Demonstration of single-shot picosecond time-resolved MeV electron imaging using a compact permanent magnet quadrupole based lens
D.Cesar, J.Maxson, P.Musumeci, Y.Sun, J.Harrison, P.Frigola, F.H.O'Shea, H.To, D.Alesini, R.K.Li
aa r X i v : . [ phy s i c s . acc - ph ] A p r Demonstration of single-shot picosecond time-resolved MeV electron imaging using acompact permanent magnet quadrupole based lens
D. Cesar, J. Maxson, P. Musumeci, and Y. Sun
Department of Physics and Astronomy, UCLA, Los Angeles, California 90095, USA
J. Harrison
Department of Electrical Engineering, UCLA, Los Angeles, California 90095, USA
P. Frigola, F. H. O’Shea, and H. To
RadiaBeam Technologies, Santa Monica, California, USA
D. Alesini
INFN-LNF, Via E. Fermi, 40-00044 Frascati, Rome, Italy
R. K. Li
SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA (Dated: today)We present the results of an experiment where a short focal length ( ∼ Transmission electron microscopy (TEM) is one of theprimary tools for materials characterization, with manyscientific and industrial applications. One of the recenttrends in TEM development is the quest for in-situ dy-namic imaging in which a sequence of micrographs arecaptured in a time-resolved mode while the sample understudy is undergoing some sort of microscopic rearrange-ment [1–3].Improving the temporal resolution of TEMs to ultra-fast time scales presents significant challenges. In orderto substantially decrease the image acquisition time itis necessary to increase the peak current by many or-ders of magnitude. But at large currents the tempo-ral resolution and transverse coherence rapidly degradedue to Coulomb interactions between the beam elec-trons [4]. Thus, state-of-the-art single shot TEM sys-tems have been limited to 10 nm 10 ns spatio-temporalresolution[5, 6]. The only known remedy has been toreduce the number of charged particles per pulse and in-tegrate over many millions of shots in order to collecta single picture [7]. This technique has produced a va-riety of scientific results [8], but it is restricted to fullyreversible processes.Single-shot picosecond transmission electron mi-croscopy (SPTEM) would fill an unmet need in the TEMcommunity to image irreversible dynamical motion atnm-ps spatio-temporal scales enabling real time study ofthe dynamics of many technologically and scientificallyrelevant microscopic processes, such as phase transitionsand dislocation motion [9]. One path to SPTEM requiresreplacing the 100 keV typical of conventional TEM’s with MeV electrons in order to take advantage of the relativis-tic suppression of the space-charge effects. This solution,discussed in detail in [10] involves a ground-up redesignin the microscope architecture, starting with the highestpeak brightness source of relativistic electrons availableto date, the radiofrequency (RF) photoinjector.RF photoguns have played a central role in the de-velopment of the high brightness beams used in XFELs[11]. By combining the high current densities available inphotoemission with the extremely high fields of a stand-ing wave RF cavity, the RF photoinjector has alreadydemonstrated the capability of generating MeV electronbeams bright enough to capture single-shot diffractionpatterns with a shutter speed of less than 100 fs [13–16].One of the main challenges for SPTEM comes fromthe fact that the high electron energy, which convenientlylimits the influence of Coloumb self-fields, comes at thecost of increased magnetic rigidity. High voltage (1-3MeV) electron microscopes were, until the advent of aber-ration correction, one of the main candidates for improv-ing the spatial resolution in TEM to atomic level [17].These machines were overburdened by large and expen-sive round solenoid lenses weighing up to several tons.The unfavorable scaling of solenoid focusing power asthe inverse square of the electron energy poses a prac-tical limit to the development of time-resolved electronmicroscopy [18, 19] and calls for the introduction of verystrong magnetic lenses and/or of novel focusing elements.Our approach borrows from experience in the field ofadvanced accelerators and involves the use of permanentmagnet quadrupole (PMQ) lenses for imaging with rela-tivistic electrons. PMQ triplets provide a compact short-focal-length lens for use by Inverse Compton Scatteringsources [20] and advanced accelerator applications [21].In this paper we report on using a ps-long 4 MeV elec-tron beam from an RF photoinjector and a strong com-pact PMQ-based lens with a focal length