Emittance Measurements of a Nanopatterned Cathode on the DC beam line

Enrique MendezUniversity of Hawaii at Manoa

(Dated: August 28, 2015)

In the generation of photoemitted electron bunches for the use in accelerators, metals are limitedby their low QE. Previous work [P. Musumeci et al., Phys. Rev. Lett. 110(2013)] has shown thatcharge yield from infrared light is increased by a factor of 120 by etching nanopatterns into thecathode. However, utility of the electron bunch is also based on its thermal emittance, or angularspread, which is conserved during transit along the beam line. In that same work, a measure of(1.4 ± 0.1) mrad was found in the emittance for a copper nanopatterned cathode held in an electricfield strength of 75 MV m−1. It is proposed that the presence of the nanopattern will alter theelectric field and likely the emittance. Measurements were taken for the same cathode in an electricfield strength of (1.6 ± 0.2) mrad. Hence no apparent effect of the electric field strength on theemittance was found.

I. INTRODUCTION

The beam brightness is a fundamental quantity deter-mined by charge and emittance. High brightness meanshigh charge and low emittance. Both semiconductorand metal photocathodes are used in the pursuit of highbrightness beams. However, whereas as semiconductorscan be tailored to have high quantum efficiency (QE),they are easily destroyed by exposure to air. Metals aremore robust and durable but have QE several orders ofmagnitude lower. Nonlinear optical processes cause thecurrent density that is emitted to be proportional to In

where I is the intensity of the incident light. It is alsoproportional to (1 − R)n, where R is the reflectivity ofthe material to the incident light[1]. Since metals arehighly reflective in the infrared (IR), which is the wave-length that is used in the UCLA’s particle beam physicslaboratory, the effect is not as efficient as it could be.Investigations were made into etching nanopatterns intothe cathode to decrease reflectivity and increase chargeyield. Previous work has shown a factor of 120 increase incharge yield[2], as well given thermal emittance measure-ments on this cathode of values (1.4± 0.1) mrad. Whatis speculated however is that the emittance is a mono-tonically increasing function of the electric field applied,and that the emittance will decrease as the electric fielddecreases.

Our goal was to set up emittance measurements on theDC beam line at UCLA which runs at a field strength5 MV m−1 and a total voltage of 30 kV . A schematic ofthe setup is given in Fig. 1. A VI1 was adapted to takea series of photos at varying currents for a solenoid scan.A MATLAB script was written to analyze these photos,extract dimensions of the beam and calculate emittancemeasurements.

1 Virtual Instrument, a program written in LabVIEW.

II. THEORY

A. Fitting Emittance

In all accelerators, the dynamics can often be describedby linear transformations. For a constant magnetic fieldaligned along the axis of the beam line, a particle withtransverse position x and angle x′ relative to the beamline axis transforms to[3](

xfx′f

)=

(cos(kz) 1

k sin(kz)−k sin(kz) cos(kz)

)(xx′

)(1)

where k = qBz2γmev

where q, me are the charge and mass of

the electron, v is the velocity of the entire beam bunch,γ = 1√

1−(v/c)2, and z is the length of the magnetic field

traversed. We denote this matrix M(k, z).Since the magnetic field is approximately constant

in small regions along the beam beam line, we canwrite the transformation matrix T for the beam line as

41.6 cm

10.4 cm

MCP

DRZ

12.5cm

56 cm

Solenoid 1Solenoid 2

87 cm

102 cm

Cath

od

e

FIG. 1. A (not to scale) schematic of the DC beam line.The upward pointing arrows represent the dipole steering (orkicker) magnets. The DRZ is a scintillating screen mounted ata 45 degree angle relative to the beam line axis and camera.The MCP (microchannel plate) is parallel to the cathode.Data in this paper was measured at the DRZ.

2

M(kn, dz)M(kn−1, dz)...M(k1, dz) where each ki is thecalculated k for the given field strength at its correspond-ing position in the beam line. This method accounts forsections of zero magnetic fields as well, as in the limit ofno magnetic fields, the matrix reduces to the standarddrift matrix

M(0, z) =

(1 z0 1

). (2)

Since we can describe the dynamics of one particle in thebeam, we can describe the dynamics of non-interactingensemble. If the matrix transformation of the beam lineis written as

T =

(B CB′ C ′

)(3)

then we can write the observed spot sizes as linear com-binations of products of B and C and the initial beamparameters[4]. If we fit the beam parameters to the datathen we will be able to calculate the geometric emittanceεg which is related to the normalized rms emittance byε = γβεg[3] where β = v/c. To ensure that the emittancemeasured isn’t due to space charge (the self repulsion ofthe beam), measurements are taken at low charges asdetermined by simulations.

