Craig, G D

Fessenden, T J

Neil, V K

Paul, A C

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Particle Accelerators1981 Vol.ll pp.239-2440031-2460/81/1104/0239$06.50/0© Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaCHARACTERISTICS OF THE ETA GUN*ARTHUR C. PAULLalyrenCe Berkeley Laboratory, University of California, Berkeley, California 94720 USAandY. K. NEIL, G. D. CRAIG, and T. J. FESSENDENLawrenc'e Liver/nore National Laboratory, University of California, Liver/nore , California 94550USA(Received June 9, 1980; in finalfonn Feb. 11, 1981)The Experimental Test Accelerator (ETA) is a linear induction device consisting of a 2.5-MV electron gun and ten0.25-MV accelerating units designed to produce a 10-kA beam of electrons at 5 MeV. Calculations with the computercode EBQ as well as experimental measurements indicate that the current produced by the gun is limited by twophenomena. The first arises from the variation of particle energy with time during the pulse. Only particles withenergy within a limited range can be transported by the focusing coils in the gun ~ therefore the variation of thegun's output current with time is determined by the coil settings. The second effect results from a collectiveinteraction at sufficiently large current to cause a virtual cathode to form a few centimeters past the extraction grid.Operation in this regime results in greatly increased beam emittance and poor beam transport through the accelerator.Results of the code calculations are compared with experimental data and found to be in good agreement.I. INTRODUCTIONThe injector for the Experimental Test Acceler-ator (ETA) is a 2.5-MY, linear-induction electrongun designed to produce 10 kA of beam current.In this paper we describe the theoretical predic-tion of the ETA gun's characteristics, and com-pare these predictions with experimental data.The beam dynamics in the ETA gun were deter-mined by calculations using the computer codeEBQ.I This is a steady-state, azimuthally sym-metric, self-consistent code. The code was usedin the design of the gun to determine the equilib-rium flow of electrons from the cathode, throughthe extraction grid, across the grid-anode regionand into the hollow anode. The geometric modelof the gun that is used in these calculations isshown in Fig. I. The washer shown is an elec-trode with potential equal to one-half the anodevoltage. Focusing solenoids are placed outside* Lawrence Livermore National Laboratory is operated bythe University of California for the Department of Energyunder Contract No. W-7405-Eng-48.This work was performed by LLN L for the Department ofDefense under DARPA (DOD) ARPA Order 3718, Amend-ment No. 12, monitored by NSWC under Contract No.N60921-80-PO-WO 188.239the anode, and a Hbucking" coil (not shown) islocated back of the cathode to reduce the axialmagnetic field on the cathode surface to a mini-mum. Particle trajectories in the gun design werefollowed a distance of about 2 m' from the cath-ode, but for this paper the trajectories were fol-lowed for only 60 cm from the cathode. The finitegrid structure is not considered.During actual operation of the gun, both thegrid voltage, VR' and the anode voltage, V(l' varyin time over a period of about 50 ns. The variationof Va with time approximates one-half of a sinewave, so the steady-state conditions simulatedwith the code are never achieved. In order togain some insight into the behavior of electronsas VR and V." are varied, we make separate cal-culations with the code for various values of VRand Va, thus generating characteristic curves ofthe gun.II. SIMULATION OF IDEAL OPERATIONIn all calculations the current, I, drawn from thecathode by the extraction grid follows the Child-Langmuir law. For a cathode of area A,1 == 2.3 x 10- 6 A VR 3/2 / d 2 • ( 1)240 A. C. PAUL ET AL.FIGURE I Geometry of the ETA gun, equipotential sur-faces, and particle trajectories for anode voltage Va = 2 MY,grid voltage VR = 10 kY, and current J = 537 A.In this relation v,,? is the grid voltage in volts andd is the cathode-grid separation taken to be 1.5cm in all calculations.In ideal operation of the gun, the anode voltageis constant in time while the beam current isturned on by applying voltage to the grid. As thegrid voltage increases the beam current increasesfrom zero to the desired maximum value. In prac-tice, testing has shown that the anode voltagerises too slowly to achieve this mode of operationwith the present gun configuration. Ideal opera-tion is simulated by making separate calculationswith the same value of v'a and different valuesof v,'?' Particle trajectories from a 10-inch-diam-eter cathode are displayed in Figs. 1, 2, and 3 forv,,, = 2 MV. In these figures the approximatelyvertical curves are equipotentials and the ap-proximately horizontal curves are particle tra-jectories. For computational convenience a Neu-mann boundary condition is imposed at z = 60cm. This artificial condition does not affect re-sults in the region of interest (z :S 40 cm).The bell-shaped curve is the axial magnetic fo-cusing field at r = O. In Fig. 1 we have v,,? = 10kV, and I = 537 A; in Fig. 2 we have v,,l? = 40FOCUSing~c-c:===:::::~__ :~ 'C8JFIGURE 2 Equipotential surfaces and particle trajectoriesfor Va = 2 MY, VR = 40 kY, and J = 4.27 kA.FIGURE 3 Equipotential surfaces and particle trajectoriesfor Va = 2 MY, VR = 60 kY, and J = 7.82 kA.CHARACTERISTICS OF THE ETA GUN 241kV and I = 4.27 kA; and in Fig. 3 we have VI?