Terawatt-scale sub-10-fs laser technology - key to generation of GW-level attosecond pulses in X-ray free electron laser

We propose a technique for the production of attosecond X-ray pulses which is based on the use of X-ray SASE FEL combined with a femtosecond laser system. A few-cycle optical pulse from a Ti:sapphire laser interacts with the electron beam in a two-period undulator resonant to 800 nm wavelength and produces energy modulation within a slice of the electron bunch. Following the energy modulator the electron beam enters the X-ray undulator and produces SASE radiation. Due to energy modulation the frequency is correlated to the longitudinal position within the few-cycle-driven slice of SASE radiation pulse. The largest frequency offset corresponds to a single-spike pulse in the time domain which is confined to one half-oscillation period near the central peak electron energy. The selection of single-spike pulses is achieved by using a crystal monochromator after the X-ray undulator. Our studies show that the proposed technique is capable to produce 300 attoseconds long single pulses with GW-level output power in the 0.1 nm wavelength range, and is applicable to the European X-Ray Laser Project XFEL and the Linac Coherent Light Source at SLAC.Comment: 19 pages, 13 figure

A new technique to generate 100 GW-level attosecond X-ray pulses from the X-ray SASE FELs

We propose a scheme for generation of single 100 GW 300-as pulse in the X-ray free electron laser with the use of a few cycles optical pulse from Ti:sapphire laser system. Femtosecond optical pulse interacts with the electron beam in the two-period undulator resonant to 800 nm wavelength and produces energy modulation within a slice of the electron bunch. Following the energy modulator the electron beam enters the first part of the baseline gap-adjustable X-ray undulator and produces SASE radiation with 100 MW-level power. Due to energy modulation the frequency is correlated to the longitudinal position within the few-cycle-driven slice of the SASE radiation pulse. The largest frequency offset corresponds to a single-spike pulse in the time domain which is confined to one half-oscillation period near the central peak electron energy. After the first undulator the electron beam is guided through a magnetic delay which we use to position the X-ray spike with the largest frequency offset at the "fresh" part of the electron bunch. After the chicane the electron beam and the radiation produced in the first undulator enter the second undulator which is resonant with the offset frequency. In the second undulator the seed radiation at reference frequency plays no role, and only a single (300 as duration) spike grows rapidly. The final part of the undulator is a tapered section allowing to achieve maximum output power 100-150 GW in 0.15 nm wavelength range. Attosecond X-ray pulse is naturally synchronized with its fs optical pulse which reveals unique perspective for pump-probe experiments with sub-femtosecond resolution.Comment: 14 pages, 13 fig

A simple method for the determination of the structure of ultrashort relativistic electron bunches

In this paper we propose a new method for measurements of the longitudinal profile of 100 femtosecond electron bunches for X-ray Free Electron Lasers (XFELs). The method is simply the combination of two well-known techniques, which where not previously combined to our knowledge. We use seed 10-ps 1047 nm quantum laser to produce exact optical replica of ultrafast electron bunches. The replica is generated in apparatus which consists of an input undulator (energy modulator), and the short output undulator (radiator) separated by a dispersion section. The radiation in the output undulator is excited by the electron bunch modulated at the optical wavelength and rapidly reaches 100 MW-level peak power. We then use the now-standard method of ultrashort laser pulse-shape measurement, a tandem combination of autocorrelator and spectrum (FROG -- frequency resolved optical gating). The FROG trace of the optical replica of electron bunch gives accurate and rapid electron bunch shape measurements in a way similar to a femtosecond oscilloscope. Real-time single-shot measurements of the electron bunch structure could provide significant information about physical mechanisms responsible for generation ultrashort electron bunches in bunch compressors. The big advantage of proposed technique is that it can be used to determine the slice energy spread and emittance in multishot measurements. It is possible to measure bunch structure completely, that is to measure peak current, energy spread and transverse emittance as a function of time. We illustrate with numerical examples the potential of the proposed method for electron beam diagnostics at the European X-ray FEL.Comment: 41 pages, 18 figure

Femtosecond Resolution Experiments at Third-Generation Light Sources: a Concept Based on the Statistical Properties of Synchrotron Radiation

The paper describes a new concept of visible pump/X-ray probe/slow detector experiments that could be performed at third-generation synchrotron light sources. We propose a technique that would allow time resolution up to femtosecond capabilities to be recovered from a long (100 ps) X-ray probe pulse. The visible pump pulse must be as short as the desired time resolution. The principle of operation of the proposed pump-probe scheme is essentially based on the statistical properties of the synchrotron radiation. These properties are well known in statistical optics as properties of completely chaotic polarized light. Our technique utilizes the fact that, for any synchrotron light beam there exist some characteristic time (coherence time), which determines the time-scale of the random fluctuations. The typical coherence time of soft X-ray synchrotron light at the exit of monochromator is in the femtosecond range. An excited state is prepared with a pump pulse and then projected with a probe pulse onto a final ion state. The first statistical quantity of interest is the variance of the number of photoelectrons detected during synchrotron radiation pulse. The statistics of concern are defined over an ensemble of synchrotron radiation pulses. From a set of variances measured as a function of coherence time (inversely proportional to monochromator bandwidth) it is possible to reconstruct the femtosecond dynamical process.Comment: 54 pages, 20 figure

Efficient frequency doubler for the soft X-ray SASE FEL at the TESLA Test Facility