B. General Particle Tracer (GPT) Model

The DC beam line (for which a schematic may be found

in Fig. 1) is implemented using a 1D ~E-field for thecathode2, a normalized 1D field map of Bz for the firstsolenoid, and the bzsolenoid function with parameterspassed to it that best fit the 1D field map of Bz for thesecond solenoid.

If we set the pulse length to 50 fs, the radius to 100 µm,the initial excess energy3 of the beam as 0.4 eV, with theinitial distribution set using the following code:

setrxydist("beam","u", radius/2, radius);setphidist("beam", "u", 0, 2*pi);setGBzdist( "beam", "u", GB, 0);setGBthetadist( "beam", "u", pi/4, pi/2);setGBphidist("beam","u",0,2*pi);settdist("beam","g",0,pulse,3,3);

with GB (γβ) defined using the excess energy given, wefind the solenoid scan given in Fig. 2.

To test the emittance fitting implementation, it is usedto fit a simulated data set. Results are plotted in Fig 2.

2 As a check that the E-field is correct, we can integrate to find avalue of −30.03 kV. The model reaches a value of −30.00 kV at9.32 mm and −30.02 kV at 10.7 mm.

3 Excess energy is defined to be the thermal energy, kT , of theelectron bunch.

40

60

80

1.5 1.6 1.7 1.8

Vari

ance

(10−9

m2)

Current (A)

Simulated Solenoid Scan

DataFit

FIG. 2. Space-charge free simulated solenoid scan done inGPT with 50 fs pulse length, 100 µm spot size radius, andan initial excess energy of 0.4 eV. An emittance is fitted onequally weighted data and found to be (36 ± 4) nm, comparedto the simulated (36.3 ± 0.2) nm. Note that the fit is accuratewhen the maximum values of the variances are approximatelytwice that of the variance at the waist.

Calculations were also performed to check whetherthe fitting algorithm would find that emittance was con-served along the beam line. It was found to be constantfrom the beginning and up to 35 cm into the beam line.

III. PROCEDURE

The current in solenoid one is fixed. Steering magnetand solenoid two currents are adjusted until the beamwaist appears on the screen. The current in solenoid twois then varied across a range of currents that cause thebeam to go through the beam waist. Multiple images aretaken at each value of the second solenoid current. Thebeam is then deflected off the screen and backgroundimages are taken for removing noise.

An average background image is calculated. Eachbeam image has the background subtracted to be usedfor analysis. Image masks are automatically generatedusing the method outlined below. The resultant croppedimages are then rotated by the calculated Larmor angle,projected along each of two perpendicular axes and fitusing Gaussians (defined by Eq. (8)) from which stan-dard deviations are taken. The set of fitted standarddeviations is then recorded for each image at a particu-lar current as the beam width. At each current value,the average beam width is calculated and an error de-termined from the standard deviation of the fitted beamwidths. The resulting averages and errors are then fittedto find the emittance as outlined in the Theory section.

IV. IMAGE ANALYSIS

In the case of low charge as is the case for taking emit-tance measurements, the beam ends up being dim. Fur-

3

thermore, in some datasets, there are dead pixels or straylight sources that distract the analysis routine. To reducethe amount of manual work required on each particulardata, a semi-automatic routine was developed to pick outdim beams.

A. Noise Management

Given just an image of a black screen there will bevariations in the pixels due to noise. If the peak beambrightness is only a few factors above the deviation in thenoise, an initial guess for the beam is hard to pick outeven when using thresholding since the noise will varyabove the average background level. That is, threshold-ing will lead to an image with a beam and various dimspots around the image.

When considering the root mean square√σxx as a

measure of the beam where

σxx =

∫(x− x)2I(x, y)dxdy∫

I(x, y)dxdy(4)

with I(x, y) being the image intensity as a function ofpixel location and x being the centroid of the image alongthe x-axis, specifically defined as

x =

∫xI(x, y)dxdy∫I(x, y)dxdy

. (5)

we have that size will be greatly over estimated due tothe noise. This is since the squaring in Eq. (4) greatlyweights large distances from the centroid despite the factthat the noise is far less dense than the signal itself.

