The numerical instability observed in the Electromagnetic-Particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity and find an instability attributed to the coupling between the beam modes of the drifting plasma and the electromagnetic modes in the system. The characteristic pattern of the instability in Fourier space for various simulation setups and Maxwell Equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of instability growth rate and makes the parameter scan for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results and good agreement is found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of | k| essentially eliminates the instability while not modifying modes of physical interest. The use of spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.

The generation of very high quality electron bunches (high brightness and low energy spread) from a plasma-based accelerator in the three-dimensional blowout regime using self-injection in tailored plasma density profiles is analyzed theoretically and with particle-in-cell simulations. The underlying physical mechanism that leads to the generation of high quality electrons is uncovered by tracking the trajectories of the electrons in the sheath that are trapped by the wake. Details on how the intensity of the driver and the density scale-length of the plasma control the ultimate beam quality are described. Three-dimensional particle-in-cell simulations indicate that this concept has the potential to produce beams with peak brightnesses between 10 20 and 10 21 A=m 2 =rad 2 and with absolute slice energy spreads of ∼Oð0.1Þ MeV using existing lasers or electron beams to drive nonlinear wakefields. We also show projected energy spreads as low as ∼0.3 MeV for half the charge can be generated at an optimized acceleration distance. DOI: 10.1103/PhysRevAccelBeams.20.111303 Research in plasma-based acceleration (PBA) driven by a laser pulse or a relativistic electron beam is very active [1] because the large accelerating gradients in plasma wave wakefields may lead to compact accelerators. PBA is also capable of self-generating electron bunches that have significant charge (Q), short duration (τ) and low normalized emittance (ϵ n ). A combination of these quantities define the normalized beam brightness B n ¼ 2I=ϵ 2 n where I ¼ Q=τ is the current. While PBA experiments have produced useful beams, they have not produced beams with the necessary brightness and energy spread needed to drive an x-ray free-electron-laser (X-FEL) [2] or the charge and emittance needed as an injector for a future linear collider [3].The electron bunches needed to load plasma wakefields are very short and need to be synchronized with the driver. Therefore, self-injection has been actively investigated. The threshold for self-injection of electrons into nonlinear three-dimensional (3D) plasma waves in uniform plasmas has been studied in simulations and experiments [4][5][6][7][8]. Even in simulations, this process does not appear to be capable of generating the high quality beams needed for X-FELs or a linear collider [9][10][11]. Therefore there has been much recent work on methods for generating high brightness beams through controlled injection. These ideas fall into three categories. In one, electrons are born inside the wake through field ionization where the wake potential is near a maximum which eases the trapping threshold [12][13][14]. There are now numerous variations of this idea in which the injection and wake excitation are separated [15][16][17]. In the second, one or more laser pulses are used to trigger injection inside one plasma wake bucket [18][19][20][21]. In the third, which we consider here, the effective phase velocity of the wake is slowed down either by a density transition from high to low density [22,23], or through ...

Phase space matching between two plasma-accelerator (PA) stages and between a PA and a traditional accelerator component is a critical issue for emittance preservation of beams accelerated by PAs. The drastic differences of the transverse focusing strengths as the beam propagates between different stages and components may lead to a catastrophic emittance growth in the presence of both finite energy spread and lack of proper matching. We propose using the linear focusing forces from nonlinear wakes in longitudinally tailored plasma density profiles to provide exact phase space matching to properly transport the electron beam through two such stages with negligible emittance growth. Theoretical analysis and particle-in-cell simulations show how these structures may work in four different scenarios. Good agreement between theory and simulation is obtained.

