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After a summary of relevant comments and recommendations from various reports over the last ten years, this paper examines the modeling needs in accelerator physics, from the modeling of single beams and individual accelerator elements, to the realization of virtual twins that replicate all the complexity to model a particle accelerator complex as accurately as possible. We then discuss cutting-edge and emerging computing opportunities, such as advanced algorithms, AI/ML and quantum computing, computational needs in hardware, software performance, portability and scalability, and needs for scalable I/O and in-situ analysis. Considerations of reliability, long-term sustainability, user support and training are considered next, before discussing the benefits of ecosystems with integrated workflows based on standardized input and output, and with integrated frameworks and data repositories developed as a community. Last, we highlight how the community can work more collaboratively and efficiently through the development of consortia and centers, and via collaboration with industry., Comment: contribution to Snowmass 2021

Computer modeling is essential to research on Advanced Accelerator Concepts (AAC), as well as to their design and operation. This paper summarizes the current status and future needs of AAC systems and reports on several key aspects of (i) high-performance computing (including performance, portability, scalability, advanced algorithms, scalable I/Os and In-Situ analysis), (ii) the benefits of ecosystems with integrated workflows based on standardized input and output and with integrated frameworks developed as a community, and (iii) sustainability and reliability (including code robustness and usability).

An overview from the past and an outlook for the future of fundamental laser-plasma interactions research enabled by emerging laser systems.

The nonlinear regime of laser-plasma interaction including both two-plasmon--decay (TPD) and stimulated Raman scattering (SRS) instabilities has been studied in three-dimensional (3-D) particle-in-cell simulations with parameters relevant to the inertial confinement fusion (ICF) experiments. SRS and TPD develop in the same region in plasmas, and the generation of fast electrons can be described accurately with only the full model including both SRS and TPD. The growth of instabilities in the linear stage is found to be in good agreement with analytical theories. In the saturation stage the enhanced low-frequency density perturbations driven by the daughter waves of the SRS sidescattering can saturate the TPD and consequently inhibit the fast-electron generation. The fast-electron flux in 3-D modeling is up to an order of magnitude smaller than previously reported in 2-D TPD simulations, bringing it close to the results of ICF experiments., Comment: 5 pages, 4 figures, 1 table

The scaling laws for laser wakefield acceleration in the nonlinear, self-guided regime [Lu et al. Phys. Rev. Spec. Top. Accel. Beams 10, 061301 (2007)] are examined in detail using the quasi-3D version of the particle-in-cell code OSIRIS. We find that the scaling laws continue to work well as the plasma density is reduced while the normalized laser amplitude is kept fixed. For fixed laser energy, the energy gain of an isolated bunch of electrons can be improved with some loss in the bunch charge by shortening the normalized pulse length until self-guiding no longer occurs, and through the use of asymmetric longitudinal profiles with rapid rise times. For example, without any external guiding a 15 J,.8\mu m laser with a pulse length of 46 fs (39 fs) is found to generate a quasi-mono-energetic bunch of 355pC (227pC) with a max energy of 3.25 (4.04) GeV with an acceleration distance of 2.43 cm (3.08cm). Furthermore, a bunch with 39.4pC and a maximum energy 4.6 GeV is produced for an asymmetric laser with a rapid rise time. Studies for 30 J and 100 J lasers are also presented.

We show via particle-in-cell simulations that small normalized magnetic fields ($\omega_c/\omega_p \ll 1$) applied perpendicularly to a light wave can significantly modify the evolution of backward stimulated Raman scattering (SRS) in the kinetic regime. The presence of the magnetic field increases the threshold for kinetic inflation and decreases the amount of reflectivity when SRS is driven significantly above threshold. Analysis indicates this arises because trapped electrons are accelerated as they surf across the wave, leading to the continual dissipation of the electron plasma waves over a wider range of wave amplitudes. The simulation parameters are directly relevant for SRS in inertial confinement fusion devices and indicate that approximately 30 Tesla magnetic fields might significantly reduce SRS backscatter.

