OPTIMIZATION OF DC PHOTOGUN ELECTRODE GEOMETRY ∗

Abstract

DC photoguns that employ electrostatic focusing to ob-tain lower beam emittance must inherently trade off be-tween focusing strength and the field at the photocathode,and are traditionally pushed to the limits of breakdownvoltage. In this paper, we numerically investigate a highlyparametrized electrostatic geometry exploring the trade-offbetween the voltage breakdown condition and electrostaticfocusing. We then compare the results to DC gun designswhere the focusing is introduced via embedded solenoidalfields. Finally, we present investigations for a multi-anodegun design that seeks to simultaneously achieve both highelectric field at the photocathode and high gun voltagewithout violating the empirical voltage breakdown condi-tion. In the most feasible cases, the electrode geometryis optimized via genetic algorithms. Designs on the op-timal front are compared with the current performance ofthe Cornell ERL prototype DC photogun.

INTRODUCTION

The design and use of DC photoemission guns for use inhigh brightness beam production has already had consider-able success in several laboratories. For such photoinjec-tors to approach the theoretical maximum brightness lim-its, the main gun design parameters– accelerating voltage,transverse focusing fields, and electric field strength at thesurface of the photocathode–must be optimized beyond thecurrent state of the art. Fundamental trade-offs exist be-tween all three quantities in the conventional one-gap de-sign, which includes a Pierce-type electrode and solenoidoptics just downstream. The goal of this work is to nu-merically analyze various gun geometries to determine theinterplay and importance of each of these design parame-ters.

The electric field at the surface of the cathode is a di-rect figure of merit for beam brightness. A larger axialfield at the photocathode surface provides more surfacecharge for extraction, which causes the theoretical max-imum brightness of the gun, set by the initial momentaof the photoemitted electrons (thermal emittance), to scalewith the Ecath, the cathode field [1]. However, the elec-tric field at the surface of the cathode must directly tradeoff with the electrostatic focusing fields, associated withthe angle of the Pierce electrode. Electrostatic gun focus-ing serves at least two roles in providing high brightness,in that it both combats the strong effect of space chargeinside the gun, and offsets the defocusing effects of the an-

∗This work supported by the NSF under Grant No. DMR-0807731† jmm586@cornell.edu

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Figure 1: Gun geometry parameters for optimization. Eachline represents a parameter varied by the optimizer. Thegeometry shown is that on the optimal front which has si-multaneously minimum focal length and maximum field onthe non-active region of the cathode electrode.

ode electrode. The trade-off between focusing fields andcathode axial field can be seen directly in the off-axis ex-pansion of the transverse field component. If z denotesthe beam direction, then the radial component can be writ-ten: Er(z) = −r∂zE(0, z)/2 + O(r3), where the leadingterm suggests that for strong focusing near the photocath-ode (negative Er ), one requires a steep decrease in theaxial field.

To simultaneously achieve both high field at the photo-cathode and strong focusing, one must increase the voltageor decrease the cathode-anode gap. For photoguns in oper-ation today, the achievable voltage is limited by the onsetof field emission which can lead to punctures in the ce-ramic HV insulator. However, this is a technological issuewhich may be alleviated by new ceramic designs, such asthe use of a segmented ceramic, in which guard rings areattached between segments. Such a design is planned foruse in the new DC gun under construction at Cornell. Ifceramic puncture is mitigated, DC photoguns are funda-mentally limited by field emission from the cathode elec-trode itself. Though the scaling of field emission currentwith voltage is well described by the Fowler-Nordheim re-

J. M. Maxson† , I. V. Bazarov, K. W. Smolenski, B. DunhamCLASSE, Cornell University, Ithaca NY 14853, U.S.A.

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lations [2], the stochastic nature of inclusion/impurity den-sity and their location makes absolute breakdown voltagesdifficult to predict for a given material. As we seek to usea realistic constraint on our simulated gun geometries, weuse empirical data compiled by Slade [2] of vacuum break-downs as a function of cathode-anode gap for large areaelectrodes. Data suggest that the highest electric fields canbe obtained for smaller gaps (< 1 cm) and modest voltages(∼100kV), however there are notable benefits to a higherenergy electron beam. Higher energy affords more rela-tivistic suppression of the space charge emittance growth,which can provide a smaller transverse beam size. Smallbeamsize reduces the effect of aberrations in the optics,particularly the defocusing due to the anode electrode, aswell as geometric aberrations in the solenoids.

