Session VO03: Beams: Plasma Wakefield Acceleration (PWFA)

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Plasma-based accelerators have the potential to drastically shrink the size and cost of conventional electron accelerators. To be useful for applications, however, the accelerator must preserve the emittance of the accelerated beam (the witness beam). The primary mode of emittance growth in a plasma accelerator is chromatic phase spreading, which can occur via multiple mechanisms. These mechanisms must be managed simultaneously to preserve the beam emittance at the levels required by colliders and light sources. Here we present a general theory for the nonlinear blowout regime that describes the chromatic emittance growth within a plasma-based accelerator due to the combination of witness beam-plasma mismatch and transverse offset between the witness beam and the wake driver. We include the effects of the plasma source density ramps, the energy gain of the beam, the loading of the wake, and the initial energy distribution of the beam. From this theory we derive tolerances on the beam offset and mismatch necessary for collider and light source applications.   

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The self-modulation of a long proton bunch, which is used for Advanced WAKefield Experiment (AWAKE)\footnote{P. Muggli et al. (AWAKE Collaboration), Plasma Phys. Controlled Fusion 60, 014046 (2018).} at CERN, can be seeded by a sharply rising bunch front, a relativistic ionization front or a short preceding electron bunch. % The electron bunch seeding scheme decouples seed wakefield parameters from those of the proton bunch. % It is therefore essential to determine the evolution of the electron bunch and how it generates wakefields in the 5-10\,MV/m range over meter scale propagation distances necessary for effective seeding. % With a low energy bunch (20\,MeV), electrons lose a large fraction of their energy. % That leads to significant evolution of the bunch longitudinal distribution and thus of the wakefields' phase. % This evolution makes the investigation of transverse matching condition to the linear wakefields complicated. % In this context, we search for a condition for the stable generation of the seed wakefields using Particle-In-Cell code FBPIC\footnote{R. Lehe et al., Comput. Phys. Comm. 203, 66-82 (2016)}. % We will present detailed simulation results and their implication for wakefields' seeding. %   

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The PWFA has emerged as a promising technology for compact accelerator stages in future advanced light-source or linear colliders. Full scale 3D simulations based on the quasi-static particle-in-cell (PIC) method are an indispensable tool for efficiently simulating complex and nonlinear physics involved in PWFA. We describe recent advances for the code QuickPIC. These include the continued development and testing of a version of QuickPIC called QPAD that expands the fields in an expansion of azimuthal harmonics that is truncated at an arbitrary order. We also describe progress in adding mesh refinement to enable simulations using witness beams with spot sizes several orders of magnitude small than the accelerator structure. The quasi-static equations are solved self-consistently on both the refined region and the entire computational domain, and the field solutions are used to advance particles following the standard QuickPIC workflow. Preliminary results will be presented. We also describe how QuickPIC has been combined with POPAS, a parallel optimization toolbox developed at ANL, to efficiently find the optimal parameters for accelerator stages based on PWFA. Preliminary results show that the toolbox can find the optimal Twiss parameters to preserve the witness beam emittance in a PWFA stage.   

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We study through numerical simulations the effect of a linear plasma density gradient on the self-modulation of a long proton bunch in plasma. % Numerical simulations give access to the details of the self-modulation process and wakefields along the bunch and along the plasma. % We obtain characteristics such as the bunch modulation frequency and wakefields frequency and phase evolution, as well as the charge of the modulated bunch. % These could then be compared to experimental results that can only be acquired at the end of the 10\,m plasma\footnote{F. Braunmueller and T. Nechaeva et al. (AWAKE Collaboration), to be submitted}. % In addition, they show the effect of the density gradient on the wakefields amplitude, a quantity so far not measured in experiments. % We use parameters that are similar to those of the AWAKE experiment\footnote{P. Muggli et al. (AWAKE Collaboration), Plasma Physics and Controlled Fusion, 60(1) 014046 (2017)}. % Detailed results will be presented. %   

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Acceleration of positron beams in a plasma-based accelerator is a highly-challenging task. However, in order to realize a plasma-based linear collider, accelerating a positron bunch with high charge and efficiency, while maintaining a low emittance and a sub-percent-level energy spread, is required. Recently, a plasma-based positron acceleration scheme was proposed in which a wake suitable for the acceleration and transport of positrons is produced in a plasma column by means of an electron drive beam [Diederichs et al., PRAB 22, 081301 (2019)]. In this talk, we present a study of beamloading for a positron beam in this type of wake. We demonstrate via particle-in-cell simulations that acceleration of high-quality positron beams is possible, and we discuss a possible path to achieve collider-relevant parameters.   

