* This work is supported by the US DOE under contract Nos. DE-FG02-02ER54672 and DE-FG02-94ER40855 (UMD), and DE-AC03-76SF00098 (LBNL) and W-7405-ENG-48 (LLNL). email: haber@umd.edu

MEASUREMENT AND SIMULATION OF THE UMER BEAM IN THESOURCE REGION*

I. Haber, S. Bernal, R. A. Kishek, P. G. O’Shea, B. Quinn, M. Reiser, Y. ZouUniversity of Maryland, College Park, MD 20742-3511

.A. Friedman, D. P. Grote, J. -L. Vay

LBNL 1 Cyclotron Road Bldg 47 Berkeley, CA, 94720-8201

AbstractAs the beam propagates in the University of Maryland Electron Ring (UMER) complex

transverse density structure including halos has been observed. A primary objective of the experimentis to understand the evolution of a space-charge-dominated beam as it propagates over a substantialdistance. It is therefore important to understand which details of the beam structure result frompropagation of the beam in the ring and which characteristics result from the specific details of theinitial distribution. Detailed measurements of the initial beam characteristics have therefore beenperformed. These include direct measurement of the density using a phosphor screen, as well aspepper pot measurements of the initial transverse distribution function. Detailed measurements of thedistribution function have also been obtained by scanning a pinhole aperture across a beam diameter,and recording phosphor screen pictures of the beam downstream of the pinhole.

Simulations of the beam characteristics in the gun region have also been performed using theWARP P.I.C. code. From these simulations, the observed behavior has been attributed to acombination of perturbations to the transverse distribution by a cathode grid that is used to modulatethe beam current, as well as the complex transverse dynamics that results from the combination of thenonlinear external focusing fields of the gun structure and the nonlinear space charge forces.

1. INTRODUCTIONEven though many of the basic characteristics

of space-charge-limited diodes have been wellknown for several decades, this knowledgedoes not usually extend to the details of theparticle distribution function that are necessaryfor predicting the downstream behavior ofmodern intense-beam systems. Furthermore,recent simulations and experiments have foundthat details of the beam distribution emergingfrom the source can have a strong influence onthe downstream beam evolution. Since thephenomena that govern the beam evolution areusually nonlinear and measurements of thebeam emerging from the gun region withadequate accuracy are often quite difficult,simulations have become a promising tool forunderstanding the behavior of space-charge-dominated beams in the source region.However, an important precursor to developinga credible predictive simulation capability thatcan reliably model the source region is the

benchmarking of the numerics againstexperimental observation.

An effort has therefore been undertaken tocompare numerical simulation againstexperiment in those cases where beamdiagnostics are sufficient to permit accuratesimulation/experiment comparisons for space-charge-dominated sources. It should be notedthat even though this work has largely beenmotivated by developing a predictive capabilityfor the highly space-charge-dominated beamsrequired for heavy ion fusion, the results areapplicable to a large class of machines. This isbecause as the intensity or luminosity of abeam at the high-energy end of an accelerator isincreased, it becomes increasingly important tooperate the source region in the space-charge-dominated regime.

Recent research comparing WARPsimulations to experimental observation of gunbehavior have centered on two experiments thatare particularly suitable for these comparisonsbecause of the diagnostic configurations.

These are the 500 KeV Source Test Stand(STS-500) diode at LLNL, and the Universityof Maryland Electron Ring (UMER).However, because the work on the STS-500 isdescribed elsewhere,[1] the description herewi l l emphas ize simulation/experimentcomparisons on UMER.

2. THE UMER GUNThe diode in the UMER experiment is a

simple Pierce geometry but with two significantmodifications. To ensure an equipotentialsurface across the anode plane, an anode gridwith approximately 86% transparency has beenplaced across the anode aperture. A moresignificant modification of the guncharacteristics results from a cathode grid with0.0254 mm diameter wires 0.15 mm apart, in awindow-screen pattern, placed 0.15 mm fromthe cathode surface. The presence of this gridcreates a triode geometry that is used tomodulate the current by varying the appliedgrid-to-cathode voltage. In the normaloperating range, the cathode-to-grid potential isset so the triode operates in a saturated state toavoid amplification of any fluctuations on thegrid pulse. A cartoon representation of the gungeometry, as well as the aperture-wheel/phosphor-screen combination is shown in Fig.1. As will be discussed below, operating with agrid-to-cathode potential sufficient to saturatethe triode significantly modifies the transversevelocity distribution from what is obtained in asimple diode. Furthermore, this modificationof the transverse distribution was found to havea significant effect on the downstreamevolution. In fact, it does not appear possible toaccurately model the downstream behaviorwithout including the modification to the beamvelocity distribution by the cathode grid.

