The temporal evolution of the charge density distribution in femtosecond laser produced electron pulses was studied using electron-laser pulse cross correlation techniques and compared to analytical predictions and simulations. The influence of propagation time and weak magnetic focusing were both investigated. Our results show that ultrashort electron pulses develop a relatively uniform internal charge density as they propagate, which is in good agreement with analytical predictions, and that weakly focusing an ultrashort electron pulse results in an increased internal charge density towards the leading edge of the pulse.
© 2013 OSA
Space-charge driven dynamics in femtosecond laser produced electron pulses are important in a number of applications, from the pulsed relativistic electron beamlines in synchrotrons and free-electron lasers to the nonrelativistic beams in ultrafast electron diffraction (UED), dynamic transmission electron microscopy (DTEM) and femtosecond photoemission electron microscopy (PEEM) . In UED or DTEM systems for example, space charge driven expansion of ultrashort electron pulses leads to pulse duration and energy distribution broadening that determines the practical limits to instrument performance. Given their importance, space-charge driven dynamics have been actively explored, primarily through simulation and theory [2–4]. These studies have lead to a number of important insights, such as the orders of magnitude on-specimen brightness advantages associated with compact electron sources for UED studies , the utility of spatially shaping the photocathode excitation pulse to generate well-behaved uniformly filled elipsoidal bunches [6, 7], and how the internal dynamics of space-charge dominated electron bunches result in linear velocity-time correlations  that can be exploited to enable pulse compression by radio frequency cavities [8–11] and potentially electrostatic reflectrons [12, 13].This work has been primarily guided by simulation since the detailed characterization of nonrelativistic, low bunch-charge ultrashort electron pulses has been challenging due to the required time resolution. Appropriate techniques exist for characterizing pulsed, relativistic electron beams that provide the ability to measure relevant beam parameters from a single pulse [14, 15], but these techniques typically operate using electro-optic sampling that relies on relativistic bunch-field enhancements making them unsuitable for characterizing the low charge, non-relativistic electron pulses used in UED experiments.
To date, the characterization of ultrashort electron pulses that has been performed focused on determination of the electron pulse duration. The conventional approach has been to employ streak-camera methods that use a beam deflection system (either deflection plates or a deflector cavity) to map the temporal information onto the spatial coordinate (i.e. in the deflection direction) at a suitable detector [16, 17]. Deflection systems with time resolution (FWHM) approaching 100 fs have recently been demonstrated [7, 18, 19]. An alternative optical approach is to perform a cross-correlation measurement using the ponderomotive interaction between a femtosecond laser pulse and the electrons in a bunch . As a characterization tool for ultra-short electron pulses this method has a number of unique advantages. First, the time-resolution of this approach is fundamentally determined by the laser spot size at the region where the electron and laser pulse interact and the laser pulse duration; i.e. the time resolution is tunable based on the laser beam properties and can readily be made below 100 fs for easily obtainable spot sizes and pulse durations (i.e. ∼10 microns and pulse duration ∼30 fs). Second, the interaction region in which the measurement is performed is the size of the laser focus, which is much smaller than the typical interaction region in a beam deflector (deflection plates or cavity). Thus, the measurement provides information on the electron pulse at a precise point in the electron beamline, not an average over an extended interaction region. This is important in systems where the electron pulse properties vary rapidly with position like many UED and DTEM beamlines. Third, the measurement operates in a pump-probe geometry similar to a UED experiment; the measurement is synchronized with the photocathode excitation pulse to within a few femtoseconds and is capable of directly determining any electron pulse arrival time jitter at the specimen position.
Here we focus on the exquisite sensitivity of the electron-laser pulse cross correlation approach to explore features of the space-charge driven dynamics beyond characterization of the electron pulse duration. We experimentally investigate details of the electron pulse envelope dynamics by using the electron-laser cross correlation method to directly measure the spatio-temporal charge density inside femtosecond laser produced electron pulses at various stages of evolution and over a range of bunch charges. We also investigate the effects of magnetic focusing on the charge density in low aspect ratio electron pulses; i.e. the beam width is much larger than the pulse length.
We use these measurements to test both analytical predictions and simulations of space-charge driven dynamics in ultrashort electron pulses and find that the results are in excellent agreement. Such details are extremely important, for example, since the effectiveness of radio-frequency electron pulse compression strategies is strongly dependent on the the detailed phase space distribution of the bunch at the RF compression cavity (i.e. both the spatio-temporal charge density and the velocity-position correlation in the electron bunch). In addition, modelling of transient UED signals requires convolution with the diffractometer impulse response function whose details are fundamentally determined by the electron pulse envelope at the specimen.
