Ultrafast Electron Diffraction (UED) sources

Introduction: Ultrafast Electron Diffraction (UED) is an indispensible tool for the study of molecular dynamics and ultrafast chemistry. Despite several advantages of the use of electrons over the use of x-rays, UED has one crucial disadvantage: Coulomb interactions limit attainable pulse duration and dilute beam quality. Several schemes are being investigated with our GPT code to study and reduce the deteriorating effects of Coulomb interactions in various UED sources.

Reversal of a 'ellipsoidal' Coulomb explosion by rf-techniques

This method relies on space-charge and well-chosen initial conditions to create an approximately ellipsoidal bunch. In theory this bunch can be recompressed by a downstream rf-cavity to conditions matching the photo-emission process. In practice pulse duration and beam quality are limited by an accumulation of small effects due to non-linear space-charge forces and non-linear external fields. In the paper listed below, the DC electrostatic field, solenoids and the rf-cavity are all imported into GPT as cylindrically symmetric field-maps, calculated by superfish. The time-consuming task of finding the optimal settings for all beamline components was partly automated with the GPT multi-dimensional optimizer.

Electron source concept for single-shot sub-100 fs electron diffraction in the 100 keV range Compression of subrelativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffractionon

JAP 102, 093501 (2007)
DOI: 10.1063/1.2801027

T. van Oudheusden, E. F. de Jong, S. B. van der Geer, W. P. E. M. Op ’t Root, and O. J. Luiten, and B. J. Siwick

PRL 105 (26), art. no. 264801 (2010).
DOI: 10.1103/PhysRevLett.105.264801

Van Oudheusden, T., Pasmans, P.L.E.M., Van Der Geer, S.B., De Loos, M.J., Van Der Wiel, M.J., Luiten, O.J.

We present a method for producing sub-100 fs electron bunches that are suitable for single-shot ultrafast electron diffraction experiments in the 100 keV energy range. A combination of analytical estimates and state-of-the-art particle tracking simulations show that it is possible to create 100 keV, 0.1 pC, 30 fs electron bunches with a spot size smaller than 500 µm and a transverse coherence length of 3 nm, using established technologies in a table-top setup. The system operates in the space-charge dominated regime to produce energy-correlated bunches that are recompressed by radio-frequency techniques. With this approach we overcome the Coulomb expansion of the bunch, providing a single-shot, ultrafast electron diffraction source concept.

We demonstrate the compression of 95 keV, space-charge-dominated electron bunches to sub-100 fs durations. These bunches have sufficient charge (200 fC) and are of sufficient quality to capture a diffraction pattern with a single shot, which we demonstrate by a diffraction experiment on a polycrystalline gold foil. Compression is realized by means of velocity bunching by inverting the positive spacecharge- induced velocity chirp. This inversion is induced by the oscillatory longitudinal electric field of a 3 GHz radio-frequency cavity. The arrival time jitter is measured to be 80 fs.

Collaboration: This project is commissioned by the Technical University of Eindhoven (TUE), Department of Physics, The Netherlands.

Megavolt electron energies to reduce space-charge forces by relativistic effects

Simulation of this approach with GPT is basically plug-and-play. All standard features borrowed from the high-energy use of GPT --such as import of rf-field maps, external lenses and accelerator structures-- are directly applicable. The Particle In Cell (PIC) space-charge model of GPT developed in collaboration with DESY and Rostock University is both efficient and accurate. A sample publication employing GPT to the 'MeV-UED' approach is listed below.

Ultrafast time-resolved electron diffraction with megavolt electron beams
Applied Physics Letters 89, 184109 (2006)
DOI: 10.1063/1.2372697

J. B. Hastings, F. M. Rudakov, D. H. Dowell, J. F. Schmerge, J. D. Cardoza, J. M. Castro, S. M. Gierman, H. Loos, P. M. Weber

A rf photocathode electron gun is used as an electron source for ultrafast time-resolved pump-probe electron diffraction. The authors observed single-shot diffraction patterns from a 160 nm Al foil using the 5.4 MeV electron beam from the Gun Test Facility at the Stanford Linear Accelerator. Excellent agreement with [GPT] simulations suggests that single-shot diffraction experiments with a time resolution approaching 100 fs are possible.

Use only a few electrons per pulse, combined with a high repetition rate

The PIC space-charge model of GPT is useless in the case of far less than a thousand electrons per bunch. The relativistic point-to-point model is the method of choice to calculate space-charge and stochastic effects between just a few electrons. A sample publication is listed below, where the authors chose to model the rf-fields by analytical expressions.

Hybrid dc–ac electron gun for fs-electron pulse generation
New Journal of Physics 9 (2007) 451

L. Veisz, G. Kurkin, K. Chernov, V. Tarnetsky, A. Apolonski, F. Krausz and E. Fill

We present a new concept of an electron gun for generating subrelativistic few-femtosecond (fs) electron pulses. The basic idea is to utilize a dc acceleration stage combined with an RF cavity, the ac field of which generates an electron energy chirp for bunching at the target. To reduce space charge (SC) broadening the number of electrons in the bunch is reduced and the gun is operated at a megahertz (MHz) repetition rate for providing a high average number of electrons at the target. Simulations of the electron gun were
carried out under the condition of no SC and with SC assuming various numbers of electrons in the bunch. Transversal effects such as defocusing after the dc extraction hole were also taken into account. A detailed analysis of the sensitivity of the pulse duration to various parameters was performed to test the realizability of the concept. Such electron pulses will allow significant advances in the
field of ultrafast electron diffraction.

Future developments

Stochastic effects (disorder induced heating) play an increasingly important role in UED sources. GPT version 3 is able to calculate all pairwise Coulomb interactions, in realistic external fields, and including relativistic effects, for ~106 particles on a normal PC.