Analytical model for the uncorrelated emittance evolution of externally injected beams in plasma-based accelerators

This article introduces an analytical formalism for the calculation of the evolution of beam moments and the transverse emittance for beams which are externally injected into plasma wakefield accelerators. This formalism is then applied to two scenarios with increasing complexity - a single beam slice without energy gain and a single beam slice with energy gain, both propagating at a fixed co-moving position behind the driver. The obtained results are then compared to particle-in-cell (PIC) simulations as well as results obtained using an semi-analytic numerical approach (SANA). We find excellent agreement between results from the analytical model and from SANA and PIC

Theoretical and numerical studies on the transport of transverse beam quality in plasma-based accelerators

This work examines effects, which impact the transverse quality of electron-beams in plasma-based accelerators, by means of theoretical and numerical methods. Plasma-based acceleration is a promising candidate for future particle accelerator technologies. In plasma-based acceleration, highly intense laser beams or high-current relativistic particle beams are focused into a plasma to excite plasma-waves with extreme transverse and longitudinal electric fields. The amplitude of these fields exceed with 10-100 GV/m the ones in today’s radio-frequency accelerators by several orders of magnitude, hence, in principle allowing for accordingly shorter and cheaper accelerators based on plasma. Despite the tremendous progress in the recent decade, beams from plasma accelerators are not yet achieving the quality as demanded for pivotal applications of relativistic electron-beams, e.g. free-electron lasers (FELs).Studies within this work examine how the quality can be optimized in the production of the beams and preserved during the acceleration and transport to the interaction region. Such studies cannot be approached purely analytical but necessitate numerical methods, such as the Particle-In-Cell (PIC) method, which can model kinetic, electrodynamic and relativistic plasma phenomena. However, this method is computationally too expensive for parameter-scans in three-dimensional geometries. Hence, a quasi-static PIC code was developed in connection with this work, which is significantly more effective than the full PIC method for a class of problems in plasma-based acceleration.The evolution of the emittance of beams which are injected into plasma modules was studied in this work by means of theoretical and the above numerical methods. It was shown that the beam parameters need to be matched accurately into the focusing plasma-channel in order to allow for beam-quality preservation. This suggested that new extraction and injection-techniques are required in staged plasma-acceleration concepts if the advantage of the short overall acceleration distance is to be sustained. Such a novel extraction method with tapered plasma-to-vacuum transitions was studied and found that it does not only facilitate the extraction but also is indispensable if beams need to be captured by beam-optics in order to be transported e.g. to some interaction region

150 years of Maxwell's (other) equations and application to plasma wakefield acceleration

In 1867, just two years after laying the foundations of electromagnetism, J. Clerk Maxwell presented a fundamental paper on gas dynamics, in which he described the evolution of the gas in terms of certain "moments" of its velocity distribution function. This inspired Ludwig Boltzmann to formulate his famous kinetic equation, from which followed the H-theorem and the connection with entropy. The present talk celebrates the 150th anniversary of the publication of Maxwell's formalism, and discusses how its generality and adaptability enable it to play a key role in efficient modeling of electron beams in plasma wakefield acceleration

Erratum: Great moments in kinetic theory: 150 years of Maxwell's (other) equations

In 1867, just two years after laying the foundations of electromagnetism,J. Clerk Maxwell presented a fundamental paper on kinetic gas theory, inwhich he described the evolution of the gas in terms of certain‘moments’ofits velocity distribution function. This inspired Ludwig Boltzmann to for-mulate his famous kinetic equation, from which followed theH-theorem andthe connection with entropy. On the occasion of the 150th anniversary ofpublication of Maxwellʼs paper, we review the Maxwell–Boltzmann formal-ism and discuss how its generality and adaptability enable it to play a key rolein describing the behaviour of a variety of systems of current interest, in bothgaseous and condensed matter, and in modern-day physics and technologieswhich Maxwell and Boltzmann could not possibly have foreseen. In particular,we illustrate the relevance and applicability of Maxwellʼs formalism to thedynamicfield of plasma-wakefield acceleratio

Great moments in kinetic theory: 150 years of Maxwell's (other) equations (vol 38, 065103, 2017)

In 1867, just two years after laying the foundations of electromagnetism,J. Clerk Maxwell presented a fundamental paper on kinetic gas theory, inwhich he described the evolution of the gas in terms of certain‘moments’ofits velocity distribution function. This inspired Ludwig Boltzmann to for-mulate his famous kinetic equation, from which followed theH-theorem andthe connection with entropy. On the occasion of the 150th anniversary ofpublication of Maxwellʼs paper, we review the Maxwell–Boltzmann formal-ism and discuss how its generality and adaptability enable it to play a key rolein describing the behaviour of a variety of systems of current interest, in bothgaseous and condensed matter, and in modern-day physics and technologieswhich Maxwell and Boltzmann could not possibly have foreseen. In particular,we illustrate the relevance and applicability of Maxwellʼs formalism to thedynamicfield of plasma-wakefield acceleratio

Emittance conservation through tailored plasma ramps in PWFA scenarios

The FLASHForward facility will offer unique capabilities or plasma-wakefield acceleration experiments. It uses high-quality beams from the FLASH accelerator to excite plasma wakefields for the exploration and improvement of novel and existing injection mechanisms.The unique nature of the plasma environment creates several challenges with regard to the conservation of the beam quality, partially due to the strong focusing fields present in the blowout region following a driver beam in the highly nonlinear regime. The beta function of a beam needs to be matched into the wakefield in order to avoid severe growth of the beam emittance - a crucial quality parameter for beam transport, staging and applications.Since the matched beta function is usually at least an order of magnitude lower than easily accessible for conventional accelerator optics, multiple schemes have been proposed to mitigate severe emittance growth by tailoring the plasma profile to adiabatically reduce the beta function to match the plasma wakefield.We will focus on an introduction of these techniques, before presenting initial results from numerical and theoretical analyses for the typical FLASH beam parameter space

Development of a non-numerical model for emittance calculation in external injection scenarios

Witness beam quality preservation (in particular energy spread and emittance) for external injection scenarios in plasma-based accelerators is a crucial requirement for downstream applications such as Free Electron Lasers. Due to the complexity of the beam-plasma interaction, extensive studies of possible mechanisms to preserve beam quality are usually done using particle-in-cell (PIC) simulations.The sheer number of possible properties and simulation settings involved result in time-consuming iterations over the corresponding parameter space. Analytical descriptions of the witness beam evolution could allow for quick optimizations and provide useful limits for further investigations. However, these models are often limited to strong assumptions and not capable of rendering higher order details of the beam evolution along the whole acceleration procedure.The study of instabilities arising from the introduction of beams with non-symmetric distributions can be efficiently tackled by means of an analytic model for the evolution of the statistical moments of the beam distributions, introduced by Mehrling et al. We report on results from the application of this model to the evolution of transverse beam properties of a witness beam in a plasma wakefield, including benchmarks with existing PIC codes such as HiPACE and the SANA model