The evolution of beam phase space in ionization-induced injection into plasma wakefields is studied using theory and particle-in-cell (PIC) simulations. The injection process causes special longitudinal and transverse phase mixing leading initially to a rapid emittance growth followed by oscillation, decay, and eventual slow growth to saturation. An analytic theory for this evolution is presented that includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces. Formulas for the emittance in the low and high space charge regimes are presented. The theory is verified through PIC simulations and a good agreement is obtained. This work shows how ultra-low emittance beams can be produced using ionization-induced injection.The field of plasma based acceleration has experienced significant progress in the past decade [1]. GeV energy gain in centimeter-scale laser driven wakes (LWFA) has been achieved in many recent experiments [2][3][4][5]. In beam driven wakes (PWFA), high gradient acceleration has been sustained over meter-scale distances leading to more than 40GeV energy gain [6][7][8]. For future applications of wakefield accelerators such as FELs and colliders, the quality of the self-injected beams in plasma waves, namely the transverse and longitudinal emittances, need to be improved and controlled. Among the many injection schemes [9,10], ionization-induced injection methods have attracted significant interests due to its simplest and flexibility [5,[11][12][13][14][15][16]. However, the injection process involves complex phase space dynamics, and the achievable final beam quality strongly depends on this evolution process. This area of research is of fundamental importance for achieving beam quality well beyond what is achievable with current technology.In this letter, we examine carefully the effects that affect the beam phase space evolution in ionization-induced injection using a combination of theory and simulations. We found the evolution typically has three stages, and each stage can impact the final beam quality. In typical cases where the injection time is limited to few inverse plasma periods (2πω −1 p ) and the charge is low, the three stages are as follows. First, when ionization is occurring, the emittance of the injected beam grows quickly in time from the initial thermal emittance. Second, immediately following ionization, the emittance slowly decreases to a minimum value. Finally, the emittance again gradually increases to saturated values. If the ionization time is more than ∼ πω −1 p then the emittance grows to the saturated level during the first stage including an oscillatory behavior before it slowly decreases. In the "high" charge limit the emittance evolves monotonically towards the same saturated value.The theory reveals that the evolution in emittance described above is due to special longitudinal and transverse phase mixing of electrons born at different times.The derived expressions clearly show how the emittance dep...

Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in which the plasma drifts towards the laser with v b can speedup the simulation by factors of γ2 ) −1 . In these simulations the relativistic drifting plasma inevitably induces a high frequency numerical instability that contaminates the interested physics. Various approaches have been proposed to mitigate this instability. One approach is to solve Maxwell equations in Fourier space (a spectral solver) as this has been shown to suppress the fastest growing modes of this instability in simple test problems using a simple low pass or "ring" or "shell" like filters in Fourier space. We describe the development of a fully parallelized, multi-dimensional, particle-in-cell code that uses a spectral solver to solve Maxwell's equations and that includes the ability to launch a laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it is based on the components of the UCLA PIC framework (UPIC). We show that by using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary γ b can be conducted without the presence of the numerical instability. We also compare the results of a few LWFA cases for several values of γ b , including lab frame simulations using OSIRIS, a EM-PIC code with a finite difference time domain (FDTD) Maxwell solver. These comparisons include cases in both linear and nonlinear regimes. We also investigate some issues associated with numerical dispersion in lab and boosted frame simulations and between FDTD and spectral solvers.

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1 direction). We show that this eliminates the main NCI modes with moderate |k 1 |, while keeps additional main NCI modes well outside the range of physical interest with higher |k 1 |. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along1 which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasmas, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

Ionization injection triggered by short wavelength laser pulses inside a nonlinear wakefield driven by a longer wavelength laser is examined via multidimensional particle-in-cell simulations. We find that very bright electron beams can be generated through this two-color scheme in either collinear propagating or transverse colliding geometry. For a fixed laser intensity I, lasers with longer/shorter wavelength λ have larger/smaller ponderomotive potential (∝ Iλ 2 ). The two-color scheme utilizes this property to separate the injection process from the wakefield excitation process. Very strong wakes can be generated at relatively low laser intensities by using a longer wavelength laser driver (e.g., a 10 μm CO 2 laser) due to its very large ponderomotive potential. On the other hand, a short wavelength laser can produce electrons with very small residual momenta (p ⊥ ∼ a 0 ∼ ffiffi I p λ) inside the wake, leading to electron beams with very small normalized emittances (tens of nm). Using particle-in-cell simulations we show that a ∼10 fs electron beam with ∼4 pC of charge and a normalized emittance of ∼50 nm can be generated by combining a 10 μm driving laser with a 400 nm injection laser, which is an improvement of more than 1 order of magnitude compared to the typical results obtained when a single wavelength laser is used for both the wake formation and ionization injection. With the transverse colliding geometry, simulations show that similarly low emittance and much lower slice energy spread (∼30 keV, comparing with the typical value of few MeV in the longitudinal injection scheme) can be simultaneously obtained for electron beams with a few pC charge. Such low slice energy spread may have significant advantages in applications relevant to future coherent light sources driven by plasma accelerators.

a b s t r a c tA hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in k space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to ensure that Gauss's Law is satisfied. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.