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-SLAC - PUB - 4221February 1987(A)

DESIGN OF A WIGGLER-FOCUSED, SHEET BEAM X BAND KLYSTRON*K. R. Eppley, W. B. Herrmannsfeldt and R. H. Miller

Stanfoid Linear Accelerator CenterStanlord Universit y, Sianlord, CA 94305

AbstractAn X band klystron using a sheet beam and wiggler focus-

ing was simulated using the 2 + t dimensional particle in cellcode MASK. Simulation of the rf cavities was by means of theport approximation used in modelling of standard klystrons.2The wigglers, which would need permanent magnets to achievethe required field strengths, were modelled using an idealizedanalytic expression with an exponential rise and a linear ta-per superimposed on a sinusoidal variation. Cavity locationsand tunings were varied for maximum output power. Beamvoltage and current were also varied to explore the effect onefficiency. Both an idealized laminar beam and a more realis-tic bea m from a gun design code were studied. For a voltageof 200 kV and current of 20 amp per linear cm efficiencies ofapproximately 50 were calculated.

IntroductionThe rf power for a future collider should be at a substan-

tially higher frequency than the SLAC frequency of 2856 MHz.Among the advantages of the higher frequency are higher gradi-ents before encountering the breakdown limit, and lower storedenergy which greatly impacts both capital cost and operatingcost of a large machine.3 Recent studies at SLAC have tendedtowards the range of frequencies between 3 and 4 times theSLAC frequency of 2856 MHz.

Scaling conventional klystrons to such high frequencieswould reduce the output power to only a few megawatts, sincethe beam current must be reduced to fit through a smallerstructure. This paper describes an alternate klystron design,which is to use a sheet beam or a hollow beam, thus permittinghigh total currents without increasing the current density tothe point that space charge effects impair the efficiency. It wasrecently pointed out that a very similar concept was proposedby R. Kompfner at Oxford in 1947, who called the device thetraveling wave klystron.

The f ocusing of sheet beams or hollow beams was developedby Sturrock. Ordinary solenoids cannot be used for such abeam, but an arrangement of dipole magnets that causes theelectrons to wiggle periodically, in the plane of the beam,provides very strong focusing. The focusing mechanism is thesame as that encountered by an electron beam passing throughthe wiggler magnet for a free electron laser; the beam is focusedtowards the median plane of the wiggler by the edge fields of thealternating dipole magnets. The focusing acti on is only in thedirection normal to the median plane, but appropriate shapingof the fields at the ends of the dipoles can also provide edgefocusing of the sheet beam. This technique is also commonlyapplied to free electron laser wiggler magnets. A schematicarrangement of the components is shown in Fig. 1. As noted,

l Work supported in part by the KEK-SLAC Collaborationand by the Department of Energy, contract DE - AC03 -76SF00515.

the focusing action is quite strong because it does notalternately focus and defocus; each edge field focuses. Theusual constraints of focusing limits and stop bands of periodicfocusing apply, but with reasonable dipole fields of about 0.1tesla, the currents that can be transported greatly exceed whatcan be realistically injected. The focusing requirements will befound to depend mostly on effects of transverse rf fields in theklystron.

The initial goal was to design a 100 MW source of X-bandpower at 11.42 GHz. The nominal starting design parametersfor this device were 200 kV beam voltage and 1000 amperestotal current in 50 linear cm. These numbers are probablynot optimal; however, it would be difficult to use much highervoltages without making the output cavity gap too wide (dueto breakdown considerations) for good coupling. Likewise, itwould be difficult to get much higher current densities f rom aconventional gun.

SHEET BEAM KLYSTRONRF Cavltles

m SmCam Iron

Fig. 1. Schematic of the sheet beam klystron showing drifttube, cavities, and wiggler magnets.

Design StudyStarting from these nominal values, we have used MASK

to design the rf interaction region to obtain maximum poweroutput. The rf cavities are modelled using the port approxi-mation described by S. Yu.~ We impose a given voltage andphase as a boundary condition. The code then calculates theinduced cur rent from the beam dynamics (once steady statehas been reached) whence the desired cavity impedences canbe obtained.

The input beam was first t aken to be purely laminar withzero transverse velocity. Parameter studies were made varyingthe cavity locations and voltages to optimize efficiency. Beamvoltage and current were then varied to explore their effect onefficiency.

