We have demonstrated generation and transport of a patterned electron beam from a Diamond Field-Emitter Array (DFEA) cathode in a radio frequency (rf) gun. DFEAs are arrays of micrometer-scale pyramids with nanometer-scale tips. They can be fabricated with base widths ranging from 3 μm to 25 μm and pitches as small as 5 μm. They have an inherent 1:0.7 base to height ratio. DFEAs operate as field-emitter cathodes and potentially produce intrinsically shaped electron beams, which are of interest for a number of accelerator applications. We report on the results of a recent experiment in which a beam, consisting of several beamlets, was produced from a DFEA cathode in an rf gun and transported 2.54 m along a beam line. A macrobunch charge of 60 pC was measured at a cathode field gradient of 15.1 MV/m.

Inherently shaped beams are advantageous for a variety of particle accelerator needs, such as reducing energy spread in the accelerating bunch due to beam loading1,2 and production of ultrashort high current electron bunches.3 One application that most benefits from an intrinsically shaped beam is beam-driven collinear wakefield accelerators.4 In this scheme, a trailing low charge witness bunch is accelerated by a wakefield excited by a higher charge longitudinally shaped drive bunch traveling in the same structure or plasma medium.5,6 A longitudinally shaped electron bunch can be produced directly in a number of ways; however, these methods have limitations due to the restricted response time of various electronic components and space charge effects. A method to produce longitudinally shaped electron bunches from a transversely shaped electron bunch by means of an emittance exchanger (EEX) has been proposed and demonstrated.7–10 Another application of shaped beams is the production of temporally shaped electron bunches at ultrafast time scales for small footprint accelerator based light-sources.11 

A transversely shaped electron beam can be produced directly from a shaped cathode,12 by using a photocathode excited by a transversely shaped laser beam13 or by the most popular method: the use of a transverse mask to intercept a portion of the beam.8–10 The disadvantages of the mask method include a beam loss of up to 80%, production of hazardous x-rays, and inconsistent beam shapes shot-to-shot due to jitter. At the Los Alamos National Laboratory, we have proposed an alternative to intrinsically produce transversely shaped electron bunches from Diamond Field-Emitter Array (DFEA) cathodes.14,15

DFEAs are arrays of diamond pyramids with exquisitely sharp tips as shown in Fig. 1. The pyramid arrays are fabricated using standard silicon wafer processing techniques, so they can be fabricated in arbitrary shapes to produce an inherently shaped beam. DFEAs produce electron beams by field-emission with typical currents as high as 30 μA per pyramid at gradients of around 10 MV/m in the direct-current (dc) regime.16,17 DFEAs emit under dc electric fields, as well as in time-varying electromagnetic fields in rf guns, as reported here. These cathodes can produce an inherently shaped beam with little to no current loss, no production of x-rays due to the use of a mask, no shot-to-shot jitter, and no drive laser required.

FIG. 1.

An SEM image of a 5 × 5 array and close up of a single diamond tip (inset).

FIG. 1.

An SEM image of a 5 × 5 array and close up of a single diamond tip (inset).

Close modal

A field-emission cathode is of particular interest for use in an rf gun because it greatly simplifies the infrastructure needed to produce the beam, operates at lower fields, and is less expensive to implement and operate than photocathodes. In addition, in an rf gun, field-emission cathodes will produce inherently shorter bunches with lower energy spread than thermionic cathodes.18 For applications with relaxed beam quality requirements and stringent power/size requirements, field-emission cathodes such as DFEAs have many advantages.

This paper reports the results of the recent experiment that demonstrated shaped beam production from a DFEA cathode in the 1.3 GHz rf gun at the Argonne Cathode Test-stand (ACT) at the Argonne National Laboratory.19–21 The DFEA reported here is a square array of 25 pyramid emitters arranged in a 5 × 5 pattern with a 25 μm base and a 400 μm pitch. This cathode sample was chosen specifically to allow for imaging of individual emitted beamlets to most easily observe an emission pattern and determine the spacing between beamlets. Electron beams were produced from this cathode at gradients varying between 12 and 22 MV/m. Out of the 25 emitters, approximately 8 emitters were active at any given time. The bunch charge was measured using a Faraday cup, and beam images were observed on several yttrium-aluminium-garnet (YAG) screens along the beamline. The beamlets were transported along the beamline over a distance of more than 2.54 m, long enough for insertion into an accelerator and the EEX.