The development of a directional, small-divergence, and short-duration picosecond x-ray probe beam with an energy greater than 50 keV is desirable for high energy density science experiments. We therefore explore through particle-in-cell (PIC) computer simulations the possibility of using x-rays radiated by betatron-like motion of electrons from a self-modulated laser wakefield accelerator as a possible candidate to meet this need. Two OSIRIS 2D PIC simulations with mobile ions are presented, one with a normalized vector potential a0 = 1.5 and the other with an a0 = 3. We find that in both cases direct laser acceleration (DLA) is an important additional acceleration mechanism in addition to the longitudinal electric field of the plasma wave. Together these mechanisms produce electrons with a continuous energy spectrum with a maximum energy of 300 MeV for a0 = 3 case and 180 MeV in the a0 = 1.5 case. Forward-directed x-ray radiation with a photon energy up to 100 keV was calculated for the a0 = 3 case and up to 12 keV for the a0 = 1.5 case. The x-ray spectrum can be fitted with a sum of two synchrotron spectra with critical photon energy of 13 and 45 keV for the a0 of 3 and critical photon energy of 0.3 and 1.4 keV for a0 of 1.5 in the plane of polarization of the laser. The full width at half maximum divergence angle of the x-rays was 62 x 1.9 mrad for a0 = 3 and 77 x 3.8 mrad for a0 = 1.5.

Many current laser wakefield acceleration (LWFA) experiments are carried out in a regime where the laser pulse length is on the order of or longer than the wake wavelength and where ionization injection is employed to inject electrons into the wake. In these experiments, the trapped electrons will co-propagate with the longitudinal wakefield and the transverse laser field. In this scenario, the electrons can gain a significant amount of energy from both the direct laser acceleration (DLA) mechanism as well as the usual LWFA mechanism. Particle-in-cell (PIC) codes are frequently used to discern the relative contribution of these two mechanisms. However, if the longitudinal resolution used in the PIC simulations is inadequate, it can produce numerical heating that can overestimate the transverse motion, which is important in determining the energy gain due to DLA. We have therefore carried out a systematic study of this LWFA regime by varying the longitudinal resolution of PIC simulations from the standard, best-practice resolution of 30 points per laser wavelength to four times that value and then examining the energy gain characteristics of both the highest-energy electrons and the bulk electrons. By calculating the contribution of DLA to the final energies of the electrons produced from the LWFA, we find that although the transverse momentum and oscillation radii are over-estimated in the lower-resolution simulations, this over-estimation does not lead to artificial energy gain by DLA. Rather, the DLA contribution to the highest-energy electrons is larger in the higher-resolution cases because the DLA resonance is better maintained. Thus, even at the highest longitudinal resolutions, DLA contributes a significant portion of the energy gained by the highest-energy electrons and also contributes to accelerating the bulk of the charge in the electron beam produced by the LWFA., Comment: 12 pages. 5 figures

In this proceeding, we show that when the drive laser pulse overlaps the trapped electrons in a laser wakefield accelerator (LWFA), those electrons can gain energy from direct laser acceleration (DLA) over extended distances despite the evolution of both the laser and the wake. Through simulations, the evolution of the properties of both the laser and the electron beam is quantified, and then the resonance condition for DLA is examined in the context of this change. We find that although the electrons produced from the LWFA cannot continuously satisfy the DLA resonance condition, they nevertheless can gain a significant amount of energy from DLA., Comment: 2014 Advanced Accelerator Concepts Workshop

We study the long-term evolution (LTE) of plasma wakefields over multiple plasma-electron periods and few plasma-ion periods, much less than a recombination time. The evolution and relaxation of such a wakefield-perturbed plasma over these timescales has important implications for the upper limits of repetition-rates in plasma colliders. Intense fields in relativistic lasers (or intense beams) create plasma wakefields (modes around {\omega}pe) by transferring energy to the plasma electrons. Charged-particle beams in the right phase may be accelerated with acceleration/focusing gradients of tens of GeV/m. However, wakefields leave behind a plasma not in equilibrium, with a relaxation time of multiple plasma-electron periods. Ion motion over ion timescales, caused by energy transfer from the driven plasma-electrons to the plasma-ions can create interesting plasma states. Eventually during LTE, the dynamics of plasma de-coheres (multiple modes through instability driven mixing), thermalizing into random motion (second law of thermodynamics), dissipating energy away from the wakefields. Wakefield-drivers interacting with such a relativistically hot-plasma lead to plasma wakefields that differ from the wakefields in a cold-plasma., Comment: North American Particle Accelerator Conference, Sep 2013, Pasadena, CA, USA (MOPAC10, ISBN 978-3-95450-138-0) http://accelconf.web.cern.ch/accelconf/pac2013/papers/mopac10.pdf 03- Alternative Acceleration Schemes, A23 - Laser-driven Plasma Acceleration, pp.90-92