3. EXPERIMENTAL MEASUREMENTSThe primary source of experimental data on

the detailed characteristic of the beam emergingfrom the gun has come from images on thephosphor screens that can be inserted into thebeam. One of these screens is placedapproximately 28.8 cm downstream from anaperture wheel that is approximately 20 mmfrom the anode plane and can be lowered intothe beam line without breaking vacuum. Thisscreen, used along with a pinhole aperture thatcan be scanned across the beam diameter, isused to measure the velocity distribution across

the beam, as well as the transverse variation inthe current density. If the beam is assumedaxisymmetric, a full transverse phase-spacedistribution is obtained. Another screen, placedon a long plunger-like mechanism that allowsthe screen to be slid along the injector line,cannot be used if any of the sections of the ringare in place. Data from the movable screen is,therefore, limited to what was obtained duringthe commissioning of the injector line.

Figure 2 is an image, under typical operatingconditions, of the fixed position phosphorscreen 28.8 cm downstream of the aperturewheel when the pinhole aperture is positionedat the beam center. The DC bias voltageapplied to the cathode-grid gap, which acts toimpede emission from the cathode in theabsence of the beam pulse, is set atapproximately -40V. During the nominal 100ns duration of the approximately 70V positivepulse applied to the grid, the grid-to-cathodepotential is estimated to be about 30V, which isthe sum of the bias voltage and applied pulsevoltage of opposite polarity. (The actualvoltage is not precisely known because themagnitude of the voltage drop, as the griddraws current during the pulse, is difficult toestimate.)

The length limitation does not permit acomprehensive discussion of the measurementsthat have been performed, however, twosurprising features to note are the observedshape of the velocity distribution, which can bedescribed as hollowed and axisymmetric, andthe transverse uniformity of this hollowedvelocity distribution which is found to beapproximately the same across the beam crosssection. This transverse uniformity of thedistribution was also seen, but in less detail, inthe previously published pepper-pot phosphorscreen images [2] obtained in an earlierexperiment.

Figure 3 is a plot of the transverse densityvariation measured, using the moveablephosphor screen placed near the anode plane,during commissioning of the injector line. Thecurve was obtained by plotting the intensity ofthe image along a diagonal cut across throughthe beam. The data presented here is only asmall but representative sample of the datataken over a variety of gun operatingconditions. However, it is still sufficient toillustrate some of the important characteristicsof the UMER gun.

4. SIMULATIONS OF THE UMER GUNBecause of the disparity in scale between the

0.15mm distance between grid wires and the0.15mm distance of these wires from thecathode surface on the one hand, and theapproximately 25mm distance to the anode,(this distance can be varied to adjust the gunperveance) it is difficult to simulate all thecharacteristics of the gun simultaneously. Atwo-pronged approach was therefore adoptedthat first examined the macroscopiccharacteristics of the gun structure bylegislating the distribution function of thecurrent emerging from the grid. The grid-to-cathode physics responsible for theexperimentally observed distribution, especiallythe hollowed velocity space, were thenexamined in the second (and still continuing)phase.

Some of the results of the macroscopicsimulations of the full diode gemoetry havealready been described.[2] AxisymmetricWARP simulations were performed assuminga transversely uniform current density injectedat the plane of the cathode grid. The magnitudeof this current was chosen to match themeasured total current after accounting for thefraction intercepted by the anode grid. A seriesof simulations was performed to examinesensitivity of the simulated profile at the planeof the phosphor screen to the assumed form ofthe injected velocity distribution. This profilewas found to be surprisingly sensitive to theassumed shape of the initial velocitydistribution. This sensitivity was unanticipatedbecause it was assumed that, as a result of thedominance of space charge potential energyover the transverse kinetic energy in the beam,the measured profile should be relativelyinsensitive to the details of the initial velocitydistribution. An additional surprise, discussedelsewhere [3] is the degree to which thedownstream behavior as the beam propagates inthe ring also depends on the detailed form ofthe initial velocity distribution.