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The Hosing Instability (HI) of a charged particle bunch in a plasma is a fundamental interaction mode. It has often been posited as imposing a limitation on beam and plasma parameters with which large energy gain can be achieved in plasma-based particle accelerators. We analyze time-resolved images of a 250 ps-long proton bunch after propagation in a 10 m-long plasma with density in the $10^{13}-10^{14}$ cm$^{-3}$ range. The bunch experiences symmetric, self-modulation of its envelope\footnote{AWAKE Collaboration, Phys.Rev.Lett.122, 054802(2019);M. Turner et al.(AWAKE Collaboration), Phys.Rev.Lett.122, 054801(2019)} along the plasma. However, non-axisymmetric events, where the centroid of the proton bunch is periodically oscillating across its propagation axis, are also observed. We attempt to determine whether these events follow predictions for HI from theory\footnote{C. Schroeder et al., Phys.Rev.E 86, 026402(2013)} and simulations. We also study the effect of misalignment between the proton bunch and the $\sim$1 mm-radius plasma column. Detailed experimental results obtained in the AWAKE experiment\footnote{P. Muggli et al.(AWAKE Collaboration), Plasma Phys. \& Contr.Fus., 60(1) 014046(2017)}, their analysis and comparison with theory and simulation results will be presented.   

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The hosing instability is still one of the main feasibility risks for plasma wakefield accelerator (PWFA) concepts. Though potential mitigation methods have been discussed extensively in the blow-out regime, less attention has been devoted to hosing in the long-beam, overdense regime\footnote{C. B. Schroeder {\it et al.}, Phys. Rev. E {\bf 86}, 026402 (2012)}$^,$\footnote{J. Vieira {\it et al.}, Phys. Rev. Lett. {\bf 112}, 205001 (2014)}$^,$\footnote{R. Lehe {\it et al.}, Phys. Rev. Lett. {\bf 119}, 244801 (2017)}, which is relevant for PWFA concepts using a long drive bunch and geared towards high-energy physics applications.\\ This work presents a fuller picture of the physics of beam hosing in the overdense regime by focusing on the development of the instability when the initial centroid oscillates at a wavelength different than the plasma wavelength $\lambda_p$. We use theory and particle-in-cell simulations with OSIRIS to show that the growth rate for beam hosing is a function of the centroid perturbation wavelength with a maximum at $\lambda_p$ (similarly to laser hosing\footnote{B. J. Duda {\it et al.}, Phys. Rev. Lett. {\bf 83}, 1978 (1999)}), and that this property can be exploited to conditionally achieve damping instead of amplification of the centroid oscillation.   

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In plasma wakefield acceleration, the witness beam's emittance needs to be preserved when it propagates through a plasma stage. The plasma includes density ramps at both the entrance and the exit. Using the Wentzel-Kramers-Brillouin (WKB) solution of a single particle's motion, analytical expressions for the evolution of the beam emittance and the Twiss parameters in an arbitrary adiabatic plasma profile are provided neglecting the acceleration of the beam inside the plasma. It is shown that the beam emittance can be preserved under the matching condition even when the beam has an initial energy spread. It is also shown that the emittance growth for an unmatched beam is minimized when it is focused to the same vacuum plane for a matched beam. The emittance evolution from 3D QuickPIC simulation results agree well with the theoretical results. The theoretical and simulation results are also used to analyze parameters for a proposed experiment on the FACET II facility.   

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Self-modulation of a long, relativistic, charged particle bunch in a dense plasma is an interesting beam/plasma interaction mode and a means to drive large amplitude wakefields ($>$1\,GV/m) for particle acceleration.\footnote{ N. Kumar et al., Phys. Rev. Lett. 104, 255003 (2010)} % By measuring the effect of transverse wakefields on the drive proton bunch, we learn about the development of transverse wakefields over the first 4\,m of plasma. % By measuring energy gain by externally injected electrons, we learn about longitudinal wakefields over the last 5\,m of plasma. % Combining these results for various experimental parameters, we conclude that experimental results are consistent with simulation ones that show the SM process saturates before the end of the 10\,m plasma.\footnote{M. Turner, P. Muggli et al., (AWAKE Collaboration) submitted to PR-AB (2020)} % This is a key piece of information for future AWAKE experiments\footnote{P. Muggli et al., (AWAKE Collaboration) Plasma Phys. and Contr. Fus., 60(1) 014046 (2017)} that will use a first, 10\,m-long plasma as self-modulator. % Acceleration will occur in a second plasma. % We present detailed experimental and simulation results. %   

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A proton bunch propagating in plasma, with its length much longer than the plasma wavelength, undergoes a self-modulation (SM) process that turns it into a train of micro-bunches with modulation at the plasma frequency\footnote{AWAKE Collaboration, Phys. Rev. Lett. 122, 054802 (2019)}. For a plasma wakefield accelerator with external electron injection, excellent control of the phase of the SM is a key pre-requisite. In the AWAKE experiment, a 10\,m-long plasma is formed by a relativistic laser ionization front (RIF), co-propagating with the proton bunch at a variable position within or ahead of the bunch. We study time-resolved images of the self-modulated bunch for plasma densities around 10$^{14}$\,cm$^{-3}$. Depending on the position of the RIF, the SM may evolve from noise as an instability or may be triggered by the RIF, and be called seeded SM. While in the first case the phase is expected to be random, the second promises phase reproducibility. We determine the timing/phasing of the SM and its reproducibility for different relative positions of the RIF within the bunch. Detailed experimental results will be presented.   