The wiggler field was modelled using an idealized analyticexpression derived from a vector potential which was a productof a sinusoid in the x1 direction (parallel to the beam) and ahyperbolic sine in the x2 direction. More freedom was obtainedby adding a product function f(xl) in the x1 direction, which

Presented at the Particle Acceler ator Conference, Washington, D.C., March 16-19, 1987

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could allow a linear ramp and/or an exponential rise. Whilethis is no longer an exact solut ion of Laplaces equation,and thus includes a non-physical current source, it is not abad approximation as long as the function f(xr) varies slowlywith respect to the wiggler period. While these wigglerexpressions will not correspond exactly the fields produced by

the permanent magnet/iron assemblies, they are a reasonablefirst approximation to the magnet design made using the codePOISSON.Initial calculations were made using an input cavit y, oneidler cavity, and an output cavity. Because of the potentialproblem of feedback if the non-cutoff TE modes were excited,it seemed desirable to keep the gain as low as possible. Weassumed that input power of the order of 10 to 20 kW at Xband could be obtained, for example fr om traveling wave tubesif klystrons were not readily available. This corresponds to avoltage of about 5 kV on the input cavity. (The precise valuewill depend on what tuning and external Q are assumed.)

The location and voltage of the second cavity control thegain but do not appear to be very critical in determiningthe maximum rf current downstr eam (which controls theefficiency). The gain of the second cavity det ermines theoptimum drift lengt h to the output stage. The voltage andlocation for the second cavity were picked to produce optimalbunching in a length that seems reasonable for constructionand simulation considerations.

It was found that higher eff iciency could be obtained by theaddition of another cavity, cor responding to the penultimatecavity in a standard tube, although the optimal voltage forthis cavity is low compared to that in a standard klystronfor the same beam voltage. The voltages and locations ofthe penultimate and output cavities were varied to optimizeefficiency.

Figure 2 shows the locations for the cavities of a four-cavity wiggler focused klystron. The figure shows the electrondistribution taken as a snapshot at a particular instant withinan rf cycle. This example is from a run in which both thetop and bottom of the klystron are simulated, thus makingfurther simulations possible in which the effects of asymetricconstruction can be examined.

l-5.6L2t All dimensions in millimeters

Fig. 2. Electron position-space distribution (not to scale) forthe wiggler focused klystron with an initially laminar beam.RF ports are shown as gaps in the blocks. All di mensions arein mm.

The phase of cavity 1 was arbitrarily set to 0. For cavities 2and 3, it was assumed that the Q would be high enough that thephase difference between voltage and induced current wouldbe about r/2. For the output cavity, the phase was varied tooptimize efficiency. The strength and slope of the ramp of themagnetic field were also varied to produce optimum bunchingwith minimal interception before the output cavity, and thusmaximum output power.

Voltages and phases are shown in Table 1 for the optimumefficiency case. The efficiency came to about 48 , or 96 MWfor 200 MW of beam power from a 50 cm wide klystron.Table 1. Cavity Voltages and Currents For the Laminar BeamCavity RF Gap Voltage (Phase) Induced Current (Phase)

1 4750 (-.lO) 6.8 (1.85)2 28840 (2.21) 39.9 (20)3 66210 (-1.40) 716. (-2.93)4 259500 (- .50) 774. (-.04)

Beam Voltage and Current Parameter StudyUsing the laminar input b eam and tapered wiggler f ields,

the voltage and current were varied to explore their effecton efficiency. The cavity voltages, etc. were optimized formaximum efficiency for each point (although not as muchtime was spent as in the initial study, so the true opt imummay be slightly higher). Efficiency was not sensitive to beamcurrent with fixed voltage up to a factor of three times thenominal current (Fig. 3). At this point efficiency began todrop. Efficiency only increased slightly in raising the voltageto 300 kV, but dropped to about 41 percent at 100 kV (withconstant perveance). The required magnetic field was roughlylinear in beam current. There was a small increase in requiredmagnetic field with higher voltage.

4o0 4000 80001-87567Jlil, CURRENT/LI NEAR METER, (amps)

Fig. 3. Efficiency versus current, 200 kV beam energy..

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It is unclear what factors limit the efficiency of the wigglerfocused klystron. For a standard klystron the efficiency wouldbe expected to increase more with lower perveance than wasobserved here. We note that for both cylindrical and flatklystrons the bunching is much better in the part of the beamnearer the walls, but in the cylindrical cae the poorly bunchedbeam near the axis contains only a small fr action of the totalcurrent, while for the flat case it contains nearly half. Thevariation in bunching might be due in part to variable rf fieldsacross the drift t ube. However, reducing the drift tub e bya factor of four in height (with corresponding reduction inbeam current and size) did not improve the efficiency. It ispossible that t he variation in focusing from the transverse rfand dc magnetic fields across the drift tube are responsiblefor the variability of the bunching. It is also possible that ifmore time had been spent on optimization in the low perveancesimulations the efficiency might have been increased further.