This is a problem as the initial parameters passedto the Gaussian fitter are the rms values. Bad ini-tal estimates lead to the fitter converging to a localminimum that does not reflect the signal. So tocompensate for this effect, it was proposed that onecould utilize a modified image with a boosted signal todetermine initial rms values and then pass this initialestimate to a fitter on the unmodified4 data. Witha boosted signal more noise can be cut and a betterinitial estimate on the rms values (and the position ofthe beam) can be made and passed to the Gaussian fitter.

To demonstrate the idea behind the signal boostingmethod proposed, we consider an N th order moment ofa one dimensional distribution which is defined to be∫

(x− x)Nf(x)dx∫f(x)dx

(6)

with x defined similarly as before. For large N , the tailsof the distribution are weighted heavily in determining

4 Not including binning and background subtraction.

the value of the integral. In analogy to such an N th ordermoment relative to x and x, take the N th order momentrelative to image number and the average backgroundnoise

σI,N (x, y) =

(1

n

n∑i=1

max (Ii(x, y)−B(x, y), 0)N

)1/N

(7)

for each pixel at (x, y). It was posited that for large N ,deviations from the noise, i.e. signals, would be weightedheavily since large intensities grow much faster under apower law than smaller values. The actual effect as afunction of N was calculated for a data set and is givenlater.

From this constructed image intensity σI,N , one canthen make dynamic masks that follow the beam for eachimage and, furthermore, calculate accurate estimates onthe beam size for passing to nonlinear fitting programs onthe unmodified image. Furthermore, binning the imagebefore performing the above calculation further reducesthe noise. Binning can be done safely since, at the beamwaist, the size of the beam is ∼ 200 µm and pixels them-selves are ∼ 20 µm

The program that has been developed uses this N th

order moment method with binning. The initial thresh-olding sets most noisy spots to zero, eroding5 sets iso-lated nonzero values to zero, smoothing with Gaussianfiltering6 generates circular neighborhoods for survivingdatapoints, thresholding the smoothed image sets a ra-dius on the neighborhoods which can then be normalizedto a mask image.

B. Determining the spot size

Taking a mask (used for cropping) determined by somemethod, the image can then be analyzed to find the beamwidth. Firstly, the beam is rotated as it travels througha solenoid by an angle equal the Larmor angle, so toensure that the beam image is in the correct orientationfor reading consistent beam widths, the cropped image isrotated by an angle opposite to the Larmor angle. Next,the rotated image is then projected onto each axis andfit with a Gaussian

F (x;A, σ, x0, y0) = y0 +Ae−12 ( x−x0σ )

2

(8)

where y0, σ, x0 and A are fit parameters. The advantageof this method is that constant background noise levels

5 Image eroding scans across the image looking at various neigh-borhoods. Each neighborhood is then set to the minimum valuein that neighborhood, thereby cutting out isolated noise spikesleft untouched by the thresholding.

6 A resource on how Gaussian filters work can be found here

4

1.51.61.71.8

Current (A)

15

10 N

1

2

3

4

SN

R

FIG. 3. Signal to Noise Ratio along a Solenoid Scan as func-tion of N , for N defined in Eq. (7). Fits were done usinga Gaussian function with a constant offset. The SNR wascalculated by taking the ratio of the amplitude of the fittedGaussian with the norm of the residuals in the fit.

can be added as a fit parameter rather than thresholdingthe noise.

For Gaussian beams, the standard deviation of the fit-ted guassian is equivalent to a root mean square measureof the data, however when the beam is not Gaussian itis not clear that this is the case. Note that the reasonthis is a possible issue is that the emittance is defined interms of the second moments, i.e. the root mean square.Fortunately, the beam is Gaussian at the beam waist dueto the nature of focusing when considered as a transfor-mation in phase space. Thus our method is limited toscans close to the beam waist.

C. Testing the Image Analysis Routine

It was postulated that in Eq. (7), that for large N ,the signal would be weighted largely against the noiseand increase the signal to noise ratio (SNR). To actuallymeasure this, analysis was carried out on images froma solenoid scan at 8 fC bunch charge. The images weremanually cropped around the beam.

We can identify each σI,N (as defined by Eq. 7) derivedfrom the original images as an image. Each σI,N was thenprojected onto an axis and fit using Eq. 8. The results arefound in Fig. 3. It is found that the best signal to noiseratio (SNR) is found for the first order moment N = 1,and the SNR actually decreases as the moment goes up.This brings up the interesting idea that perhaps one canincrease the SNR by using fractional N . The results areplotted in Fig. 4.