We analyze the use of a relativistic laser pulse with a controlled frequency chirp incident on a rising plasma density gradient to drive an acceleration structure for proton and light-ion acceleration. The Chirp Induced Transparency Acceleration (ChITA) scheme is described with an analytical model of the velocity of the snowplow at critical density on a pre-formed rising plasma density gradient that is driven by a positive-chirp in the frequency of a relativistic laser pulse. The velocity of the ChITA-snowplow is shown to depend upon rate of rise of the frequency of the relativistic laser pulse represented by $\frac{\epsilon_0}{\theta}$ where, $\epsilon_0 = \frac{\Delta\omega_0}{\omega_0}$ and chirping spatial scale-length, $\theta$, the normalized magnetic vector potential of the laser pulse $a_0$ and the plasma density gradient scale-length, $\alpha$. We observe using 1-D OSIRIS simulations the formation and forward propagation of ChITA-snowplow, being continuously pushed by the chirping laser at a velocity in accordance with the analytical results. The trace protons reflect off of this propagating snowplow structure and accelerate mono-energetically. The control over ChITA-snowplow velocity allows the tuning of accelerated proton energies., Comment: Proceedings of IPAC2012, New Orleans, Louisiana, USA, pp.2654-2656, 07 Accelerator Technology and Main Systems, T25 Lasers, ISBN 978-3-95450-115-1. http://accelconf.web.cern.ch/accelconf/ipac2012/papers/weppd059.pdf

We have investigated the role that the transverse electric field of the laser plays in the acceleration of electrons in a laser wakefield accelerator (LWFA) operating in the quasi-blowout regime through particle-in-cell code simulations. In order to ensure that longitudinal compression and/or transverse focusing of the laser pulse is not needed before the wake can self-trap the plasma electrons, we have employed the ionization injection technique. Furthermore, the plasma density is varied such that at the lowest densities, the laser pulse occupies only a fraction of the first wavelength of the wake oscillation (the accelerating bucket), whereas at the highest density, the same duration laser pulse fills the entire first bucket. Although the trapped electrons execute betatron oscillations due to the ion column in all cases, at the lowest plasma density they do not interact with the laser field and the energy gain is all due to the longitudinal wakefield. However, as the density is increased, there can be a significant contribution to the maximum energy due to direct laser acceleration (DLA) of those electrons that undergo betatron motion in the plane of the polarization of the laser pulse. Eventually, DLA can be the dominant energy gain mechanism over acceleration due to the longitudinal field at the highest densities., Comment: 12 pages, 7 figures

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [A. Lifschitz et al., J. Comp. Phys. 228 (5) (2009) 1803-1814] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion after only the first harmonic. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r-z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r-z and a gridless description in $\phi$. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples, for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.

The relativistically induced transparency acceleration (RITA) scheme of proton and ion acceleration using laser-plasma interactions is introduced, modeled, and compared to the existing schemes. Protons are accelerated with femtosecond relativistic pulses to produce quasimonoenergetic bunches with controllable peak energy. The RITA scheme works by a relativistic laser inducing transparency to densities higher than the cold-electron critical density, while the background heavy ions are stationary. The rising laser pulse creates a traveling acceleration structure at the relativistic critical density by ponderomotively driving a local electron density inflation, creating an electron snowplow and a co-propagating electrostatic potential. The snowplow advances with a velocity determined by the rate of the rise of the laser's intensity envelope and the heavy-ion-plasma density gradient scale length. The rising laser is incrementally rendered transparent to higher densities such that the relativistic-electron plasma frequency is resonant with the laser frequency. In the snowplow frame, trace density protons reflect off the electrostatic potential and get snowplowed, while the heavier background ions are relatively unperturbed. Quasimonoenergetic bunches of velocity equal to twice the snowplow velocity can be obtained and tuned by controlling the snowplow velocity using laser-plasma parameters. An analytical model for the proton energy as a function of laser intensity, rise time, and plasma density gradient is developed and compared to 1D and 2D PIC OSIRIS simulations. We model the acceleration of protons to GeV energies with tens-of-femtoseconds laser pulses of a few petawatts. The scaling of proton energy with laser power compares favorably to other mechanisms for ultrashort pulses.

This is the working summary of the Accelerator Science working group of the Computing Frontier of the Snowmass meeting 2013. It summarizes the computing requirements to support accelerator technology in both Energy and Intensity Frontiers.

Using particle-in-cell simulations, we examine hot electron generation from electron plasma waves excited by stimulated Raman scattering and rescattering in the kinetic regime where the wavenumber times the Debye length (k\lambda_D) is greater than 0.3 for backscatter. We find that for laser and plasma conditions of possible relevance to experiments at the National Ignition Facility (NIF), anomalously energetic electrons can be produced through the interaction of a discrete spectrum of plasma waves generated from SRS (back and forward scatter), rescatter, and the Langmuir decay of the rescatter-generated plasma waves. Electrons are bootstrapped in energy as they propagate into plasma waves with progressively higher phase velocities.