of ∼ µ m-scale spatial res-olution. The quadrupoles used in our experiment weremeasured to have field gradients of nearly 600 T/m,which to our knowledge set a new record for the strongestquadrupoles ever built. Magnification factors larger than30x have been achieved. These results represent the firstexample of single shot ps-time resolved transmission elec-tron microscopy.The experiment was performed at the UCLA PegasusLaboratory [22] where a 1.6 cell S-band RF gun, fabri-cated using a brazeless clamped design [23] is used togenerate a high brightness electron beam. In order tomaximize image sharpness, the photoinjector is operatedin an ultra-low emittance configuration in which the laserspot on the cathode is minimized (8 × µ m). This isachieved by illuminating the photocathode from a 72 ◦ port located in the first cell of the RF cavity, which allowsthe use of a high power final focus lens ( f =17.5 cm). Thesmall source size enables minimization of the initial phasespace area, which is preserved during transport becausethe beam rapidly expands transversely into a uniformlyfilled ellipsoid [24].The beam is transported to the microscope sampleplane located 3.7 m from the cathode using a two solenoidcondenser which provides flexibility in choosing sampleillumination. The tranverse beam parameters are char-acterized by inserting a thin (20 µ m) YAG screen locatedshortly before the sample plane. The screen is imaged byan in-vacuum optical microscope objective with a 1 µ mspatial resolution limited by a narrow depth of focus. Onthis screen the rms spot can be made as small as 3 µ m,with a normalized emittance (measured by scanning thesolenoid current) of 5 nm, for a 20 fC beam. For largerbeam charges (up to 100 fC), as employed in the exper-iments, the normalized emittance is measured below 20nm in agreement with simulations performed using theGeneral Particle Tracer (GPT) code [30]. The electronbeam duration was measured to be 0 . ± . RF gun
Gun solenoid Condenser solenoid
Sample plane z(m) R M S s po t s i z e ( µ m ) ε n ( mm - m r ad ) PMQ triplet
FIG. 1. Schematic of the MeV TEM Pegasus beamline. Theevolution of the RMS spot size and normalized emittance ǫ n along the beamline from a GPT simulation for a 50 fC beamcharge are also reported. Note the axis break. Each PMQ is made up of a 16 sector Halbach-stylearray of grade N35SH NbFeB wedges [25] wire electri-cal discharge machined and assembled inside a precisionmachined aluminum keeper (see Fig. 2). The 3D magne-tostatic solver Radia [26] is used to compute the effectivemagnetic lengths (6.2 mm and 3.6 mm) and peak gra-dients (597 T/m and 495 T/m) for the long and shortquadrupoles respectively. Due to the small aperture sizeit was challenging to obtain accurate Hall probe measure-ments of the field profile. A summary of the parametersof the PMQ triplet as well as the results of the magneticmeasurements is shown in Table I. A vibrating wire tech-nique was used to measure the integrated field gradients[27] which, within the relatively large error due to thecalibration uncertainties, were found in good agreementwith the expected values.A custom-design Al stage making use of flexures, dis-placed by linear piezo actuators, is used to adjust thelongitudinal position of individual PMQs. The vibratingwire technique was used to determine the offsets and pre-align the magnets on the stage. The range of motion inthe flexure-based stage (about 0.75 mm) allows achievingan imaging condition for a relatively wide range of inputbeam energies, i.e. between 3.5 and 4.75 MeV.A picture of one of the assembled PMQs as well as thefull triplet setup is shown in Fig. 2. The total weightof the PMQs and the flexure stage is less than 2 pounds.The wedge magnetization orientations as well as the mag-netic field in the central plane of the quadrupole are alsodisplayed. Field maps for each of the fabricated mag-nets (including the individual wedge dimensions and thegaps originating from manufacturing errors) have beenobtained using 3D magnetostatic simulations.These field maps permit detailed simulations of themicroscope column beam dynamics. We begin by solv-ing a linear transport model of hard-edge quadrupoles tofind out the beamline distances required to achieve animaging condition with equal magnifications in x and y at the detector plane. We then refine the calculation byusing the quadrupole gradient profile along the beamline TABLE I. Parameters for the PMQ triplet. The reference position is measured from the sample plane.