FIELD AND EMITTANCEOPTIMIZATION

The current photogun in operation in the Cornell ERLinjector prototype features a Pierce-type electrode paircontaining essentially three geometrical parameters: thecathode-anode gap (d=50 mm), the cathode focusing angle(α = 25◦), and the radius of the arc which terminates theelectrode. We seek first to understand the effect of a higherdegree of geometry parameterization on the trade-offs be-tween: 1) the reduction in maximum electric field on thecathode electrode (which would contribute to field emis-sion), 2) the increase in the photocathode field, and 3) thedecrease in focal length. Here, we define the focal lengthof the gun as a the axial distance from the photocathodethat an electron emitted slightly off axis ( r ∼1 mm) takesto cross the z axis.

An optimizer was developed that first parameterizes theelectrode geometry as shown in Fig. 1. The geometry pa-rameters that are varied are the cathode-anode gap, the an-gle and length of the cathode cone, as well as the intro-duction of an arbitrary number of terminating arc radii, en-forced to be tangential, with a fixed voltage of 500kV. Theoptimizer first generates an input file for the field solverPOISSON [4], then extracts the field map and figures ofmerit, including the focal length (calculated via particletracking), the cathode field, as well as the maximum fieldat the surface of the cathode. The geometry was allowedto vary from α ≈ 0 to greater than 40◦, and the gap al-lowed to vary between 30-70 mm. The optimizer itself wasgenetic in nature, which is beneficial for such multivariateoptimizations, in that the optimizer regularly “mutates” so-lutions to sample regions sufficiently beyond local (false)minima.

Multiple runs were performed with different constraintsand objectives. In the first of these runs, the objectives wereminimum focal length and minimization of the largest fieldon the non-photoemitting portion of the cathode. The cur-rent Cornell gun has a maximum field of 13 MV/m, and aphotocathode field of 5 MV/m. The solution with maxiu-mum field closest to 13 MV/m is presented in Fig. 1. This

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Figure 2: Full-beamline emittance optimization for variedbunch charges.

solution also has a photocathode field of 5 MV/m, but anincrease in focusing of approximately 5%, with α = 26.5◦.This was achieved via the flattening of the arc closest to theanode, but in other respects highly resembles the existingCornell geometry.

A second optimization was performed to maximize thefield on the cathode, while simultaneously minimizing thefocal length. The optimal solutions reveal a strong de-crease in focusing for field strengths beyond 6MV/m, withthe optimizer pushing for flatter cathodes with decreasinggap. Specifically, an increase of the photocathode fieldto 7 MV/m requires an increase in focal length by a fac-tor of 10, which is essentially the zero focusing regime.Thus, both optimization runs demonstrate insensitivity ofthe trade offs to higher degrees of parameterization. There-fore, further optimization must center on the relative im-portance of voltage, gap, and focusing on final emittance,with smaller number of gun geometry parameters.

Next, an optimization was performed with a simplifiedgun geometry (only angle, gap and voltage varied) on anASTRA [5] simulation of the Cornell ERL injector. Eachof the downstream beam parameters, (optics, cavity phasesand fields) as well as the laser pulse and bunch charge wereoptimized. The optimizer structure, function, and all pa-rameters can be found in Ref. [3]. The results of finalemittance vs. bunch charge are plotted in Fig. 2. Thesewere for an initial electron distribution with a mean trans-verse energy of 120 meV, which is the value that has beenmeasured previously [6] in photoemission from GaAs pho-tocathodes with λ = 520 nm light. It must be noted thatthe optimal emittances are dominated by thermal emittance(70-85%), suggesting that the optics may be chosen to can-cel both space charge emittance growth and optics aberra-tion effects. Thus, the optimizer pushed for higher gradi-ents (∼ 6 MV/m) and correspondingly smaller angles (9-11◦), with a nearly constant gap and voltage of d=55mmand V=470 kV. Furthermore, it is also clear that this resid-ual focusing remains due to a constraint on a laser pulselength of Δt < 10 ps, which introduces extra space charge

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2 Sources and Medium Energy Accelerators

Anode Coil:50mmx50mmMax B: 420 G

Beam

Cathode Coil:Max B: 50 G

External Coil:15cmx15cmMax B: 420 G

Figure 3: CAD drawing of gun assembly, showing anodecoil, and two bucking coil options: embedded solenoid(within cathode) and external solenoid (both shown inblue).

repulsion near the cathode as compared to that of a longerbunch.

