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An important aspect of plasma wake field accelerators (PWFA) is stable propagation of the drive beam. In the under dense plasma regime, the drive beam creates an ion channel which acts on the beam as a strong thick focusing lens. The ion channel causes the beam to undergo multiple betatron oscillations along the length of the plasma. There are several advantages if the beam size can be matched to a constant radius. First, simulations have shown that instabilities such as hosing are reduced when the beam is matched [1]. Second, synchrotron radiation losses are minimized when the beam is matched. Third, an initially matched beam will propagate with no significant change in beam size in spite of large energy loss or gain. Coupling to the plasma with a matched radius can be difficult in some cases. This paper shows how an appropriate density ramp at the plasma entrance can be useful for achieving a matched beam. Additionally, the density ramp is helpful in bringing a misaligned trailing beam onto the drive beam axis. A plasma source with boundary profiles useful for matching has been created for the E-164X PWFA experiments at SLAC.
Plasma-based acceleration (PBA) is being considered as the basis for a future linear collider,where electrons and positron bunches must collide with extremely small spot sizes. In order to be focused to such spot sizes the beams must have extremely small emittances. Thus one challenge to a PBA collider is preserving the emittance of the accelerated beams. In this dissertation, the evolution and preservation of the witness beam emittance in aplasma-based accelerator in the nonlinear blowout regime is investigated using theory and particle-in-cell simulations. It it found that the use of plasma density ramps as matching sections are beneficial for emittance emittance growth mitigation and preservation even when the witness beam is focused so tightly within the plasma that its space charge force pulls ions inwards within the beam. In order to study the evolution of a beam in the wakefield, details of the motion ofa single beam particle in the accelerating and focusing fields of a nonlinear wakefield are presented. The exact solution to the transverse equation of motion of a single beam particle under the assumption of adiabatic acceleration is derived. Approximate and thus simpler solutions are provided under the assumptions that plasma density also changes adiabatically. Some important concepts, including the beam's envelope equation, geometric emittance, normalized emittance, single and beam C-S parameters, transport matrices, and matching are reviewed and elaborated upon. Emittance evolution and the importance of matching are discussed in the context of a uniform plasma. Using the approximate solution (WKB solution) of a single particle's motion, analyticalexpressions for the evolution of the beam emittance and the C-S parameters in an arbitrary adiabatic plasma profile are provided neglecting the acceleration of the beam inside the plasma. It is shown that the beam emittance can be preserved when the beams C-S parameters are matched to the entrance of the density profile even when the beam has an initial energy spread. It is also shown that the emittance growth for an unmatched beam is minimized when it is focused to the same vacuum plane as for a matched beam. The emittance evolution without ion motion is studied using 3D particle-in-cell QuickPIC simulation and the results agree well with the theoretical predictions. In some of the proposed experiments for the recently commissioned FACET II facility,the matching condition may not be perfectly satisfied and the wake may not be perfectly symmetric. It is shown that for a given set of beam parameters that are consistent with FACET II capabilities, the emittance growth can still be minimized by choosing the optimal focal plane even when the assumptions of the theory are not satisfied. Additional considerations for FACET II experiments were investigated. The plasma source is a lithium plasma confined by a helium buffer gas. The plasma is formed from field ionization which can lead to a nonlinear focusing force inside the helium buffer gas due to its high ionization potential leading to a nonuniform transverse profile for the plasma. It is found in simulations that for an initial beam emittance of 20 [mu]m, the helium ionization is found to be small and the witness beam's emittance can still be preserved. Emittance evolution for beam and plasma parameters relevant to a single stage of amulti-staged plasma-based linear collider (LC) is investigated. In some plasma-based LC designs the transverse space charge forces for extreme accelerating beam parameters are expected to pull background ions into the beam which can lead to longitudinally varying nonlinear focusing forces and result in emittance growth of the beam. To mitigate this, the use of an adiabatic plasma density ramp as a matching section is proposed and examined using theory and PIC simulations. The witness beam is matched to the low density plasma entrance, where the beam initially has a large matched spot size so the ion motion effects are relatively small. As the beam propagates in the plasma density upramp (downramp), it is adiabatically focused (defocused) and its phase space distribution evolves slowly towards an equilibrium distribution including the effects of the adiabatically changing ion motion. Simulation results from QPAD, a new quasi-3D, quasi-static PIC code, show that within a single acceleration stage, this concept can limit the projected emittance growth to only ∼2% for a 25 GeV, 100 nm emittance witness beam and ∼20% for a 100 GeV, 100 nm emittance witness beam. The trade-off between the adiabaticity of the plasma density ramp and the initial ion motion at the entrance for a given length of the plasma density ramp is also discussed. Additional issues for building a plasma based linear collider are discussed. Preliminaryparticle-in-cell simulation results which examine and illustrate problems like staging, shaped witness beam (for improved beam loading), emittance growth and hosing of a witness beam with an initial offset, ion motion triggered by the driver, and asymmetric witness beams are presented. The implications of these issues on a plasma based linear collider are discussed. Simulation results for witness beams with initial energy of 500 GeV such as would exist in a final stage of a PBA linear collider or an afterburner are presented.