Figure 4 is a plot of the radial densityvariation of the simulated distributionpropagated to plane of the phosphor screen.Note that since the simulation is axisymmetric,only half of the distribution from the center tothe outer edge is plotted, in contrast to thedensity plot in Fig. 3 in which both halves ofthe measured beam are plotted to explicitlyexhibit the degree of asymmetry in theexperiment. By varying the injected velocity

distribution to obtain qualitative agreement withthe measured transverse variation in the currentdensity, a surprising degree of detailedagreement was observed to what were initiallythought to be measurement anomalies. Becausethese features, such as the dip in density at thebeam center and the small shoulder out fromthe center, appear in both the simulated andmeasured density they appear to be real, if notcompletely understood, features of the beamevolution. It should be noted that suchagreement is absent if the initial distribution isvaried significantly from the assumed form.

Although the shape of the central density dipin the simulation differs from the measuredcentral dip, from the left to right asymmetry inthe experimental curve shown in Fig. 3 it seemsclear that the depression in the measureddistribution is not centered on the diameter cutacross the beam that was used to generate theplot. This occurs because the densitydepression near the center of the beam isslightly displaced. This displacement isthought to result from a slight misalignment ofthe gun as well as the possibility that thesimulation geometry does not precisely mirrorthe “as-constructed” gun geometry. Inaddition, the sharpness in the dip in thesimulated curve in Fig. 4 might be exaggeratedby slight numerical inaccuracy in the simulationat the beam center. An additional source ofpotential disagreement between simulation andmeasurement is the simplified, two-parameterfit for the initial velocity distribution, which ischaracterized by oppositely-directed Gaussiandistributions of specified width and separation.Similar comments apply to the slight shouldersin the density curves, seen in both thesimulation and experiment, as well as the slightskirt at the beam edge. While the shoulders inthe two curves do not correspond precisely inlocation or shape, such shoulders are a featureboth in simulations and measurement over arange of parameters.

The dips, as well as the shoulders, wereunexpected because the normalized beamemittance in the simulation of 12.5 mm is onlyabout 2.5¥ the intrinsic emittance calculatedfrom the product of the 0.1 eV cathodetemperature and the emitter radius. This led toan expectation of a laminarity for the particleorbits that was not expected to produce suchstructure.

The simulations of the macroscopic guncharacteristics were performed assuming an

initial hollowed distribution. Simulations havealso been undertaken to understand themechanisms that can produce this hollowing.Three-dimensional simulations that resolve thevery fine scale of the cathode grid at the sametime as simulating the much larger diode as awhole are an ambitious undertaking. Instead,three-dimensional WARP simulations wereundertaken that examine a single 0.15 mmsquare cell in the periodic array of grid cellsnear the beam center. Periodic boundaries, aswell as fourfold transverse symmetry, wereassumed in the simulation so that the modeldoes not include any transverse influenceassociated with the evolution of the beam edgeor with any beam compression from thetransverse focusing applied by the Piercegeometry.

Because the dynamics of virtual cathodeformation near the emitter surface anddownstream of the grid are important to theresulting distribution [4] the cathode wasmodeled by injecting several times the expectedChild- Langmuir current from the cathodesurface and following the self consistenttemporal evolution as a virtual cathode isformed. It should be noted that the finest gridused to model the 0.15mm square region 25mm long, with the assumption of fourfoldtransverse symmetry in the two transversedimensions, was 2048 by 32 by 32. This gridwas not completely adequate to resolve thelongitudinal dynamics so that some possiblynonphysical transient behavior [5] wasobserved. Nevertheless, though refinement ofthe simulations is currently underway, thequalitative features observed are believed to becorrect, particularly because of the extent thatthey mirror experimental observation.

What is observed in the simulations is thatfor small grid to cathode potentials, the virtualcathode forms between the cathode and grid,and observed downstream transverse velocitydistribution function is monotonicallydecreasing with velocity and some observedsquaring of the distribution, as opposed to theaxisymmetry expected without the grid,matches experimental observation. However,above a threshold in the magnitude of the grid-to-cathode voltage of approximately 30 V, avirtual cathode is formed downstream of thecathode grid and the experimentally observedhollowing in the transverse velocity distributionis seen in the simulations. Figure 4 is a particlescatter plot of the downstream velocitydistribution obtained from one such a

simulation. While the current simulations arenot fully converged numerically, and furtherrefinement is in process, nevertheless thequalitative features of the experiment have beenreproduced.

5. CONCLUSIONSBoth experimental observation and

simulation have revealed a significant level of,unexpected, complexity in the evolution of thedetails of the beam distribution function as thebeam traverses the diode region. For asufficient grid-to-cathode potential difference ahollowing is observed in the transverse velocitydistribution.