A separate method to alleviate the tradeoff between elec-trostatic focusing and photocathode field would be to intro-duce magnetostatic focusing via solenoid coils within thegun assembly. A possible configuration would be to placea solenoid coil within the anode assembly itself. Such is theconfiguration shown in Fig. 3. However, for the low emit-tance limits of high brightness machines such as the Cor-nell ERL injector, the presence of nonzero magnetic fieldat the surface causes an increase in the emission emittancedue to the presence of the vector potential in the Hamilto-nian. To mitigate this growth, a bucking coil of oppositepolarity is placed behind the cathode to cancel the field atthe photocathode surface. This could be most completelyaccomplished via the inclusion of an embedded solenoidcoil within the cathode electrode itself.

However, floating a solenoid coil at high voltage intro-duces a number of additional complexities. There mustbe an isolated means of generating the solenoid power,perhaps by inclusion of an external motor surrounded byinsulating material, or by the alteration of the existingHV power supply. Furthermore, perhaps up to 50W (forthe layout shown) of additional power must be dissipatedwithin the cathode structure. Another option would be toplace a bucking coil outside of the gun chamber (shownin blue), where the increased distance to the photocathoderequires that the solenoid bore increase significantly. Thishowever causes greater cancellation of the anode coil fieldbeyond just the photocathode surface, and reduces overallfocusing (∼ 10%).

We must also note that the addition of solenoid focus-ing in actual application can cause emittance growth viasolenoid abberations, due to terms cubic in the magneticfield, analogous to the second term in Eq. 1. We calculatein Ref. [3] that for a rigid, collimated beam, the normal-ized emittance growth due to aberrations scales with thebeam size as εnx ∝ σ4

x, as well as with the derivative of

the magnetic field as: εnx ∝ ∫(∂zBz)

2 dz, which are bothproblematic for anode solenoid fields, considering the shortextent of the coil package, and the large beam size at theanode.

THE DUAL GAP GUN

It is possible to envision a photogun which features twoanodes–one at intermediate voltage (∼100kV) and smallgap (<10mm), for the purpose of creating strong field atthe photocathode, and a ground anode much farther away toprovide maximal energy gain (500kV or greater). Success-ful implementation could yield a solution to the breakdowntrade-off between cathode field and voltage present in one-gap designs, but initial investigations into possible geome-tries has presented difficulty in supplying adequate focus-ing. With the close proximity of the first anode, the effectof the ∂zEz focusing term is suppressed for the Pierce elec-trode form, and the effect of anode defocusing is increased.A possible solution to increase focusing may be to roundthe photocathode itself, as is done in high power thermionicguns, combined with the Pierce cone. Modest radii of cur-vature (greater than twice the photocathode radius) of thephotocathode can provide focal lengths commensurate witha corresponding flat photocathode with α = 25◦. This cur-vature naturally also experiences trade-off between pho-tocathode field and focusing, but considering the proxim-ity of the first anode, significant field enhancements at thecathode compared to the one-gap case may be achieved.

CONCLUSIONS

In this report, we have first demonstrated the insensi-tivity of the one-gap Pierce electrode geometry trade-offbetween focusing fields and fields at the photocathode tohigh degrees of geometry parameterization. Next, using asimplified model of the electrodes and a full beamline opti-mization, we determine the (emittance) optimal parametersto be α = 10◦, V=470kV, and d=55mm. Next generationadditions to photogun designs, such as embedded solenoidfocusing and the use of an intermediate anode are arguedto be viable partial solutions to many one-gap trade-offs.

REFERENCES

[1] I.V. Bazarov, et al. PRL 102 (2009) 104801.

[2] Slade, P. G. The vacuum interrupter: theory, design, and ap-plication. CRC Press (2008).

[3] I.V. Bazarov, ”Comparison of DC and SRF PhotoemissionGuns For High Brightness High Average Current Beam Pro-duction”, submitted March 2011.

[4] J. Billen and L. Young, Los Alamos Laboratory TechnicalReport No. LA-UR-96-1834, 2000.

[5] K. Floettmann, ASTRA.

[6] I. Bazarov et al., J. Appl. Phys., 103 (2008) 054901.

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