Effect of Realistic Input BeamA more realistic input condition was obtained by using the

electrostatic EGUN code to calculate the beam distribution atthe input to the drift tube. The gun calculation assumed nomagnetic field, so MASK used a magnetic field which was ini-tially zero and turned on exponentially. Another modificationwas to increase the field just before the penultimate cavity tocompensate for the transverse momen tum impulse from thatcavity. The voltages and currents are shown in Table 2. Forthis design the x1 locations of the cavities were as in the lam-inar case, but some variation in the xz size of the drift tubewas made. The final efficiency ended up to be similar to thelaminar case, about 50 . These findings are tentative becausethe modelling of the turn-on of the magnetic field at the beaminput was a rather crude approximation of the field that wouldbe produced by the actual magnets.Table 2. Cavity Voltages and Currents for the Realistic BeamCavity RF Gap Voltage (Phase) Induced Current (Phase)

1 4490 (-.lO) 5.2 (1.69)2 28900 (2.51) 47.7 (1.06)3 83640 (-1.12) 759. (-2.69)4 260400 (-.40) 832. (.14)

Radio Frequency Cavity ConsiderationsThe initial concept of the rf cavity design was that the

cavities should operate at cutoff so that the field would not haveany variation is strength along the length of a cavity. We nowbelieve that t olerances, and the close proximity of many modesat cutoff, make this solution impractical. A bettersolutionwas suggested by P. McIntyre6 who would use traveling wavecavities which create a bunch t hat is tilted with respect to thedirection of motion of the electrons. We now believe that asmall shear in the pattern of rf currents on the beam is nota problem, and that traveling wave cavities can be used, even

placed on a line normal to the beam direction, provided thatthe phase velocity of the desired mod e is the same for eachcavity. These traveling wave structures are actually tunedresonant rings, with a directional coupler for the input andthe output cavities. Except for the resonant r ing, the devicenow closely resembles the sketches from Kompfner from 194 7.

The use of traveling waves in the interaction cavities causesan additional complication to the electron dynamics, due to thetransverse magnetic fields that must accompany the travelingwave. These magnetic fields are normal to the plane of thesheet beam and accordingly act to de5ect the electron orbitswithin the plane of the sheet beam. The transverse magneticfield and the longitudinal electric f ield have their maxima inthe same place, and the direction of the magnetic field is suchthat the de5ection on the beam is in the direction oppositeto the power fl ow for particles which are phased to give upenergy to the rf fields. For the parameters of the 100 MWklystron being studied here, and for waveguide with a groupvelocity of us = 0.7c, the magnetic field is about 0.1 tesla in theoutput cavity. This is clearly not negligible and it thus becomesmandatory to study the klystron with a three dimensionalcode in order to adequately simulate the process in the outputtraveling wave cavity. For the particles in the bunch that isbeing decelerated, it is possible t o lzrgely compensate for thisdeflection by adjusting the fields in the wiggler magnets so thatthe electrons enter the output cavity at an appropriate angle.

ConclusionsA wiggler-f ocused sheet beam klystron with efficiencies

of about 50 percent and power ar ound 200 MW per linearmeter appears theoretically attainable. If gun design permitssubstantially higher perveance without increasing the drifttube size, up to a factor of three higher power may be possiblewithout much loss in efficiency.

References1. A. Palevsky and A. T. Drobot, YApplication of E-M

P.I.C. Codes to Microwave Devices, in Proceedings,Ninth Conferenc e on Numerical Simulation of Plasmas,paper PA-2, Northwester n University, Evanston, Illinois,June 30-July 2, 1980.

2. s. Yu, Particle In Cell Simulation of High PowerKlystrons, SLAC/ AP-34, September 1984.

3. P. Wilson, Future e+e- Linear Colliders and Beam-Beam Effects, SLAC-PUB-3985, May 1986, presented atStanford Linear Accelerator Conference, J une 2-6, 1986.

4. J. Lawson, private communication.5. P. Sturrock, Stanford MicrowaveLaborat ory Reports 595

and 596, May 1959.6. P. McIntyre, private communication.

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