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    Design of a High Duty Cycle, Asymmetric EmittanceRF Photocathode Injector for Linear Collider ApplicationsJ. B. Rosenzweig, Eric ColbyUCLA Department of Physics

    405 Hilgard Ave, Los Angeles, CA 90024G. Jackson and T. NicolFermi National Accelerator LaboratoryP.O. Box 500. Batavia , IL 60510Abstract

    One of the attractive features of thesuperconducting approach to linear collider designis that the transverse emittances demanded aremuch larger than in normal conducting schemes.For TESLA design parameters, the damping ringsappear to be relatively large and expensive, and it istherefore of some interest to look into alternativesources. For electrons, a promising source candidateis an rf photocathode. In this paper, we presentconceptual design work towards development of anasymmetric emittance rf photocathode source whichcan operate at the TESLA repetition rates and dutycycle, and is capable of emitting beams with therequired emittances and charge per pulse.

    1. INTRODUCTIONIn linear colliders, the transverse emittances

    are generally asymmetric, for a variety of reasons.The most compelling have to do with amelioratingthe effects o f the beam-beam interaction bYcolliding flat beams (a,>> Oy). This allows thebeamstrahlung energy loss and spurious paircreation to be minimized, while at the same timeloosening the constraints on the final focus systemand allowing the beams to collide at a small angle,easing the task of disposing the beatn exhaust. Inaddition, the standard way of obtaining lowemittance e* beams is through the use of dampingrings, which naturally give horizontal emittanceswhich are much larger than vertical (E, >> Ed).For the TESLA design parameters, however,the higher average current allows for relaxation ofthe beam sizes at the final focus. This in turnimplies that the emittances can be substantial largerin an SRF linear collider. In fact the TESLAparameter sets usually specify horizontal andvertical normalized emittances of 25-50 and 1 mm-mrad, respectively. These numbers are nearly twoorders of magnitude larger than the correspondingnormal conducting linear collider designs specify.These numbers are, in fact, near the present state of

    the art in rf photo-cathode technology. This state ofaffairs naturally has prompted the suggestion thatthe electron beam in an SRF collider might becreated by an rf photocathode source, doing awaywith the electron damping ring.II. ASYMMETRIC EMITTANCE RFPHOTOCATHODE GUNS

    There is considerable experience in prod-using symmetric high brightness photocathodesources, whose charge per bunch and product oftransverse emittances E,E, are near that demandedby TESLA designs. Unfortunately, it is not possibleto produce an asymmetric emittance beam from asymmetric beam which has a smaller emittance inone plane than the original symmetric emittance(see discussion in the Appendix). Thus one muststart with an asymmetric beam, o, >> o,,.

    The scaling of the emittances with beam andrf parameters rf photocathode sources has beenexamined in previous work.[ I] The emittances arisefrom three sources: the effective temperature of thephotoelectrons (which is usually ignorable), thetime-dependence of the transverse rf fields, andspace charge.The rf contribution to the rms emittances is,following Kim[2]Erf = &Wkp$*Ywhere W = eE, / m,?, and E, and k, are the rfelectric field amplitude and wave-number,respectively. This scaling pushes one to longer rfwavelength and impacts the large dimension (x inour case) emittance much more severely than thesmall dimension.The space charge contribution has beenestimated from simulations and model calculationsto be, with laser injection phase (pO,

    1xc 2 NArer(xy)= 7o,*,Wsin(cp,)It is also interesting to note that the productof the emittances takes the form

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    QJc 5 [ w-, 1exp(-3.JwoY )7w 0x0, *The exponential term is on the order of unity, andso, at first glance, it would seem that one can makethe emittances arbitrarily small by raising aXoY,but this option is suppressed by the scaling of the rfcomponent to the emittance. In addition, theminimizing of E, is ultimately constrained by thelongitudinal space charge limit on minimum beamspot size[l], which is

    oxoy 2 2%~,W sin(cp,) *This limit has been verified ex&rimentally[3]. Useof a beam at this limit allows us to rewrite the emit-tance product as

    [ 1J,yFE; 5 0.04 - w ozaThis points out the need to maximize the beamlength, which can be exploited if one can circum-vent the scaling of E;,,,). This point will bereturned to below.

    III. DESIGN: BEAM DYNAMICSIt is clear that we would like to design asource at as low a frequency as possible since weare pushed towards large 0:. We also need,however, large accelerating gradients (large W),which implies higher frequencies. A good optimumappears to be at 1300 MHz, which is convenientlythe TESLA rf frequency. We have examined thebehavior of an asymmetric beam in a 1.5 cell 1300MHz standing wave n-mode gun, with parametersas listed in Table 1, by inputting an asymmetricbeam profile into a form of PARMELA which usesa point-by-point space charge calculation algorithm.

    Beam sizes (a,, cry, a,) %0.25, 2 mmBeam population N, 5 x 1oOAccelerating field E, 90 MV/mFinal energy Eb 8 MeVFinal emittances E,,E, 95,4.5 mm-mrad

    Table 1. parameters or PARMELA design calculation of,?symmetric mittnnce rf photocathodesource.For the input beam charge and dimensions

    given, our final scaling law gives &r&T 2 400(mm - mrad)2 which is in fact very close to what isobtained by the simulation. We have fallen short of

    the TESLA design goals ( E,E, I50 (mm - mrad))by a factor of 2 to 4 in both transverse dimensions.This is not as discouraging as it may seem, sinceboth the rf and space charge contributions to theemittance can be mitigated. Dynamical correctionof the space-charge derived emittance is practicedat LANL and preliminary calculations[4] indicatethat it may allow TESLA design emittances to beobtained in a 1300 MHz photoinjector. In addition,we are presently examining the effects of using anasymmetric cavity, using the 3-D electromagneticcode ARGUS, to minimize E! .