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The self-modulation (SM) of a long proton bunch in plasma was recently demonstrated experimentally\footnote{AWAKE Collaboration, Phys. Rev. Lett. 122, 054802 (2019), M. Turner et al. (AWAKE Collaboration), Phys. Rev. Lett. 122, 054801 (2019)} at AWAKE\footnote{P. Muggli et al. (AWAKE Collaboration), Plasma Physics and Controlled Fusion, 60(1) 014046 (2017)}. Time-resolved images of the modulated proton bunch after 10\,m of plasma reveal many details of the SM process, especially near its seed point, the start of the modulation. We look at micro-bunches and defocused proton regions along the bunch acquired with different experimental parameters (seed wakefields' amplitude, plasma density, plasma density gradient, beam density, etc.) to study the wakefields they have experienced and that the bunch is driving. Understanding the self-modulation process and wakefields' development is not only interesting, but also important for future experiments that will rely on a self-modulated proton bunch to drive wakefields in a second plasma, an accelerator. Analysis of the experimental results and comparison with theory and simulation results will be presented.   

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Current modeling for laser-plasma accelerators is often performed with the help of particle-in-cell (PIC) codes. While accurate, these codes require to resolve the smallest spatial/temporal scales, usually corresponding to the laser wavelength/frequency. As a result, full PIC simulations are computationally expensive. Reduced models such as the ponderomotive guiding center solver (PGC) can overcome this limitation and provide significant speedup. This technique, for example, enables computational speedups of several orders of magnitude for the modeling of the seeded self-modulation instability (SSM), which is the core principle of the AWAKE experiment at CERN. Here, we present 3d simulations of the full 10m AWAKE experiment using the massively parallel, fully relativistic PIC code OSIRIS with a self-consistent ionization model for PGC to model the SSM. We compare with results obtained from simulations using half-cut proton bunches. We also discuss the growth of hosing instability arising from misalignment between the laser pulse and the proton beam.   

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The AWAKE experiment [1] relies on the self-modulation of a long proton bunch in plasma [2] to effectively drive wakefields and accelerate an externally injected electron bunch to GeV-level energies [3]. In future experiments we will use a first 18\,MeV, short electron bunch placed ahead of the proton bunch to seed self-modulation of the entire bunch in a first plasma section. To accelerate a second, 150\,MeV bunch with narrow energy spread and preserved incoming emittance, we will exploit full blow-out of plasma electrons, loading of wakefields and beam matching to the plasma ion column [4]. Parameters of both beams must be adjusted to produce suitable seed and accelerating wakefields. We will present the requirements for the two bunches to effectively seed the self-modulation process and to produce a high-quality, high-energy electron bunch. We will also discuss necessary preliminary experimental studies, diagnostics and experimental setup to achieve these goals.\\ $[1]$P. Muggli et al. (AWAKE Collaboration), Plasma Phys. and Contr. Fus., 60(1) 014046 (2017)\\ $[2]$M. Turner et al. (AWAKE Collaboration), Phys. Rev. Lett. 122, 054801 (2019)\\ $[3 ]$AWAKE Collaboration, Nature 561, 363 (2018)\\ $[4]$V.B. Olsen et al., Phys. Rev. Accel. Beams 21, 011301 (2018)\\   

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Wakefield acceleration schemes are typically limited either by dephasing or depletion of the driver. The AWAKE project at CERN avoids these issues by using the SPS proton beam to accelerate an externally injected electron bunch, paving the way to high energy gain in a single stage. However, such a scheme brings with it additional challenges, not least the merging of the electron and proton beamlines. Simulations play a vital role in understanding the fundamental physics which set the tolerances for injection. We here present recent results on the witness constraints for an accelerated beam suitable for applications, and the development in simulation tools which was necessary to allow this work.   

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The concept of using plasma lenses to focus high energy electron beams is old, yet it has seen little use in practice. This is in part because the many varieties that have been considered are often limited by fundamental constraints that can lead to unmanageable aberrations in the focal quality. Here we present a largely unexplored and underutilized incarnation of the plasma lens: the underdense plasma lens (UPL). Unlike most plasma lenses, the UPL operates passively in a regime where the plasma density is lower than the driving electron beam density, resulting in the nonlinear blowout of plasma electrons and the formation of a wake behind the head of the electron beam. The UPL can produce focusing strengths orders of magnitude stronger than conventional quadrupole magnets found in accelerators while being orders of magnitude more compact. In addition, the focusing is linear and axisymmetric, allowing for aberration-free focusing. This type of electron beam optic is an attractive solution to the problem of matching beams to plasma wakefield accelerators. It may also find use as a final focus device for applications such as a future lepton collider or in high energy energy density physics research. Experimental plans to study the UPL at SLAC’s FACET-II facility will be presented.