The Plasma Wakefield Accelerator (PWFA) is an advanced accelerator concept which possess a high acceleration gradient and a long interaction length for accelerating both electrons and positrons. Although electron beam-plasma interactions have been extensively studied in connection with the PWFA, very little work has been done with respect to positron beam-plasma interactions. This dissertation addresses three issues relating to a positron beam driven plasma wakefield accelerator. These issues are (a) the suitability of employing a positron drive bunch to excite a wake; (b) the transverse stability of the drive bunch; and (c) the acceleration of positrons by the plasma wake that is driven by a positron bunch. These three issues are explored first through computer simulations and then through experiments. First, a theory is developed on the impulse response of plasma to a short drive beam which is valid for small perturbations to the plasma density. This is followed up with several particle-in-cell (PIC) simulations which study the experimental parameter (bunch length, charge, radius, and plasma density) range. Next, the experimental setup is described with an emphasis on the equipment used to measure the longitudinal energy variations of the positron beam. Then, the transverse dynamics of a positron beam in a plasma are described. Special attention is given to the way focusing, defocusing, and a tilted beam would appear to be energy variations as viewed on our diagnostics. Finally, the energy dynamics imparted on a 730 [micro]m long, 40 [micro]m radius, 28.5 GeV positron beam with 1.2 x 10[sup 10] particles in a 1.4 meter long 0-2 x 10[sup 14] e[sup -]/cm[sup 3] plasma is described. First the energy loss was measured as a function of plasma density and the measurements are compared to theory. Then, an energy gain of 79 [+-] 15 MeV is shown. This is the first demonstration of energy gain of a positron beam in a plasma and it is in good agreement with the predictions made by the 3-D PIC code. The work presented in this dissertation will show that plasma wakefield accelerators are an attractive technology for future particle accelerators.
A plasma wakefield accelerator (PWFA) uses a plasma wave (a wake) to accelerate electrons at a gradient that is three orders of magnitude higher than that of a conventional accelerator. When the plasma wave is driven by a high-density particle beam or a high-intensity laser pulse, it evolves into the nonlinear blowout regime, where the driver expels the background plasma electrons, resulting in an ion cavity forming behind the driver. This ion cavity has ideal properties for accelerating and focusing electrons. One method to insert electrons into this highly-relativistic, transient structure is by ionization injection. In this method, electrons resulting from further ionization of the ions inside the wake are trapped and accelerated by the wakefield. These injected electrons absorb the energy of the wake, resulting in a reduced accelerating field amplitude; this phenomenon is known as beam loading. This thesis discusses experiments that demonstrate how ionization injection can, on the one hand, lead to excessive beam loading and be a detriment to a PWFA, while on the other hand, it may be taken advantage of to produce bright electron beams that will be necessary for applications of a PWFA to a free electron laser (FEL) or a collider. These experiments were part of the FACET Campaign at the SLAC National Accelerator Laboratory and used FACET's 3 nC, 20.35 GeV electron beam to field ionize the plasma source and drive a wake. In the first experiment, the plasma source was a 30 cm column of rubidium (Rb) vapor. The low ionization potential and high atomic mass of Rb made it a suitable candidate as a plasma source for a PWFA. However, the low ionization potential of the Rb+ ion resulted in continuous ionization of Rb+ and injection of electrons along the length of the plasma. This resulted in heavy beam-loading, which reduced the strength of the accelerating field by half, making the Rb source unusable for a PWFA. In the second experiment, the plasma source was a column of lithium (Li) vapor bound by cold helium (He) gas. Here, the ionization injection of He electrons in the 10 cm boundary region between Li and He led to localized beam loading and resulted in an accelerated electron beam with high energy (32 GeV), a 10% energy spread, and an emittance an order of magnitude smaller than the drive beam. Particle-in-cell simulations indicate that the beam loading can be further optimized by reducing the injection region even more, which can lead to bright, high-current, low-energy-spread electron beams.