A schematic of the ACT is shown in Fig. 2. At the front of the test stand is an L-band normal-conducting high gradient single-cell rf gun. The beamline includes the following components: three YAG screens at various distances from the gun exit (YAG1 at 0.43 m, YAG2 at 1.57 m, and YAG3 at 2.54 m), two Faraday cups (FC1 and FC2 coincident with YAG1 and YAG3, respectively), gun solenoids (GSol1, GSol2), and a beamline solenoid (BSol). The vacuum pressure in the system was 5×109 Torr during the experiment. The rf pulse length was 6 μs with a repetition rate of 2 Hz.

FIG. 2.

ACT beamline schematic showing gun solenoids, coincident elements Faraday cup 1 (FC1) and imaging screen (YAG1), beam solenoid (BSol), a second imaging screen (YAG2), coincident elements Faraday cup 2 (FC2), and imaging screen (YAG3).

FIG. 2.

ACT beamline schematic showing gun solenoids, coincident elements Faraday cup 1 (FC1) and imaging screen (YAG1), beam solenoid (BSol), a second imaging screen (YAG2), coincident elements Faraday cup 2 (FC2), and imaging screen (YAG3).

Close modal

During the experiment, the gradient on the cathode was adjusted by changing the rf power coupled into the gun. Simulations of the cavity determine the field at the cathode based on the input rf power. We start with a low cathode gradient and increase the field until there is an image on the first YAG screen. This is not necessarily the threshold for emission, due to the inherent noise of the measurement system. We then determine if the emission level is above the noise threshold on the Faraday cup.

The image of nine beamlets on YAG1 at 14.9 MV/m is shown in Fig. 3. Some of the glow around the beamlets in the image is due to emission from the edge of the cathode disk and some is due to the wide energy spread of the emission current itself. The beam was ballistically transported further by adjusting the beamline solenoid, BSol, to focus the beamlets onto YAG2 and finally onto YAG3. Bsol was optimized at a field of 365 Gauss. Figure 4 shows the beam at 15.1 MV/m as it was transported through the beamline. The use of the solenoid, Bsol, also eliminated extraneous emission from the cathode edge, which was verified by beam images on YAG2 and YAG3. The beam was rotated by the magnetic field of BSol, between YAG1 and YAG2. No focusing elements were used between YAG2 and YAG3. The beamlets' brightness varied significantly for different emitting tips, and thus, the average current per tip is a low estimate of what high performing tips were likely contributing. All tips were determined to be sharp by SEM imaging.

FIG. 3.

An image of 9 beamlets on YAG1 at the cathode gradient of 14.9 MV/m.

FIG. 3.

An image of 9 beamlets on YAG1 at the cathode gradient of 14.9 MV/m.

Close modal
FIG. 4.

Image of 3 beamlets on YAG1 at 15.1 MV/m (a); images of 8 beamlets on YAG2 after Bsol solenoid optimization (b); and the same 8 beamlets transported on to YAG3 (c).

FIG. 4.

Image of 3 beamlets on YAG1 at 15.1 MV/m (a); images of 8 beamlets on YAG2 after Bsol solenoid optimization (b); and the same 8 beamlets transported on to YAG3 (c).

Close modal

Bunch charge was measured using FC1 and FC2, and we report charge collected on FC2 here for its accuracy. The maximum bunch charge measured from this array was 60 pC. This particular rf gun was designed to provide 1–100 nC bunch charge between 30 MV/m and 100 MV/m with a photocathode.21,22 The bunch charge we measured is extremely high for this gun considering the very small emission area of the eight tips. Using the bunch charge measured on FC2 and derived parameters, we estimate average per-tip current, maximum average per-tip current, peak current, and per-tip emission area. Bunch charge, measured consecutively at decreasing cathode gradients on FC2, is plotted in Fig. 5(a). Previous testing has shown that the tips have a breakdown limit above 15 MV/m gradient; 15.1 MV/m was determined to be a gradient at which we could operate for an extended time without incurring cathode damage. Figure 5(b) shows bunch charge vs gradient plotted in Fowler-Nordheim (FN) coordinates.23 We use the linear portion of these data, the black line in Fig. 5(b), to fit β, the field enhancement factor at the tips, and Ae, the effective emission area. Assuming β is constant, it can be determined from24 

β=2.84×109ϕ1.5s450.
(1)

Here, ϕ is the work function measured using a Kelvin probe to be 4.9 eV, and s is the slope of the fitted line. This very high field enhancement factor corresponds to exceptionally sharp emitter tips. Likewise, we determine the effective emission area Ae using24 

Ae=10y0ϕ1.755.7×1012×104.52ϕ0.5β5490nm2,
(2)

where y0 is the y-intercept of the fitted line.

FIG. 5.