Design Gradient Effective length Measured G × L Reference design positionFirst quadrupole
597 T/m 6.16 mm 3.3 ± Second quadrupole -597 T/m 6.16 mm 3.6 ± Third quadrupole
495 T/m 3.6 mm 1.7 ± axis, z . Finally, tracking the particle trajectories in thefull PMQ triplet magnetic field maps was used to esti-mate the transverse tolerance to misalignment and theaberrations of the system. The results are shown in Fig.3. The calculated spherical aberrations for the manufac-tured PMQs are 8.9 mm and 75.2 mm in the horizontaland vertical plane respectively. The asymmetry couldbe reversed by using the vertically focusing quadrupolefirst instead of the horizontally focusing one. It was alsofound that for each quadrupole an angular misalignmentof ± µ rad and a transverse displacement of 50 µ m withrespect to the central beam trajectory were required inorder to avoid degradation of the image quality.A 20 ± µ m thick Cu ‘UCLA’ sample target was fab-ricated using lithographic techniques with varied featuresizes from 5 µ m to 100 µ m. The target was mountedon a 3 mm standard TEM holder and inserted in thebeamline using a micrometer translation stage 500 µ mfrom the front face of the first PMQ. A HeNe laser co-propagating with the electron beam was used to alignthe sample to the axis of the PMQ triplet and the mainbeamline. The image was collected using a 100 µ m thickYAG screen lens-coupled to a Princeton Instrument PI-MAX III intensified camera. The point spread function(psf) of this phosphor screen-based imaging system (not FIG. 3. a) Aberrations for the PMQ triplet b) Tolerances tomisalignment of the three-element lens. The shaded area isobtained calculating the rms size of the beam at the detec-tor plane after tracking a very small source of electrons with1 mrad divergence when each quadrupole is displaced in arandom direction in the transverse plane by a fixed amount. to be confused with the psf of the microscope itself whichdepends on the magnification) is estimated to be 50 µ mrms, mostly attributable to the screen thickness.An optical image of the sample is shown next to a rep-resentative single-shot electron image of the sample inFig. 4 (a,b). All of the sample features are clearly visiblein the electron image, as is a contaminant which was in-troduced above the ‘U’ during sample preparation. Theskewness of the electron image is accentuated by align-ment error so that the sample does not sit precisely per-pendicular to or centered on the PMQ axis. The dimen-sions of the letters in the electron image can be used tocompute a magnification of 32x and 25x in the horizontaland vertical plane respectively in fair agreement with thedesign magnification of 25x Fig. 4 (c,d). The astigma-tism in the system is caused by the quadrupole placementand could be removed by fine-tuning the quadrupole po-sitions.A quantitative comparison of the simulated andrecorded electron images requires a complete understand-ing of the electron imaging apparatus. Start to end sim-ulations of the image formation process are performedtaking into account multiple elastic and inelastic scatter-ing of electrons inside the sample. This is included in theparticle tracking simulations by assigning an additionaldivergence and energy spread for particles that hit themetallic sample, accounting for the multiple elastic scat-tering and inelastic collisions, respectively [33, 34]. Thefull simulation (Fig. 4) shows that contrast is createdwhen scattered electrons are clipped by the aperture ofthe magnets. Additional contrast is provided by the im-perfect imaging of the lower energy electrons. FIG. 4. a)Optical and b)electron image of the nanofabricated‘UCLA’ target. c) Simulated distribution at the target. Thecolor-coding indicates division between scattered and unscat-tered particles d) Simulated distribution at the image plane.
In both simulation and experiment, the highest resolu-tion electron images are obtained at the maximum sam-ple illumination flux, n e =18 electrons/ µ m . Musumeciand Li [10] showed that as the charge density is increasedbeyond a certain optimum level, space charge effectsand point-to-point scattering will cause image blurring.Given the relatively small magnification factor and largefeature sizes, the impact of Coulomb scattering could notbe measured in this experiment. Nevertheless, by vary-ing the condenser lens strength, we were able to quantifythe effect of changes in the illumination flux on the imagesharpness.In Fig. 5 we show the resolution in both experimentaland simulated images quantified as the standard devi-ation of the centroid positions of the error-function fitsto the line-outs taken along the edge of the ‘L’ in the‘UCLA’ sample. The data points are obtained from a se-ries of images captured with different condenser solenoidsettings and beam charges (to vary n e ). GPT simulationsare then performed using the measured illumination flu-ences. Both data and simulation show that the erroron these positions (and therefore the image sharpness)improves as the fluence is increased. Assuming Pois-son statistics for the signal we expect the spatial resolu-tion in the image to scale as 1/ n e according to the Rosecriterion[29]. The inherent psf of the detector systemfurther limits the spatial resolution. In order to quantifythis, a gaussian blur of 20 µ m (at the detector plane,and therefore 0.7 µ m at the sample plane considering the30x magnification) was taken into account when comput-ing the simulated images. The main difference betweenthe experimental and simulated curves is their asymp-totic high-fluence-limit, which can be traced back to thedifferences between the simulated and real point spreadfunctions discussed above. Fig. 5 serves to show thatthe resolution of the current microscope setup could befurther enhanced by improving the detection system [32].For small image features, the resolution becomes in- Fluence (e /µm ) R e s o l u t i o n ( µ m ) - FIG. 5. Microscope resolution as a function of charge forsimulated (blue) and measured (gold) data. The error bars onthe simulations are due to the random particle initialization.The solid lines show the 1 /n e scaling for the resolution. tertwined with contrast such that understanding and im-proving contrast is a necessary component of a high mag-nification system. Contrast is defined from the image in-tensity as ( I max − I min ) / ( I max + I min ). In Fig. 6 weshow four simulated curves demonstrating the effect thatadding an objective aperture would have on the imagecontrast. The two solid lines show the simulated contrastfor copper and gold versions of the ‘UCLA’ target. Theeffect of the iris size is more dramatic for the Cu sincecopper scatters the electrons less than gold. The rmsangular and energy spread size of the gaussian distribu-tions of the particles hitting the samples are θ Cu = 0 . E Cu = 29 keV and θ Au = 0 .