    F 1s2.

    bx 0.5

    0 0 5 10 15 20 25 30z W-0Figure 1: Evolution of the rms beam envelopes n 1.5 cell gun.The beam dynamics in the gun are domin-

    ated by the alternating gradient rf focusings, as isshown in Figure 2. Beam transport after the gunmust also be optimized to produce no emittancedegradation. One common focusing element whichis not allowed is the solenoid. Even if one achievesa linear nx rotation to uncouple the beam, chromaticfocusing (and rotation) effects, as well as space-charge effects (even at 8 MeV, the transverse+ .electric field will produce an E x B rotationdependent on position in the beam), will destroy thesmaller emittance E,.

    IV. DESIGN: DUTY CYCLE EFFECTSThe TESLA duty cycle presents some diffi-cult challenges to rf photocathode source design.The most obvious is in rf power, both average andpeak. The shunt impedance of our gun design is

    ZT = 27 MQ / m, and thus the peak power is 15MW. This peak power must be applied for about 1msec, with a one percent duty cycle. During eachpulse 800 bunches are extracted at a one MHz rate.3022

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    This is problematic in terms of bothobtaining and dissipating the rf power. A thermaland structural analysis was performed, in which theaverage power (150 kW) was not found to bedifficult to handle. This is not surprising, as theGrumman/BNL gun[6] has a similar average power,with a smaller mass. The peak power and the longrf pulse, may be more serious an issue. Fig. 2 showsthe maximum temperature in the structure for thetransient case, and we see that the peak temperaturerise per pulse is only 15 degrees. The structuralanalysis is not complete, however, and so the issueof the effect of the heating on rf performance is notresolved. Also of impact on this design is the lackof a commercial klystron with the required specific-ations; the closest models in performance arepresently the Thomson TH 2115 and TD2104U.

    380

    360

    340s-~ 320

    300

    280

    I 111,111 111,111 1.1 .0 0 . y> :

    0 i.b\9. j 0 .\:\ ?0., I 4ox : -6 .A&;, 0. 0 I 6

    cc

    III II. .I. I.. mm.0 0.2 0.4 0.6 0.8 1t (set)Figure 2. Transient profile of m,aximum temperature n rfphotocathodegun structure.

    The other major problem associated theTESLA time structure is that of obtaining a uniform(in laser energy) 800 pulse train at a 1 MHz rateduring the rf pulse. This subject is still under study.Appendix: Impossibility of reducing the minimumemittunce in a transverse phuse plune

    The normalized rms emittances areconstrained to evolve in certain ways. In particularthe invariance of the determinant of the beam (Tmatrix under linear transport gives the condition

    EXE, = constant = E,2.where the rms emittances are defined byES (x2)(x~2) (xxy

    EY (y2)(yt2) - (YY).There are also many invariants associatedwith higher moments of the Vlasov equation, asdiscussed by Rangajaran, et a1.[7] Of particular

    interest is a second order moment, whichconsidering only transverse phase space isE; = Et + Ey+ 2(xy)(x y) - 2(Xy)(X y).This invariant moment is a constant of themotion even if the x and y phase space planesbecome coupled. Note that if one introduces aninfinitesimal coupling to a previously uncoupledsystem, it must be by applying a skew quadrupolekick, which only changes the last term in the aboveequation. In that case, it is easy to show that a kickof this form causes this additional term to be

    positive, (xy)(x y) > 0. Thus the rms emittancesmust grow if one couples the phase space planes, inorder to preserve the invariance of E, .Because of this, if one begins withuncoupled phase space planes, one must alwayscompletely uncouple the phase space planes inorder to obtain a minimum sum of squares of theemittances. Now we have a second constraint on theemittances, derived from the second order invariant,

    Ez = constant = EZ + Et.If we now apply both constraints on theemittances, we can derive a condition for the final

    state emittances in terms of the initial emittances E,and E,, as follows. We have

    E; = E,20 e;, and Et = E,&,,.Solving this system for the final emittances, wehaveE5.y E;* &,4-4c4y-T = ES, or &to.

    The final emittances, under this uncoupledcondition, can take on only the value of either ofthe initial emittances. Leaving the emittancesunchanged is obtained by any total transformationwhich contains a rotation of nx, and exchange ofthe two emittances by any transformationcontaining a rotation of (n + +)7C n integer).

    REFERENCES1. J. Rosenzweig and S. Smolin, to be published inProceedings of the Port Jeflcrson Advanced Accel-erator Concepts Workshop (AIP, 1993).2. K.J. Kim, Nucf. Instr. Meth. A 275,201 (1989).3. P. Davis, et al., these proceedings.4. R.Sheffield, private communication.5. S. Hartman and J. Rosenzweig, Phys. Rev. E 47,2031 (1993)..6. I. Lehrman, et al., 1992 Linear Accel. Conf.,Proc., 280 (AECL-10728, Chalk River 1992).7. G. Rangarajan, et al., Proc. of 1989 IEEE Part.Accef. Collf., 1280 (IEEE, 1989).

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