A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

Lehe, Rémi; Kirchen, Manuel; Andriyash, Igor; Godfrey, Brendan B.; Vay, Jean‐Luc

doi:10.1016/j.cpc.2016.02.007

Cited by 238 publications

(149 citation statements)

References 42 publications

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“…In order to seed the hosing instability, the witness bunch was shifted transversally by an initial uniform offset x c (ξ, 0) = 0.12 µm. The simulations were performed with the spectral quasi-cylindrical code FBPIC [26] using the azimuthal modes m = 0 and m = 1. (This is sufficient because the fields of the unperturbed, symmetrical beam are entirely contained in the mode m = 0, and because the perturbations due to the small offset x c create additional contributions in the modes m > 0 with a typical amplitude (x c /r b ) m [6].…”

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confidence: 99%

Saturation of the Hosing Instability in Quasilinear Plasma Accelerators

et al. 2017

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The beam hosing instability is analyzed theoretically for a witness beam in the quasi-linear regime of plasma accelerators. In this regime, the hosing instability saturates, even for a monoenergetic bunch, at a level much less than standard scalings predict. Analytic expressions are derived for the saturation distance and amplitude and are in agreement with numerical results. Saturation is due to the natural head-to-tail variations in the focusing force, including the self-consistent transverse beam loading.PACS numbers: 41.75.Jv,52.38.Kd The beam hosing instability is a major concern for both conventional accelerators and plasma-based accelerators. In both cases, this instability can exponentially amplify the small misalignments between the beam and the accelerating structure, and potentially lead to a strong degradation of the beam emittance, or even to complete disruption of the beam. Thus the hosing instability (which is related to the well-known beam-breakup instability) has been actively studied in its various regimes [1]. This includes the long-bunch, weakly-coupled regime [2,3] applicable to low-current bunches in conventional accelerators, as well as the long-bunch [4-6] and short-bunch [7-12] strongly-coupled regimes, which are of interest for beams propagating in plasmas or ion channels.In particular, the short-bunch, strongly-coupled regime is relevant to the evolution of the witness beam in plasma-wakefield acceleration (both for the beam-driven and laser-driven scheme). In this case, the exponential growth of the hosing instability as a function of the acceleration distance has raised concerns regarding the feasibility of a plasma-based particle collider [13]. However, these predictions have been made in the context of the blow-out (or bubble) wakefield regime, i.e. when the driver (beam or laser) is strong enough to expell all the plasma electrons, forming a co-moving ion cavity [14][15][16][17][18]. Plasma accelerators may also operate in the quasi-linear regime, where the driver excites a plasma density perturbation that is a fraction of the background plasma density [19]. In this Letter, we show that the sustained exponential growth of the hosing instability, which indeed applies for monoenergetic beams in the blow-out regime, does not occur in the quasi-linear regime. Instead, in the quasi-linear regime, the instability can rapidly saturate, and leads only to a moderate amplification of the beam misalignment.This early saturation is due to the head-to-tail spread in betatron frequency that naturally occurs across the bunch in the quasi-linear regime. It is indeed well-known that a head-to-tail spread in betatron frequency can mitigate the hosing instability [1,20]. However, in the blowout regime, the focusing force of the wakefield is independent of the longitudinal coordinate, and thus any head-to-tail spread in betatron frequency necessarily requires an energy spread in the bunch. Owing to the typically large beam-loading for high efficiency, large energy spreads (e.g. a few percents [11]...

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Saturation of the Hosing Instability in Quasilinear Plasma Accelerators

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“…A qualitative picture based on particle-in-cell (PIC) simulations provides valuable insight in comparing the two injection methods. Using a quasi-cylindrical PIC code [30], simulations were performed with laser and plasma parameters representative of the experimental conditions (described above). Figure 4 shows results for the two cases, (a,c) density down-ramp injection and (b,d) ionization injection.…”

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Measured Emittance Dependence on the Injection Method in Laser Plasma Accelerators

et al. 2017

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“…A lot of effort has been taken to reduce the numerical dispersion of Maxwell solvers, especially for the LPA simulations using PIC codes [6]. Several approaches have been proposed including spectral methods [7][8][9][10][11][12], filtering [13][14][15][16][17], directional splitting [18,19] and modified computation stencils [15,16,[20][21][22][23][24][25][26][27][28]. In the latter methods the stencil for the computation of the spatial derivatives of the fields is extended.…”

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A systematic approach to numerical dispersion in Maxwell solvers

Blinne

Schinkel

Kuschel

et al. 2018

Computer Physics Communications

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The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which deviate from the correct values. The solution to Maxwell's equations in more than one dimension results in non-physical predictions such as numerical dispersion or numerical Cherenkov radiation emitted by a relativistic electron beam propagating in vacuum.Improved solvers, which keep the staggered Yee-type grid for electric and magnetic fields, generally modify the spatial derivative operator in the Maxwell-Faraday equation by increasing the computational stencil. These modified solvers can be characterized by different sets of coefficients, leading to different dispersion properties. In this work we introduce a norm function to rewrite the choice of coefficients into a minimization problem. We solve this problem numerically and show that the minimization procedure leads to phase and group velocities that are considerably closer to c as compared to schemes with manually set coefficients available in the literature. Depending on a specific problem at hand (e.g. electron beam propagation in plasma, high-order harmonic generation from plasma surfaces, etc), the norm function can be chosen accordingly, for example, to minimize the numerical dispersion in a certain given propagation direction. Particle-in-cell simulations of an electron beam propagating in vacuum using our solver are provided. $ c 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

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A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

Cited by 238 publications

References 42 publications

Saturation of the Hosing Instability in Quasilinear Plasma Accelerators

Saturation of the Hosing Instability in Quasilinear Plasma Accelerators

Measured Emittance Dependence on the Injection Method in Laser Plasma Accelerators

A systematic approach to numerical dispersion in Maxwell solvers

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