2. Experimental Methods
The electron optical configuration used in this experimental study of ultrashort electron pulse dynamics is shown in Fig. 1 along with the laser beam geometry used for the ponderomotive measurement. The electron source consists of a DC photoelectron accelerator and single magnetic solenoid lens. The accelerator comprises a photocathode electrode housing, a bulk copper photocathode and an anode. In these experiments the photocathode electrode is held at voltages ranging from −50 to −95kV and and the anode is held at ground through electrical contact with the surrounding vacuum chamber. The amplified femtosecond laser source used to generate the electron beam and perform the cross correlation measurements is a Spectra Physics Spitfire Pro XP producing 3 W (3mJ/pulse, 1kHz) of 35 fs pulses centered at wavelength of 800 nm. Roughly 1W of the total laser output is used to pump a Coherent OPerA Solo optical parametric amplifier to produce the 250 nm femtosecond laser pulse used to generate the photoelectron pulses through front-side excitation of the copper photocathode, and 300 mW (800 nm) is used in each arm of the pump line for the cross-correlation measurement (described in more detail below). The magnetic lens placed immediately after the acceleration region is used to focus the electron beam at a Gatan Ultrascan 1000 transmission electron microscope CCD camera used to detect the electrons.
The electron-laser pulse cross correlations were performed by deflecting electrons using the ponderomotive interaction. This force is experienced by charged particles in a spatially inhomogeneous, oscillating electromagnetic field and is proportional to the gradient of the field intensity:20] and then demonstrated using a single ultrashort laser pulse , with the deflection of the electrons within the pulse that interacts with the laser field providing the means to obtain a cross-corelation between both the electron and laser pulses. The difficulty encountered using this method is that the laser pulse energy required is relatively high(∼10 mJ) and thus can not easily be performed with most table-top chirped-pulse amplification systems. A solution to this problem was found by using two counter-propagating laser pulses with a common polarization in place of a single laser pulse to create a standing wave at their intersection. The intensity envelope in the standing wave configuration varies on a length scale of λ/2 (∼400 nm) as opposed varying over the length of the entire laser pulse (∼12 μm for a 40 fs pulse). This results in a dramatic increase in the strength of the ponderomotive force and allows for the measurement to be performed using most table top amplifier systems as described in detail in Hebeisen et al..
A schematic of the experimental setup for the electron-laser cross correlation measurements can be seen in Fig. 2. The relative delay, τ, between the two laser pulses is set using a linear delay stage in order to place their intersection within electron beam, this remains constant throughout the measurements. The arrival of the two laser pulses relative to the electron pulses is controlled using a second optical delay, t. The laser pulses are focused to a focus size of 85±5 μm and are overlapped in space with the electron beam, which ranges in diameter from 1 mm to 3 mm, using a ∼ 200 μm pinhole placed at forty-five degrees. Placing a pinhole immediately in front of the interaction region selects a specific transverse portion of the electron beam for investigation. In these studies the pinhole is aligned with the center of the electron beam although the principle of the measurement is identical for other transverse spatial locations in the beam; the full three dimensional spatio-temporal charge density of the electron pulses can be recovered if efforts are made to scan the beam across the pinhole.
The signal is obtained by analyzing images of the electron beam at different delays between the electron and the two pump pulses in the manner described by Hebiesen et al. . For a delay, t, the signal is calculated using
The electron-laser cross correlation measurements performed were compared with both simulations and analytical predictions of the propagation dynamics of ultrashort electron pulses. The simulations were performed using the General Particle Tracer (GPT) software from Pulsar Physics. GPT is a full 3D particle tracking software which models charged particles in electromagnetic fields. The space charge model used in these simulations models relativistic point-to-point interaction between all particles. Pulses containing more than 5000 electrons were simulated using 5000 macro particles, each with a charge of q = Q/N, where Q is the total bunch charge and N is the number of macro particles. Simulations performed using electron bunches with less than 5000 electrons included pair-wise interactions between all electrons. Fields maps were generated using the specifications of the home-built electron gun and magnetic lens used in the measurements using Poisson Superfish. In order to compare the simulation results to the measurements performed, all macro particles with a radial position outside of the radius of the pinhole were discarded at the virtual measurement position (which is the same as the actual measurement position). The remaining macro particles were then binned along the time coordinate and then convolved with a Gaussian function of the same width as the impulse response.