= 60 kV and I = 7.82 kA. In these three cal-culations the focusing solenoids are set to providea maximum axial magnetic field B, = 520 G onaxis at a point about 40 cm from the cathode asshown in Fig. I. The trajectories display the fo-cusing from the azimuthal magnetic self-field inthe grid-anode region. This focusing force in-creases with the total current.III. WAVEFORM LIMITED TRANSPORT6 1.5t (ns)FIGURE 5 Oscillograms of voltage and beam current: (a)anode voltage and cathode current vs time: (b) beam currentvs time at the gun output for five values of the peak axialmagnetic field. The dashed curve is the cathode current.(b)100t (ns)20values are chosen just below the limiting currentfor virtual cathode formation. At V(/ :s I MV thebeam collapses downstream from the peak mag-netic field, while for V(/ 2': 1.5 MV all of the cur-rent is transported.This phenomenon can easily be seen in exper-iments by changing the strength of only the firstgun focus coil and observing the current pulse atthe gun output. Figure 5 shows experimental re-sults obtained on December 5. 1979, when a 10-inch-diameter cathode was used. As shown inFig. 5(a) the system timing was such that thecurrent pulse emitted from the cathode was de-layed by approximately 20 ns with respect to theanode voltage pulse. As a result, particles in theleading edge of the current pulse had more energythan those in the trailing edge. Figure 5(b) showsoscillograms of the gun output current as the cur-rent in the gun focus coil was varied. Transmis-sion of the low energy particles in the trailingedge of the current pulse is improved by loweringZ(cm)FIGURE 4 Beam envelopes for various values of anodevoltage. In these calculations the value of the current isslightly below the limiting current for virtual cathode for-mation.The code calculations indicate that under certaincircumstances current can be accelerated in thegrod-anode region, but not be transported pastthe peak of the axial magnetic field. This occursat low anode voltage when particles do not haveenough energy to traverse the region of Be = 500gauss. This peak value of Bz is set to transportparticles with higher energy, and the low energyparticles are over-focused. The beam collapsesradially and the code results become unreliablebecause particles are removed from the calcu-lation when their axial velocity becomes nega-tive. Figure 4 shows the calculated beam enve-lope for various anode voltages. The maximumBz on axis is 520 gauss, and the beam-current242 A. C. PAUL ET AL.4OL.....------I----oL.-~-------"""""------------o16~..::L.12+-oJ'"cQ.)~~:::::JU 8EroQ.)co420 -........,......--ro-------r---r--oor------,.---,1 2 3Anode voltage, VA (MV)FIG URE 6 Limiting beam current for virtual cathode for-mation vs anode voltage for 4 cathode diameters.IV. VIRTUAL CATHODE FORMATIONthe current in the coil, while transmission of therelatively high energy particles in the leadingedge and central portion of the current pulse isdegraded. The dotted envelope of these oscillo-grams is the current pulse emitted from the cath-ode, and it represents the maximum current thatcould be expected at the gun output. Our usualprocedure is to ~ ~tune" the transport for maxi-mum peak current. This procedure results in theselection of a waveform such as that labeled ··0. "These oscillograms also illustrate two otherphenomena that deserve comment. First, thepulse width of the beam current injected into theaccelerator is determined by the relative timingof the cathode current and anode voltage as wellas by the waveforms of these pulses. In generalthis timing depends on many factors in the op-eration of the system, and as a result the timingadjustment is difficult to optimize. Second, as thefield produced by the first focus coil is adjustedhigher than optimum, the pulse width narrowsfurther and the peak amplitude decreases.The formation of a virtual cathode limits the max-imum current that can be accelerated by the gun.The current drawn from the cathode by the gridenters the grid-anode region and is acceleratedif the anode voltage is sufficiently high. If theanode voltage is not sufficiently high, the resultsof the calculations show that a virtual cathodeforms near the axis a few cm downstream fromthe grid. The code is not