This paper describes an effective frequency doubler scheme for SASE free electron lasers. It consists of an undulator tuned to the first harmonic, a dispersion section, and a tapered undulator tuned to the second harmonic. The first stage is a conventional soft X-ray SASE FEL. Its gain is controlled in such a way that the maximum energy modulation of the electron beam at the exit is about equal to the local energy spread, but still far away from saturation. When the electron bunch passes through the dispersion section this energy modulation leads to effective compression of the particles. Then the bunched electron beam enters the tapered undulator and produces strong radiation in the process of coherent deceleration. We demonstrate that a frequency doubler scheme can be integrated into the SASE FEL at the TESLA Test Facility at DESY, and will allow to reach 3 nm wavelength with GW-level of output peak power. This would extend the operating range of the FEL into the so-called water window and significantly expand the capabilities of the TTF FEL user facility.Comment: 17 pages, 13 figure

Transverse self-fields within an electron bunch moving in an arc of a circle

As a consequence of motions driven by external forces, self-fields (which are different from the static case) originate within an electron bunch. In the case of magnetic external forces acting on an ultrarelativistic beam, the longitudinal self-interactions are responsible for CSR (Coherent Synchrotron Radiation)-related phenomena, which have been studied extensively. On the other hand, transverse self-interactions are present too. At the time being, existing theoretical analysis of transverse self-forces deal with the case of a bunch moving along a circular orbit only, without considering the situation of a bending magnet with a finite length. In this paper we propose an electrodynamical analysis of transverse self-fields which originate, at the position of a test particle, from an ultrarelativistic electron bunch moving in an arc of a circle. The problem will be first addressed within a two-particle system. We then extend our consideration to a line bunch with a stepped density distribution, a situation which can be easily generalized to the case of an arbitrary density distribution. Our approach turns out to be also useful in order to get a better insight in the physics involved in the case of simple circular motion and in order to address the well known issue of the partial compensation of transverse self-force.Comment: 23 pages, 14 figure

Roadmap of internationalization : development and implementation of an entry strategy for the Portuguese Beachwear Company Miitik

Miitik, a premium beachwear Start-up, seeks international growth to increase sales. Currently, the company mainly operates on the Portuguese market, but already gained some international experience by sporadically exporting to customers in Luxembourg and the United Kingdom. However, the Start-up is lacking a strategic approach in order to target international markets. Bearing this in mind, the company would like to find out about potential countries and is interested in a detailed entry strategy to overcome challenges small companies face in the process of internationalization. The thesis provides a deep study of relevant measures for the formulation of an entry strategy. Analyzing macro-economical factors helped to assess the potential of the chosen market Germany. The literature on internationalization suggests a four-step approach to develop an entry strategy. Based on the findings and the capabilities of the company, direct exports were selected as the most suitable entry mode. Further recommendations regarding the creation of brand awareness and distribution channels were drawn.Miitik é uma marca premium de fatos de banho que procura alcançar o mercado internacional para aumentar as suas vendas. Actualmente, a empresa opera no mercado Portugês embora já tenha ganho alguma experiência internacional ao vender para clientes no Luxemburgo e no Reino Unido. Contudo, a Start-up não apresenta uma estratégia para chegar aos mercados internacionais. Desta forma, a empresa pretende saber quais os potenciais países e qual a estratégia de entrada no mercado para ultrapassar os desafios que pequenas empresas enfrentam no processo de internacionalização. Esta dissertação apresenta um estudo pormenorizado relativamente às melhores medidas para formular uma estratégia de entrada no mercado. A análise aos factores da envolvente macro-económica permitiu avaliar o potencial do mercado escolhido, o mercado alemão. A literatura relativa à internacionalização sugere quatro passos para desenvolver uma estratégia de entrada. Tendo em conta o estudo realizado e as capacidades da empresa, exportação é a melhor abordagem à entrada no mercado. Ainda são consideradas recomendações relativas à estratégia de notoriedade e percepção da marca e aos canais de distribuição

Scheme for Attophysics Experiments at a X-ray SASE FEL

We propose a concept for production of high power coherent attosecond pulses in X-ray range. An approach is based on generation of 8th harmonic of radiation in a multistage HGHG FEL (high gain high harmonic free electron laser) configuration starting from shot noise. Single-spike phenomena occurs when electron bunch is passed through the sequence of four relatively short undulators. The first stage is a conventional "long" wavelength (0.8 nm) SASE FEL which operates in the high-gain linear regime. The 0.1 nm wavelength range is reached by successive multiplication (0.8 nm $\to$ 0.4 nm $\to$ 0.2 nm $\to$ 0.1 nm) in a stage sequence. Our study shows that the statistical properties of the high-harmonic radiation from the SASE FEL, operating in linear regime, can be used for selection of radiation pulses with a single spike in time domain. The duration of the spikes is in attosecond range. Selection of single-spike high-harmonic pulses is achieved by using a special trigger in data acquisition system. The potential of X-ray SASE FEL at TESLA at DESY for generating attosecond pulses is demonstrated. Since the design of XFEL laboratory at TESLA is based on the use of long SASE undulators with tunable gap, no special place nor additional FEL undulators are required for attophysics experiments. The use of a 10 GW-level attosecond X-ray pulses at X-ray SASE FEL facility will enable us to track processes inside atoms.Comment: 21 pages, 12 figures, submitted to Optics Communication