2, ∆ E Au = 68 keV forcopper and gold respectively. The contrast of a coppertarget for an aperture equal to the gap between the PMQmagnets (3.5 mm) is 0.43, in close agreement with the0.42 contrast obtained from analysis of the line profilesof the ‘L’ in the electron images. Also shown are twodashed lines showing the results of simulations of imageformation for objects having sizes similar to the psf ofthe detection system. In such cases the differences be-tween gold and copper samples are significantly smalleras the contrast is dominated by the resolution, not bythe sample scattering properties. These simulations canbe compared to the measured contrast from 5 µ m barson gold and copper TEM 2000 grids, shown in Fig 6above and below the ‘L’, respectively. Future single-shottime-resolved TEMs will require using an iris to increasethe percentage of scattered electrons which are clipped.Diffraction contrast could also be obtained by positioningslits at the back focal plane(s) of the lens.In conclusion these experiments demonstrate the firstsingle shot, ps time-resolved electron images using highbrightness relativistic beams from an RF photoinjectorand the design and construction of a record-high gradientPMQ-based objective lens. This compact lens design canbe used in subsequent magnification stages to approach Iris Diameter (mm) C o n t r a s t AuCu
FIG. 6. Simulated contrast as a function of the objective irisaperture for copper and gold targets having feature sizes sim-ilar (dashed) or well under (solid) the spatial resolution ofthe microscope. Also shown are the contrast of the 3 samples(UCLA target and Cu and Au TEM grids) observed experi-mentally using the PMQ gap as iris aperture. the spatial resolution limits of the instrument. While theaberration coefficients of the quadrupole lens might seemhigh to conventional TEM microscopists, single shot pi-cosecond TEM simulations indicate that the final spa-tial resolution after the addition of multiple magnifica-tion stages will be limited by space charge blurring [10].Besides the reduction in cost, size and higher focusingpower, quadrupole-based lenses might also offer an ad-vantage over round lenses due to the smaller charge den-sity that is obtained in elliptical cross-overs. The resultsreported in this paper validate the simulation models ofthe beam dynamics in the relativistic electron columnand image formation process, paving the way towardsthe use of bright relativistic electron sources to achievethe long-range goal for single-shot time-resolved TEM ofbeing able to follow defect dynamics in materials with10 nm spatial resolution and ps temporal resolution.This work was partially supported by DOE STTRgrant No. de-sc0013115 and National Science Foundationgrant PHY-1415583. The authors want to acknowledgeA. Murokh and G. Andonian for useful discussions.the spatial resolution limits of the instrument. While theaberration coefficients of the quadrupole lens might seemhigh to conventional TEM microscopists, single shot pi-cosecond TEM simulations indicate that the final spa-tial resolution after the addition of multiple magnifica-tion stages will be limited by space charge blurring [10].Besides the reduction in cost, size and higher focusingpower, quadrupole-based lenses might also offer an ad-vantage over round lenses due to the smaller charge den-sity that is obtained in elliptical cross-overs. The resultsreported in this paper validate the simulation models ofthe beam dynamics in the relativistic electron columnand image formation process, paving the way towardsthe use of bright relativistic electron sources to achievethe long-range goal for single-shot time-resolved TEM ofbeing able to follow defect dynamics in materials with10 nm spatial resolution and ps temporal resolution.This work was partially supported by DOE STTRgrant No. de-sc0013115 and National Science Foundationgrant PHY-1415583. The authors want to acknowledgeA. Murokh and G. Andonian for useful discussions.