3. Results and Discussion
Initial measurements were performed with the goal of monitoring the evolution of the temporal charge density distribution of ultrashort electron pulses as they propagate. The electron pulse energies were varied in these measurements which provided the ability to probe the pulses at different times during their evolution. Figure 3 shows the results of measurements performed on pulses containing 7.5±0.2×104 electrons (Ne = 7.5 ± 0.2×104) with energies, E, of 55 kV, 65 kV and 75 kV with a photocathode to measurement distance, d, of 26.8 cm, as well as the results of the corresponding simulations. These results clearly demonstrate that ultrashort electron pulses evolve to a relatively uniform charge density along the axis of propagation and they are in excellent agreement with the GPT simulations performed. This tendency was observed in earlier simulations , and was predicted to be a robust feature of ultrashort electron pulses. In addition to these simulations, an analytical one dimensional model proposed by Reed  predicted similar behaviour. This model states that initially low aspect ratio pulses would develop a uniform charge density on time scales long compared to a characteristic time,4]). Cross correlation measurements were performed on pulses with various energies while the on axis charge density of the pulses and the propagation time was extracted from GPT simulations that are in quantitative agreement with the measurements. Table 1 shows the results of these measurements and simulations and it can be seen that, qualitatively, they support equation 4; although the charge density decreases as the pulses propagate, |ρ|t2 remains constant. This trend was found to continue when the energy was held constant and the charge was varied. A four-fold increase in bunch charge resulted in only a slight increase (<10%) in the local on axis charge density at the interaction region. This demonstrates that for propagation times t ≫ τ an increase in bunch charge simply translates into a proportional increase in the electron pulse duration, since the local charge density tends towards a constant in this limit (Eq. 4) as predicted in . This is an important consideration in the design of ultrafast electron beam lines.
Measurements and simulations were also performed in order to study the effect of magnetic focusing on the charge density distribution within the pulses. Focusing conditions were chosen which resulted in collimated to slightly divergent electron beams; this was done in order to maintain a low aspect ratio as well as to ensure that the pinhole selected a portion of the pulse representative of the local charge density. Figure 4 shows the results of cross-correlation measurements and GPT simulations performed on pulses with various bunch charges using a focusing current approximately 60% greater than the measurements shown in Fig. 3. The impulse response of the measurement can be seen in the short Gaussian traces from low bunch charge pulses which, in these measurements, is approximately 500 fs. The expected increase in pulse length with increasing bunch charge is apparent here, although the key feature to note is the increasing local charge density towards the leading edge of the pulses(positive delay) as a result of the increased focusing power. In order to provide a more complete picture of this effect, the charge density distribution of an entire pulse as a function of the radial distance from the pulse propagation axis, R, and the longitudinal position, Z, is compared in Fig. 5 in both a focused and an unfocused state. Here the redistribution of the charge density caused by the magnetic lens is apparent; the focusing causes an increase in the local charge density towards the leading edge of the pulse. This can be seen in the region of the pulse near R = 0. The portion of the pulse on which the cross correlation measurements were performed is the section beneath the white dashed line and there is excellent agreement between the simulations and the measurements.
In conclusion we have demonstrated that electron/laser pulse cross correlation measurements provide the ability to probe the spatio-temporal charge density distribution of non relativistic ultrashort electron pulses with excellent sensitivity. Using this technique, electron pulse propagation dynamics were studied and compared with analytical and numerical models. The results show that the pulses develop a relatively uniform charge density as they propagate and are in excellent agreement with predictions. The effect of focusing on the charge density distribution of ultrashort electron pulses was also studied and simulations of the focusing induced charge density redistribution were presented. These results provide valuable insight into evolution of ultrashort electron pulses which could potentially be used to improve current electron pulse compression techniques which depend sensitively on the details of the electron charge density distribution. Finally, with only slight modifications to the techniques presented here, a measurement of the complete three dimensional charge density distribution of ultrashort electron pulses would be possible.
This work was supported by the Canada Foundation for Innovation (CFI), Canada Research Chairs (CRC) program, Fonds de Recherche du Québec: Nature et Technologies (FQRNT) and the Natural Sciences and Engineering Research Council of Canada (NSERC). V.M. and R.P.C. gratefully acknowledge the support of NSERC CGS-D and PGS-D fellowships.
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