1.51.61.71.8

Current (A)

181

51313 N

1

2

3

4

5

6

SN

R

FIG. 4. Signal to Noise Ratio along a Scan Using FractionalN , for N defined in Eq. (7)

V. BEST PRACTICES IN MEASUREMENT

The largest time cost in taking data is the time spentin finding the beam after some change in the alignmentof the optical system has caused it to be lost. It has beenfound that at 3 A the beam is so defocused that glancingover the nanopattern will show up on the MCP with nocurrent in any of the steering magnets. However, the(first) steering magnets’ hysterisis (at least in the verticaldirection) can be strong enough to deflect the beam andcause it to disappear.

The diffraction pattern that the laser beam makes asit passes through the irises also significantly affects howwell fine tuning the beam position changes charge out-put. First, the diffraction pattern is circularly symmetricwhen aligned properly. However, often what is brightestis not the center of the diffraction pattern but the out-ermost fringe near the boundary of the iris (Aperture 1in Fig. 6) opening. If the iris is opened too large, onewill have to align the nanopattern on the outer fringefor highest yield. To fix this problem reduce the openingradius of the intensity limiting aperture until the spotappears uniform on the virtual cathode.

VI. DATA

800 nm incident laser light comes in at a pulse lengthof 50 fs and illuminates the nanopattern. The resultingcharge is then accelerated to 30 keV energies. The elec-trons then impinge upon a scintillating screen known asa DRZ.

Emittance measurements were taken at three currentsin the first solenoid (Isol1): 1.96 A, 1.54 A, and 1.45 A forvarious charges. Assuming uniform illumination of thenanopattern, which has a radius of r = 100 µm, the root

5

0

0.5

1

1.5

2

2.5

5 10 15 20 25Ther

mal

Em

itta

nce

(mm·m

rad

mm

rms

)

Charge (fC)

εx/σεy/σεr/σ

FIG. 5. Second Solenoid Scan taken at Isol1 = 1.96 A. Sim-ulations are done in GPT for various initial excess energiesand fit to the data. The thermal emittance as a functionof charge for a simulated beam with initial excess energy of1.7 eV is plotted.

Virtual

Cathode

Aperture

Aperture2

3

Aperture 1Lens

To the Chamber

Splitting Mirror

From the Laser

Mirror 1

Mirror 2

FIG. 6. Optical Setup. Light enters intensity modulated dueto polarizers not shown here. It is then reduced in intensitythrough aperture 1, passed through a lens with 50 cm focallength and then passes through two apertures used for align-ment. They are used only in alignment and remain open after.The virtual cathode and photocathode are equidistant fromthe lens.

mean square of the beam bunch is σ = r/2 = 50 µm,the thermal emittances are given by ε

50 µm where ε is the

emittance. The thermal emittance graphs are given be-low in Fig. 5 and Fig. 7. In Fig. 5, The simulatedthermal emittance of the a beam with an excess energythat best fits the data is plotted as well. One datapointwas obtained at Isol1 = 1.54 A and at 8 fC bunch chargeto give thermal emittances of εx/σ = (2.9± 0.8) mradand εy/σ = (2.5± 0.7) mrad. Taking a weighted averageof the emittances at 1.94 A in Fig. 5 given by

εavg =

∑i wiεi∑i wi

(9)

where each wi is the inverse of the corresponding errorof the ith emittance measurement εi. Taking the error inthe average to be

δεavg =1∑i wi

√∑i

(wiδεi)2 (10)

0

1

2

3

4

5

5 10 15 20 25Ther

mal

Em

itta

nce

(mm·m

rad

mm

rms

)

Charge (fC)

εx/σεy/σ

FIG. 7. Second Solenoid Scan taken at Isol1 = 1.45 A.

0

1

2

3

1 1.5 2 2.5

Wei

ghte

dSquare

Res

idual

(10−7)

Excess Energy (eV)

Excess Energy Fit

FIG. 8. Residuals of Initial Excess Energy Fit. Simulationswere ran in GPT to return emittances as a function of excessenergy for each of the charges in the Isol1 = 1.96 A solenoidscan. The result is plotted here, we find that the fit is mini-mized for (1.7 ± 0.1) eV

Noting that each product wiδεi = 1 by definition

δεavg =1∑i wi

√N (11)

where N is the number of emittance measurements. Tak-ing this emittance and dividing by the rms spot size yieldsa value of (1.6± 0.2) mrad for the thermal emittance.

VII. ANALYSIS

The thermal emittances was found to vary by a factorof two for different scans. The smallest value appearedat Isol1 = 1.96 A and the larger values at Isol1 = 1.45 Aand 1.54 A. It appears that the first solenoid causes anincrease in the emittance.