Though the hollowed velocity distributiondoes not appear to cause a large increase in thetransverse beam emittance, some of thetransverse structure observed during beampropagation in the diode region appears todeviate from what would be expected using thelaminar orbit structure expected in a the highlyspace-charge-dominated region that ischaracteristic of a low emittance gun structure.

The agreement that has been seen betweensimulation and observation promotessubstantial confidence in using the simulationsas a tool for understanding the significantfeatures of the space-charge physics. Alsoimportant, the detailed characterization of thebeam distribution function of the beam that hasbeen obtained by moving a small apertureacross the beam should provide, along with thesimulations, a valuable tool in predicting thedetailed evolution of the beam propagation inthe UMER ring.

REFERENCES

[[1] J. W. Kwan, F. M. Bieniosek, W.L. Waldron,J-L. Vay, G.A. Westenskow, E. Halaxa, I.Haber, “Production of a High BrightnessBeam from a Large Surface Source,” HIF-2004

[[2] I. Haber, S. Bernal, C. M. Celata, A.Friedman, D. P. Grote, R. A. Kishek, B.Quinn, P. G. O’Shea M. Reiser, J-L. Vay,“Collective Space-Charge Phenomena in theSource Region,” Nucl. Instr. and Methods A519 (2004) 396.

[3] R.A. Kishek, S. Bernal, C.L. Bohn, D. Grote,I. Haber, H. Li, P.G. O'Shea, M. Reiser, andM. Walter, “Simulation and experiments withspace-charge-dominated beams,” Physics ofPlasmas 10 (2003) 2016.

[4] Y. Zou, H. Li, M. Reiser, and P.G. O'Shea,"Theoretical Study of Transverse EmittanceGrowth in a Gridded Electron Gun,” Nucl.Instr. and Methods A 519 (2004) 432.

[5] J-L. Vay, P. Colella, J.W. Kwan P.McCorquodale, D.B. Serifini, A. Friedman,D.P. Grote, G. Westenskow, J.-C. Adam, A.Heron, and I. Haber, "Application ofAdaptive Mesh Refinement to Particle-in-CellSimulations of Plasmas and Beams," Physicsof Plasmas 11 (2004) 2928.

FIGURE CAPTIONS

Fig. 1. Schematic representation of the UMER gun geometry illustrating the presence of cathodegrid (G) close to the emitter surface (K), as well as an anode grid (A) across the gun exit that isused to insure an equipotential at the anode plane. A wheel-mounted pinhole aperture (W)slightly downstream from the anode plane can be rotated across the beam to measure thevelocity distribution across the beam by capturing the angular beam spread on a phosphorscreen (S) 28.8 cm downstream.

Fig. 2. Phosphor screen image 28.8 cm downstream of a 0.5 mm pinhole at the beam center showingthe hollowed transverse velocity distribution that can be caused by the cathode grid when thegrids to cathode potential is sufficiently high. The calibration arrow is transverse distance onthe image divided by the distance to the pinhole. The faint circle at the outside of the picture isthe outer edge of the 3.175 cm diameter phosphor.

Fig. 3. Plot of intensity across a diameter taken from a phosphor screen image of the full beam 6 cmdownstream of the anode plane showing the radial current density variation across the beam.

Fig. 4 Plot of the radial density variation from a WARP simulation of gun where a specifiedcurrent matching the measured total current is inject at the cathode grid plane with a specifiedhollow transverse velocity distribution. The velocity distribution consists of transverselycounterstreaming Gaussian distributions with a thermal spread corresponding to 0.2 eVtemperature and separated by 4 times that thermal spread.

Fig.5. Particle plot of the velocity space from a WARP simulation of a small region in the beamcenter corresponding to single cell of the periodic rectangular cathode grid, with fourfoldtransverse symmetry and periodic transverse boundary conditions. When a sufficiently large, inthis case 30 V, potential is applied between the grid and the cathode a virtual cathode is formeddownstream of the grid and a hollowed velocity distribution similar to what is seen experimentallyis observed.

K

G A

25 mm 288 mm20 mm

W S

Fig. 1

x¢ = 0.02

Fig. 2

Fig. 3

Fig. 4

-0.02 0.00 0.02

-0.02

0.00

0.02

0

200

400

600

800

1000

1200

1400Y' vs X'

X'

Y'

z window2 = 2.3580e-02, 2.4080e-02

Step 11500, T = 0.0045e-6 s, Zbeam = 0.0000 mSImulation of full diode length16x16x1024

I. Haber, D. P. Grote warp r2 me10

71

Fig. 5