There are many astrophysical and laboratory scenarios where kinetic effects play an important role. These range from astrophysical shocks and plasma shell collisions, to high intensity laser-plasma interactions, with applications to fast ignition and particle acceleration. Further understanding of these scenarios requires detailed numerical modelling, but fully relativistic kinetic codes are computationally intensive, and the goal of one-to-one direct modelling of such scenarios and direct comparison with experimental results is still difficult to achieve. In this paper we discuss the issues involved in performing kinetic plasma simulations of experiments and astrophysical scenarios, focusing on what needs to be achieved for one-to-one direct modeling, and the computational requirements involved. We focus on code efficiency and new algorithms, specifically on parallel scalability issues, namely on dynamic load balancing, and on high-order interpolation and boosted frame simulations to optimize simulation performance. We also discuss the new visualization and data mining tools required for these numerical experiments and recent simulation work illustrating these techniques is also presented., Comment: 10 pages, 5 figures

A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the Particle-In-Cell code OSIRIS., Comment: 5 pages, 2 figures, to appear in Physical Review Letters

We use the quasi-static particle-in-cell code QuickPIC to perform full-scale, one-to-one LWFA numerical experiments, with parameters that closely follow current experimental conditions. The propagation of state-of-the-art laser pulses in both preformed and uniform plasma channels is examined. We show that the presence of the channel is important whenever the laser self-modulations do not dominate the propagation. We examine the acceleration of an externally injected electron beam in the wake generated by 10 J laser pulses, showing that by using ten-centimeter-scale plasma channels it is possible to accelerate electrons to more than 4 GeV. A comparison between QuickPIC and 2D OSIRIS is provided. Good qualitative agreement between the two codes is found, but the 2D full PIC simulations fail to predict the correct laser and wakefield amplitudes., Comment: 5 pages, 5 figures, accepted for publication IEEE TPS, Special Issue - Laser & Plasma Accelerators - 8/2008

Three-dimensional Particle-in-Cell (PIC) simulations with the code QuickPIC are used to illustrate the typical accelerating structures associated with the interaction of an intense laser beam with an underdense plasma in the blowout regime. Our simulations are performed with an externally injected electron beam, positioned in the region of maximum accelerating gradients. As the laser propagates in the plasma, almost complete electron cavitation occurs, leading to the generation of accelerating fields in excess of 1 GeV/cm., Comment: 2 pages, 1 figure, accepted for publication IEEE TPS Special Issue Images in Plasma Science

The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for Laser WakeField Acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample Particle-In-Cell (PIC) simulation of a 30f sec, 200T W laser interacting with a 0.75cm long plasma with density 1.5*10^18 cm^-3 to produce an ultra-short (10f s) mono-energetic bunch of self-injected electrons at 1.5 GeV with 0.3nC of charge. For future higher-energy accelerator applications we propose a parameter space, that is distinct from that described by Gordienko and Pukhov [Physics of Plasmas 12, 043109 (2005)] in that it involves lower densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high., Comment: 22 pages, 5 figures

The results from 2.5-dimensional Particle-in-Cell simulations for the interaction of a picosecond-long ignition laser pulse with a plasma pellet of 50-$\mu m$ diameter and 40 critical density are presented. The high density pellet is surrounded by an underdense corona and is isolated by a vacuum region from the simulation box boundary. The laser pulse is shown to filament and create density channels on the laser-plasma interface. The density channels increase the laser absorption efficiency and help generate an energetic electron distribution with a large angular spread. The combined distribution of the forward-going energetic electrons and the induced return electrons is marginally unstable to the current filament instability. The ions play an important role in neutralizing the space charges induced by the the temperature disparity between different electron groups. No global coalescing of the current filaments resulted from the instability is observed, consistent with the observed large angular spread of the energetic electrons., Comment: 9 pages, 6 figures, to appear in Physics of Plasmas (May 2006)

A three-dimensional viscous structured/unstructured hybrid scheme has been developed for numerical computation of high Reynolds number turbomachinery flows. The procedure allows an efficient structured solver to be employed in the densely clustered, high aspect-ratio grid around the viscous regions near solid surfaces, while employing an unstructured solver elsewhere in the flow domain to add flexibility in mesh generation. Test results for an inviscid flow over an external transonic wing and a Navier-Stokes flow for an internal annular cascade are presented.

Three-dimensional flow fields inside the Consortium impeller were analyzed with a Navier-Stokes code. The numerical results at the design and off-design conditions are compared with the experimental data.