Bunch charge measured on FC2 at different cathode gradients (a); the same data from (a) plotted in FN coordinates (b).

FIG. 5.

Bunch charge measured on FC2 at different cathode gradients (a); the same data from (a) plotted in FN coordinates (b).

Close modal

We estimate the average per-tip current using our bunch charge measurements of 60 pC at a field of 15.1 MV/m and the number of observed emitting tips, 8. We find the average per-tip charge per macropulse to be 7.5 pC. Dividing this charge by the flat-top macropulse duration of 6μs, we compute the average current emitted per macropulse to be approximately 1.25 μA per tip. This is a significantly low estimate because the tips only emit and current only transports out of the gun for a small fraction of the macropulse. We also estimate the maximum average per-tip current by using the enhanced field-emission model,23 which allows us to approximate the maximum current in the derived emission envelope. Equation (10) from Ref. 23 gives us the field-emission current, IF, in Amps, resulting from our effective emitting area,

IF(t)=1.54×106×104.52ϕ0.5Aeβ2Ec(t)2ϕ×exp(6.53×109ϕ1.5βEc(t)),
(3)

where E(t) is the experimentally fitted local electric field at the pyramid tips. This field has a maximum of 6.8 GV/m.

Figure 6 illustrates the time structure of the field-emission current. The blue curve is the normalized amplitude of the rf field at the cathode measured inside the gun cavity using an rf pickup. The red curve is the normalized FN emission envelope plotted using Eq. (3), with the area under the curve corresponding to the total charge measured on the Faraday Cup. The black lines represent the bursts of emission current induced by rf micropulses. Using the maximum E(t) in Eq. (3), we determine the maximum average emission current to be 2.9 μA per emitter. This value corresponds to the peak value of the red curve in Fig. 6. This estimated per tip current gives us a baseline measurement for understanding the single tip emission to inform dense array experiments that are complicated by emission suppression due to the electric field on nearby tips.

FIG. 6.

The blue (solid) curve is the measured rf power in the gun during one 6 μs macropulse, and the red (dashed) curve is the derived FN emission envelope based on the fitted emission properties and Fig. 5(b). The black lines represent short bursts of emission current from each 769.2 ps micropulse.

FIG. 6.

The blue (solid) curve is the measured rf power in the gun during one 6 μs macropulse, and the red (dashed) curve is the derived FN emission envelope based on the fitted emission properties and Fig. 5(b). The black lines represent short bursts of emission current from each 769.2 ps micropulse.

Close modal

We further estimate the peak micropulse current by multiplying the maximum average current found above by the duration of the rf period to determine the charge in the single peak micropulse: 2.9μA×769.2ps=2.23fC. We then use Eq. (3), this time using the sinusoidal rf micropulse for E(t), and plot the normalized current in Fig. 7. The micropulse charge is the integral of the current over the time duration, allowing us to determine the peak micropulse current to be 29.4 μA, similar to the analysis in Refs. 25 and 26.

FIG. 7.

The temporal shape of the micropulse current from Eq. (3) for the micropulse occurring at the peak of the red emission curve in Fig. 6.

FIG. 7.

The temporal shape of the micropulse current from Eq. (3) for the micropulse occurring at the peak of the red emission curve in Fig. 6.

Close modal

Finally, we estimate the emission area of each emitting pyramid. First, we take the effective emission area of the array, 5490nm2, and divide it by the eight emitting tips observed in a corresponding YAG image. Taking the square root of this number, we find that each tip was emitting from an area of approximately 26nm2. This dimension corresponds to the very sharp tip of the pyramid, indicating that only very tips of the pyramids are emitting, a long-standing hypothesis.

In conclusion, we have demonstrated patterned beam production in an rf gun and transport of the beam over 2.54 m while maintaining the initial pattern of the array. The beam was produced by a DFEA cathode with 25 pyramids in a 1.3 GHz rf gun. Initial experiments show very promising results for the DFEA cathodes: we demonstrated high per-tip current and the ability to maintain the shape (or pattern) of the initial beam during transport. These results show strong potential for DFEAs in other patterns to produce intrinsically shaped beams. Further experimentation on different array geometries is in progress.

The authors gratefully acknowledge the support of the Los Alamos National Laboratory (LANL), Laboratory Directed Research and Development (LDRD) program. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by the Los Alamos National Laboratory (Contract No. DE-AC52-06NA25396) and Sandia National Laboratories (Contract No. DE-NA-0003525). The work at AWA was funded through the U.S. Department of Energy Office of Science under Contract No. DE-AC02-06CH11357. The use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

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