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 ...

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.

An improved description for nonlinear plasma wakefields with phase velocities near the speed of light is presented and compared against fully kinetic particle-in-cell simulations. These wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term S≡−1enp(ρ−Jz/c), where ρ and Jz are the charge and axial current densities, respectively. Previously, the sheath source term was described phenomenologically with a positive-definite function, resulting in a positive definite wake potential. In reality, the wake potential is negative at the rear of the ion column which is important for self-injection and accurate beam loading models. To account for this, we introduce a multi-sheath model in which the source term, S, of the plasma wake can be negative in regions outside the ion bubble. Using this model, we obtain a new expression for the wake potential and a modified differential equation for the bubble radius. Numerical results obtained from these equations are validated against particle-in-cell simulations for unloaded and loaded wakes. The new model provides accurate predictions of the shape and duration of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying loaded wakefield. We present beam loading results for laser wakefields and discuss how the model can be improved for laser drivers in future work. Finally, we discuss differences between the predictions of the multi- and single-sheath models for beam loading.

A new method of controllable injection to generate high quality electron bunches in the nonlinear blowout regime driven by electron beams is proposed and demonstrated using particle-in-cell simulations. Injection is facilitated by decreasing the wake phase velocity through varying the spot size of the drive beam and can be tuned through the Courant-Snyder (CS) parameters. Two regimes are examined. In the first, the spot size is focused according to the vacuum CS beta function, while in the second, it is focused by the plasma ion column. The effects of the driver intensity and vacuum CS parameters on the wake velocity and injected beam parameters are examined via theory and simulations. For plasma densities of ∼ 10 19 cm −3 , particle-in-cell (PIC) simulations demonstrate that peak normalized brightnesses 10 20 A/m 2 /rad 2 can be obtained with projected energy spreads of 1% within the middle section of the injected beam, and with normalized slice emittances as low as ∼ 10 nm.Over the past few decades, plasma-based acceleration (PBA), driven by either a laser pulse (LWFA) [1] or particle beam (PWFA) [2], has attracted significant interest in compact particle accelerator and x-ray free-electron-laser (XFEL) applications due to the high accelerating fields ∼ 10 − 100 GV/m they generate [3][4][5][6][7][8][9][10][11][12]. While the generation of ultra-relativistic electron beams through selfinjection in an evolving plasma wake has been observed in LWFA experiments [5][6][7][8] and demonstrated in simulations [13][14][15][16], the beams produced to date do not exhibit the sufficiently low energy spreads σ γ and high normalized brightnesses B n = 2I/ǫ 2 n required to drive XFEL devices [17] where I and ǫ n represent the current and normalized emittance, respectively. In recent years, electron injection schemes involving field ionization [18][19][20][21][22][23] or the use of a plasma density down ramp (DDR) [24][25][26][27][28] have shown tremendous potential for high quality beam generation for XFEL applications.In this Letter, we propose and demonstrate a new method of controllable injection using an electron beam driver whose spot size is decreasing in the nonlinear blowout regime to control the wake phase velocity and hence induce electron trapping. As when using a DDR, this proposed method relies on gradually elongating the ion column or cavity length as the drive beam propagates. In this scheme, injection can be achieved by focusing the electron beam driver over spot sizes, σ r , ranging from the scale length of the blowout radius ∼ r b to spot sizes much less than r b . A schematic of this process is shown in in Fig. 1(a). For spot sizes in this range, we will show that the ion column length and blowout radius slightly increase as σ r decreases and become insensitive to variations in σ r when σ r ≪ r b . Therefore, self-injection can be induced by controlling the focusing of the drive beam. This new approach is also a physically simpler alternative to injection methods such as DDR and Ionization, which require sh...

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid both in vacuum and in plasma there are many numerical issues that may arise which can lead to incorrect physics. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented. Two types of errors to these expressions are identified. The first arises from errors to the numer-ator of the integrand and leads to unphysical fields that are antisymmetric about the particle. The second arises from errors to the denominator of the integrand and lead to Cerenkov like radiation in "vacuum". These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers -the Yee solver and the FFT based solver. Although the Cerenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cerenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and OSIRIS results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS. Results from the customized solver are also presented. This solution will be useful for a beam of particles that all move in one direction with a small angular divergence.