Interestingly, what has been found is that at low cur-rents the beam is highly elliptical indicating the presenceof, at minimum, a quadrupole magnetic moment. Thefact that the beam has smaller emittances and shows upas circular around the beam waist, at higher currents,indicates the possibility that the quadrupole moment is

6

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Bea

mSiz

e(m

m)

Position (m)

Beam size along the Beam line

0

1

2

3

1 1.5 2 2.5 3

Bea

mW

idth

(mm

)

Current (A)

Spotsizes vs. Current in Solenoid One

I1 = 1.45 A, I2 = 0.8 A,I1 = 1.96 A, I2 = 1.7 A,

23 cm42 cm

FIG. 9. GPT Simulations of spot size along the beam line.Current in the second solenoid is off in second plot and thereare no space charge effects. 23 cm is the location of the steer-ing magnet. 42 cm is the location of solenoid two. Note thatthe first solenoid focuses on the second solenoid at 1.8 A aswas verified experimentally. In the first plot, the beam sizeis plotted as a function of position along the beamline. Thescreen is at 86 cm.

actually in the steering magnets (perhaps due to differenthysterisis effects in the dipole pairs). What is possible isthat the solenoid is strong enough to focus the beam tobe at the waist as it travels through the steering magnetsthereby causing the electron beam to sample less of thequadrupole moment.

What has been found during experimentation is thatthe first solenoid focuses on the second solenoid at 1.8 Aso it is not immediately ruled out that the first solenoidis causing the beam to pass through a waist as it trav-els through the kicker. To determine whether or not thebeam is sampling nonlinear fields in the second solenoidor the quadrupole fields in the kicker magnets. Simu-lated beam size is plotted as a function of the various

solenoid one currents in Fig. 9. Note that at low currents∼ 1.4−1.5 A, the beam size is large at both the kicker andthe second solenoid. At 1.9 A the beam is about half thesize at both the kicker and the solenoid, leaving it inde-terminate that if the ellipticity and increase in emittanceis due to either of the two, which has the dominant effector whether both play a role or not. To test whether it isnot the kicker magnet one can run a solenoid scan at 2.2A at which the beam size at the solenoid is identical tothose at 1.45, where problems have been observed, but isminimal at the kicker.

VIII. CONCLUSION

The smallest thermal emittance measured was foundto be (1.6± 0.2) mrad which gives an upper bound onthe thermal emittance. This value agrees well with pre-vious measurements[5] of (1.4± 0.1) mrad done at fieldstrengths of 75 MV m−1. We have found then that theelectric field does not have a significant effect on emit-tance.

A. Further Work

Further work needs to be done to examine the emit-tance growth due to the the first solenoid before moreaccurate thermal emittances can be measured. Investi-gations into non-Gaussianity of the beams compared torms only fitting with reduced noise experiments need tobe carried out.

B. Acknowledgements

The author would like to thank Jared Maxson for thelarge amount of time he invested in helping with gather-ing the data, and fleshing out these results. The authorwould like to thank both Pietro Musumeci, David Ce-sar, and Jared for teaching the author about the worldof accelerator physics. All obtained results would havenot been possible with the work of Evan Threlkeld andDorian Johnson in maintaining and modifying the DCbeam line during the course of the REU. Furthermore,none of this research nor learning experience ever havehappened without funding from the NSF.

[1] P. Musumeci, L. Cultrera, M. Ferrario, D. Filippetto,G. Gatti, M. S. Gutierrez, J. T. Moody, N. Moore, J. B.Rosenzweig, C. M. Scoby, G. Travish, and C. Vicario,“Multiphoton photoemission from a copper cathode illu-minated by ultrashort laser pulses in an rf photoinjector,”Phys. Rev. Lett. 104 (2010).

[2] W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surfaceplasmon subwavelength optics,” Nature 424 (2003).

[3] Max Hachmann, Transverse emittance measurement atREGAE via a solenoid scan, Master’s thesis, UniversitatHamburg (2012).

[4] H. Wiedemann, Particle Accelerator Physics I, 2nd ed.(Springer-Verlag).

[5] R. K. Li, H. To, G. Andonian, J. Feng, A. Polyakov, C. M.Scooby, K. Thompson, W. Wan, H. A. Padmore, andP. Musumeci, “Surface-plasmon resonance-enhanced mul-tiphoton emission of high-brightness electron beams from

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a nanostructured copper cathode,” Phys. Rev. Lett. 110(2013).