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Space charge effects in ultrafast electron diffraction and imaging
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Image of FIG. 1.
FIG. 1.

(Color online) Electron point-projection imaging technique and results. (a) Schematic of the experiment. For illustration purposes, the angular span of the shadow is significantly increased from typical values ≤1 mrad. For this reason, the projection is nearly linear. (b) The snap-shots of the normalized shadow images at selected times. The magnification of the projection imaging is ≈33.

Image of FIG. 2.
FIG. 2.

(Color online) The results of electron point-projection imaging. (a) The CoM frame expansion dynamics of electron pulses with longitudinal pulse length σ z . The solid lines through the experimental data (symbols) are from N-particle simulations. (b) Dependence of pulse length on the electron sheet density at time 100 ps for various F and F a settings, showing a universal power-law increase with exponent roughly γ = 0.5. Predictions based on mean-field (Ref. 3) and one-dimensional (1D) fluid (Ref. 29) models are also presented.

Image of FIG. 3.
FIG. 3.

(Color online) (a) The symbols represent the values of γ found at different delay times. The solid line represents results from an analytical Gaussian model (AGM) simulation using broadened initial longitudinal velocity spread due to near cathode space charge effect extracted by fitting the early time σz trajectory, which is presented in Fig. 4(c) and the text. (b) The symbols are the linescans of the shadow images recorded on the phosphor/CCD screen produced by photoelectrons (Σ = 7.12 × 1013 e/m2) at different times. The linescans are fitted with a Gaussian profile (solid lines). A top-hat profile (dashed line), convoluted with the projection geometry, is also drawn for comparison. The magnification of the projection imaging is ≈33.

Image of FIG. 4.
FIG. 4.

(Color online) (a) The normalized “initial” longitudinal phase space employed in the N- particle simulations, which is parameterized by a thermal parameter a and scaled by the initial length σ zi and momentum spread σ pz . (b) The percentage change in the pulse length σ z obtained at 100 ps as a function of a. (c) The initial longitudinal velocity spread, Δυ z (t = 0), obtained by fitting N-particle trajectories to the imaging data depicted in Fig. 2(a). The extraction field F a applied is 0 at the five lowest Σs, 0.32 MV/m at 40 × 1012 e/m2 and at 70 × 1012 e/m2.

Image of FIG. 5.
FIG. 5.

(Color online) The symbols represent the experimental longitudinal pulse length (σ z ) of the photoelectron pulses with different densities tracked at different times. The solid line represents the analytical Gaussian model simulation using the different initial longitudinal velocity spread specified by Fig. 4(c) and the initial slope of phase space set to 0. The dotted line represents the analytical Gaussian model simulation using a constant initial longitudinal velocity spread Δυ z (Δt = 0) = 0.084 μm/ps.

Image of FIG. 6.
FIG. 6.

(Color online) Momentum cut model for selecting electrons for photoemission used in the three step model. (a) The electron energy distribution before and after photoexcitation. In this model, the electrons are assumed to escape the cathode surface before thermalization and thus have the same Fermi-Dirac (FD) energy spread (exaggerated for illustration purpose) defined at the temperature prior to photoemission. The shaded area (E ≥ E F  + Φ eff ) represents the electron population that is qualified for photoemission. (b) The selection of electrons in the three-dimensional momentum phase space that are qualified for photoemission. The electron must have an energy larger than E F  + Φ eff , as described in (a); it must also have a minimum longitudinal momentum () to overcome the work function in order to escape the surface, as specified by the shaded area.

Image of FIG. 7.
FIG. 7.

(Color online) (a) The photoelectron velocity spread in the longitudinal (Δυ L ) and transverse (Δυ T ) directions. The solid symbols represent results obtained using N-particle simulation, and the hollow symbols represents results obtained by integrating the analytical equation reported in Ref. 39. (b) The longitudinal velocity distribution of photoelectrons generated by N-particle simulation based on the three step model.

Image of FIG. 8.
FIG. 8.

(Color online) (a) Schematic of an extended three step model for intense photoemission. The net work function Φ′ is the sum of the Schottky potential Φ Sch , the surface dipole potential Φ dp , and the intrinsic work function Φ w . (b) The quantum efficiency derived based on modified TSM (dashed line) for Φ w  = 4.26 eV and the experimental data with a fit to a constant behavior at low field and a linear behavior at high field. (Inset) The electron escape ratio, R esp , is calculated, including the dipole field of the virtual cathode and its image for Φ w  = 4.26 eV. (c) Electron pulse sheet density as a function of fluence for high applied field and for zero applied field (inset).

Image of FIG. 9.
FIG. 9.

(Color online) Concept of an electron beam injector column for ultrafast electron microscope demonstrated using an N-particle simulation of electron pulse propagation in an electron beam column with an RF cavity. (a) Phase space adjustment before and after the RF cavity. (b) The corresponding real space pulse profile at each electron optical components. The simulation is performed using 104 electrons per pulse at 30 keV using the initial condition a = 1, as specified in Fig. 4(a).

Image of FIG. 10.
FIG. 10.

(Color online) (a) Space-charge-limited temporal resolutions in ultrafast electron diffraction (UED) and microscopy (UEM) systems. Solid squares and hollow diamonds show the Coulomb-explosion-led pulse lengthening calculated for 100 keV UEM system (squares) with cathode-to-sample distance of 70 cm and 30 keV UED system (diamonds) with cathode-to-sample distance of 5 cm. The rectangular shaded areas depict experimental resolutions reported in current UED and UEM systems. In comparison, the solid stars and circles show the improvements in temporal resolution by employing an RF recompression in the UEM beam column (see panel (b)) optimized for nano-area diffractive imaging (stars) and for single-shot UED (circles). (b) Photoelectron pulse trajectory along an RF-enabled UEM column. The shaded regions represent the locations of the electron optical elements. (c) A scale-up view of the pulse profiles near the sample plane for nano-area diffractive imaging containing 105 electrons/pulse. An aperture with radius of 15 μm is employed to thin out the peripheral electrons to achieve a divergence angle α ≤ 1.7 mrad. The minimum transverse radius σ T is 0.64 μm, and the minimum longitudinal pulse length σL is 0.80 μm. (d) A scale-up view of the pulse profiles near the sample plane for an ultrafast single-shot UED containing 108 electrons/pulse. The minimum transverse radius σT is 51 μm, and the minimum longitudinal pulse length σL is 0.88 μm.


Generic image for table
Table I.

Location of electron optical components in the UEM column.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Space charge effects in ultrafast electron diffraction and imaging