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 ...

During the past two decades of research, the ultra-relativistic beam-driven plasma wakefield accelerator (PWFA) concept has achieved many significant milestones. These include the demonstration of ultra-high gradient acceleration of electrons over meter-scale plasma accelerator structures, efficient acceleration of a narrow energy spread electron bunch at highgradients, positron acceleration using wakes in uniform plasmas and in hollow plasma channels, and demonstrating that highly nonlinear wakes in the 'blow-out regime' have the electric field structure necessary for preserving the emittance of the accelerating bunch. A new 10 GeV electron beam facility, Facilities for Accelerator Science and Experimental Test (FACET) II, is currently under construction at SLAC National Accelerator Laboratory for the next generation of PWFA research and development. The FACET II beams will enable the simultaneous demonstration of substantial energy gain of a small emittance electron bunch while demonstrating an efficient transfer of energy from the drive to the trailing bunch. In this paper we first describe the capabilities of the FACET II facility. We then describe a series of PWFA experiments supported by numerical and particle-in-cell simulations designed to demonstrate plasma wake generation where the drive beam is nearly depleted of its energy, high efficiency acceleration of the trailing bunch while doubling its energy and ultimately, quantifying the emittance growth in a single stage of a PWFA that has optimally designed matching sections. We then briefly discuss other FACET II plasma-based experiments including in situ positron generation and acceleration, and several schemes that are promising for generating sub-micron emittance bunches that will ultimately be needed for both an early application of a PWFA and for a plasma-based future linear collider.

The production of ultra-bright electron bunches using ionization injection triggered by two transversely colliding laser pulses inside a beam-driven plasma wake is examined via three-dimensional (3D) particle-in-cell (PIC) simulations. The relatively low intensity lasers are polarized along the wake axis and overlap with the wake for a very short time. The result is that the residual momentum of the ionized electrons in the transverse plane of the wake is much reduced and the injection is localized along the propagation axis of the wake. This minimizes both the initial thermal emittance and the emittance growth due to transverse phase mixing. 3D PIC simulations show that ultra-short (∼8 fs) high-current (0.4 kA) electron bunches with a normalized emittance of 8.5 and 6 nm in the two planes respectively and a brightness greater than 1.7 × 10 19 A · rad −2 · m −2 can be obtained for realistic parameters. The demonstration of the Linac Coherent Light Source (LCLS) as an X-ray free electron laser (X-FEL) [1] has given impetus to research on the fifth-generation light sources [2]. The goal is to make X-FELs smaller and cheaper while decreasing their wavelength and increasing their coherence and intensity. The FEL performance is partially determined by the brightness of the electron beam that traverses the undulator. The brightness is defined as B n = 2I/ǫ 2 n where I is the beam current and ǫ n is the normalized emittance of the beam. In order to make the length of the undulator needed to drive the SASE-FEL [3] into saturation, shorter, high current (∼kA), multi GeV electron beams with ǫ n ∼ 10nm will be needed. These emittances are an order of magnitude smaller than those from state-of-the-art photoinjector RF guns [4]. In this letter, we show the generation of ultrabright electron bunches using ionization injection triggered by two transversely overlapping laser pulses inside a beam-driven wake in plasma. In our scheme, the relatively low intensity lasers are polarized along the wake axis and overlap with the wake for a very short time. Particle-in-cell (PIC) simulations using OSIRIS [5] show that this geometry reduces the residual momentum of the ionized electrons in the transverse plane and localizes them along the propagation axis of the wake leading to an electron beam with a brightness greater than 10 19