNKOBRACPOz / mm30 40 50 60 70 80 90 100U / V-100-80-60-40-20020406080100rel. Potential Comparison at r=0IGUNKOBRACPOFigure 3: Difference of the potential calculated by the three codes from average potential. Theupper plot corresponds to rx,y = ± 15 mm and the lower one to r = 0 mm.4z / mm0 20 40 60 80 100 120r / mm0246810121416Ray Tracing ComparisonIGUNCPOKobraFigure 4: Tracking of test-rays through one cell of the GEL. All codes agree.Table 2: Output beam parameters for a 240 π mm mrad emittance beam through a three–cellGEL. The initial distribution used is based on the measured emittance at the entrance of theGEL. εi,f are the initial and final emittances, IDA is the current into a double aperture cup.KOBRA IGUN CPO experimentrays 15000 500 11000ε4rms,i [π mm mrad] 240 233/241 242 242ε4rms,f [π mm mrad] 420 234/421 434 365IDA / mA 41 36.5 41 25IDA / mA (scaledc) 33.5 29.8 33.5 25c) Taking into account losses at the grids.square apertures of 5.9 mm spaced 44 mm apart, with the first aperture positioned 30 mmdownstream of the GEL exit grid. In Table 2, the input and output parameters are summarizedfor all codes and compared to the experiment. For the 2D-code IGUN the input rays weretransformed to polar coordinates (r, θ) and the result re-mapped to Cartesian coordinates. Sincein IGUN all problems are radially symmetric, the apertures represent circles and hence thecurrent was scaled by 4πfor comparison with a square aperture. IGUN uses only 500 rays whichleads to different emittances in x and y. A similar behaviour was seen with CPO when only upto 1000 rays could be used.5 ConclusionThree codes for simulation of low–energy ion dynamics were compared to each otheras well as to known solutions and experimental data. The codes reproduce an approximateanalytical solution for space–charge calculations to within 2%. Differences of the potentialsfrom the field solvers are in the order of 10−3 of the maximum voltage. Single rays tracedthrough a test case coincide.When simulating the low–energy line of the CERN LIS, the three codes exhibit goodagreement. However, comparison with the experimental data shows an underestimation of theemittance by 20% and an overestimation of the transmitted current by 30%.The simulations presented here do not include the following characteristics of the real5line: (i) variation of the beam parameters during the current pulse; (ii) more accurate represen-tation of the GEL structure (including for example the grid wires); (iii) space-charge compen-sation. Furthermore, the average beam parameters include experimental errors and the effect ofthe measurement equipment on the beam itself. Further simulations can begin by taking theseprocesses into account.The characteristics of LIS (current, emittance, extraction geometries) change with differ-ent laser configurations and target materials. The good agreement between different codes andexperiments shows that with these tools the estimation of source parameters within acceptabletolerances is possible, limiting tedious and costly experiments.References[1] P. Ostroumov, LIS LEBT on the base of electrostatic gridded lenses, unpublished.[2] P. Spa¨dtke, KOBRA3-INP User Manual, version 3.39 (2000).[3] R. Becker, W. B. Herrmannsfeldt, IGUN - A Program for the Simulation of Positive IonExtraction including Magnetic Fields, Rev. Sci. Instrum. 63 (4), p.2756-2761 (1992).[4] Welcome to CPO, Help file for the CPO package, version 3.1e (2001).[5] D. Cubric, B. Lencova and F. H. Read, Comparison of the Finite Difference, Finite Elementand Surface Charge Methods for electrostatic charged particle optics, Electron Microscopyand Analysis 1997, Institute of Physics Conference Series 153, 91-94 (1997).[6] D. Cubric, B. Lencova, F. H. Read, J. Zlamal, Comparison of the Finite Difference, FiniteElement and Surface Charge Methods, Nucl. Instr. Meth. (1999).6

Comparison of Simulation Codes for the Beam Dynamics of Low-Energy Ions

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