capable of calculationsbeyond this point. The calculated limiting currentthat can be accelerated is very nearly a linearfunction of Va' It is shown to be linear in theartist's rendition in Fig. 6 for various diametercathodes, but the actual theoretical curves dropslightly below the lines at higher values of Va, asshown in Fig. 7 for a 10-inch-diameter cathode.All experimental results discussed in this sectionwere obtained with a 10-inch-diameter cathode.For each value of the limiting current shownin Fig. 6 there is a corresponding value of VA-'found from Eq. (1). In Fig. 8 the value of VA-'required to extract the limiting current is plottedvs Va' Values of VA-' above a given curve resultin virtual cathode formation. Calculations indi-cate that the value of VA-' is critical, and a variationof 1 kV in VA-' is sufficient to cross from a region12~.::£+-oJC 8Q.)~~:::::JUQ.)-00..c 4+-oJroUOL-_L-_.J.....-_....I...-_~_.....J-.._--L-_--'"o 0.8 1.6 2.4Anode voltage (MV)FIG URE 7 Limiting beam current for virtual cathode for-mation vs anode voltage for a 10-inch-diameter cathode anddata points indicating eight separate experiments.CHARACTERISTICS OF THE ETA GUN 243~0.."~«10 12FIGURE 9 Peak beam current measured at the cathode andseveral positions in the accelerator for the experiments rep-resented in Fig. 7.Distance from cathode 1m)EOG00'--------'--'1'------'------'-----=-----:':-----:10.----,-----r----,----,------,------,transported to the end of the accelerator is high.These results are shown in Figs. 7 and 9. Figure7 shows values of cathode current vs V" for eightexperiments. Three data points represent cath-ode current above the computationally deter-mined limiting current, and five data points rep-resent cathode current below this limiting current.Figure 9 shows the peak beam current measuredat the cathode and various positions along theentire accelerator for the experimental parame-ters shown in Fig. 7. When the cathode currentlies above the limiting current in Fig. 7, only one-fourth to one-third of the current extracted fromthe cathode reaches the current monitor 6 m fromthe cathode. When the cathode current lies belowthe limiting current in Fig. 7, at least three-fourths of the cathode current reaches the endof the machine.A possible explanation of these results is thatindeed a virtual cathode does form downstreamfrom the grid, but the virtual cathode can act asa source of electrons. No calculations can beperformed with the EBQ code in the regime ofvirtual cathode formation, but it is known thatplasma oscillations occur in a virtual cathode.Particles can be emitted with large random ve-locities so that any beam accelerated from a vir-tual cathode would have poor quality (i.e., theemittance is high) and be impossible to transportefficiently. The virtual cathode forms in a smallregion near the axis, but the time-dependent elec-432O'------'--...J.....-'------'--...J.....-'------'----'o160>..::.t.<..:J> 1200)'OlC1J+-'0> 80l:J...<..:l40200Anode voltage, V A (MV)FIGURE 8 Limiting grid voltage for virtual cathode for-mation vs anode voltage for 4 cathode diameters.of good beam production (below the curve) tovirtual cathode formation (above the curve).It is not surprising that the maximum currentthat can be accelerated does not obey the rela-tivistic Child-Langmuir law for a one-dimen-sional diode in the grid-anode region. 2 The grid-anode spacing is less than the diameter of theanode. The equipotential surfaces are compli-cated and change significantly as the currentchanges, so that the configuration of acceleratingelectric field bears scant resemblance to a planardiode.Experiments with a lO-inch-diameter cathodeshow that there is a definite difference betweenthe beam behavior operating above and that op-erating below the limiting grid voltage. The codecannot be used in the calculations once a virtualcathode is formed. In the experiment, current isindeed accelerated, and some of it is transportedto the end of the gun (about 2.5 m from the cath-ode). However, the transported current de-creases drastically in the full 10m of the ETAaccelerator. When operating below the limitinggrid voltage, the fraction of the cathode current244 A. C. PAUL ET AL.tric field generated in this region extends overthe entire beam cross-section, distorting the tra-jectories of particles outside the region. Thus theemittance of the entire beam is increased to thepoint that only a small fraction of the particlesemitted from the cathode are transported to theend of the accelerator.REFERENCES1. A. C. Paul and V. K. Neil, Computational Studies of BeamDynamics in the ETA Gun, IEEE Trans. Nucl. Sci. NS-26, 4242 (1979).2. J. E. Bohs and D. Kelleher, J. App. Phys. 40, 6 (1969).See also H. R. Jory and A. W. Trivelpiece, J. App. Phys.40 10 (1969).

Characteristics of the ETA gun

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