Laser wakefield accelerators produce accelerating gradientsup to hundreds of GeV/m, and recently demonstrated 1-10 MeV energy spreadat energies up to 1 GeV using electrons self-trapped from the plasma. Controlled injection and staging may further improve beam quality bycircumventing tradeoffs between energy, stability, and energyspread/emittance. We present experiments demonstrating production of astable electron beam near 1 MeV with hundred-keV level energy spread andcentral energy stability by using the plasma density profile to controlselfinjection, and supporting simulations. Simulations indicate that suchbeams can be post accelerated to high energies, potentially reducingmomentum spread in laser acceleratorsby 100-fold or more.
In this dissertation, a new method for producing ultra-bright electron beams in nonlinear plasma wave wakes driven by an electron beam driver is explored using particle-in-cell simulations and analytic theory. In order to understand this process an accurate description of a nonlinear wakefield is required. These nonlinear 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 $S \equiv -\frac{1}{en_p}(\rho-J_z/c)$, where $e$ is the electron charge, $n_p$ is the plasma number density, $\rho$ is the charge density, and $J_z$ is the axial current density. Previously, the sheath source term was described phenomenologically with a positive-definite function thereby 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, in the first part of this dissertation a multi-sheath model in which the source term, $S$, of the plasma wake can be negative in regions outside the ion bubble is introduced. Using this model, a new expression for the wake potential and a modified differential equation for the bubble radius is obtained. 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. The multi-sheath model is also applied to beam loading in laser wakefields. Areas where the multi-sheath model can be improved for laser drivers in future work are discussed. In the second part of this dissertation, 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 focusing the drive beam spot size. Two regimes are examined. In the first, the spot size is focused according to the vacuum Courant-Snyder (CS) beta function while, in the second, it is self-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 $\sim 10^{19} ~\centi\meter^{-3}$, particle-in-cell (PIC) simulations demonstrate that peak normalized brightnesses $\gtrsim 10^{20}~\ampere/\meter^2/\rad^2$ can be obtained with projected energy spreads of $\lesssim 1\%$ within the middle section of the injected beam and with normalized slice emittances as low as $\sim 10 ~\nano\meter$. In the last part of the dissertation, a predictive model for injection using the self-evolving driver method in the plasma focusing regime is developed. The model is used to characterize how the wake evolution and final injected beam parameters scale with the driver parameters. Parameter scans of PIC simulations using different drivers are performed and compared with the model predictions. In particular, the dependence of the injected beam parameters with the diffraction length, energy, intensity, spot size, and duration of the driver is examined. It is found that injection and optimal beam loading can be simultaneously achieved. The multi-sheath model is also used to study the beam loading effects from the injected bunch in this case. PIC simulation results indicate that the injected beam can be efficiently accelerated to $18.27$ GeV with a projected energy spread of $ 0.49\%$ and peak normalized brightess of $B_n \sim 10^{20}~\ampere/\meter^2/\rad^2$ for a plasma density of $\sim 10^{19} ~\centi\meter^{-3}$.
In the pursuit of discovering the fundamental laws and particles of nature, physicists have been colliding particles at ever increasing energy for almost a century. Lepton (electrons and positrons) colliders rely on linear accelerators (LINACS) because leptons radiate copious amounts of energy when accelerated in a circular machine. The size and cost of a linear collider is mainly determined by the acceleration gradient. Modern linear accelerators have gradients limited to 20-100 MeV/m because of the breakdown of the walls of the accelerator. Plasma based acceleration is receiving much attention because a plasma wave with a phase velocity near the speed of light can support acceleration gradients at least three orders of magnitude larger than those in modern accelerators. There is no breakdown limit in a plasma since it is already ionized. Such a plasma wave can be excited by the radiation pressure of an intense short pulse laser. This is called laser wakefield acceleration (LWFA). Much progress has been made in LWFA research in the past 30 years. Particle-in-cell (PIC) simulations have played a major part in this progress. The physics inherent in LWFA is nonlinear and three-dimensional in nature. Three-dimensional PIC simulations are computationally intensive. In this dissertation, we present and describe in detail a new algorithm that was introduced into the Particle-In-Cell Simulation Framework. We subsequently use this new quasi three-dimensional algorithm to efficiently explore the parameter regimes of LWFA that are accessible for existing and near term lasers. This regimes cannot be explored using full three-dimensional simulations even on leadership class computing facilities. The simulations presented in this dissertation show that the nonlinear, self-guided regime of LWFA described through phenomenological scaling laws by Lu et al., in 2007 is still useful for accelerating electrons to energies greater than 10 GeV. Fortunately, in many situations the physics of LWFA is nearly azimuthally symmetric and the most salient three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed by Lifschitz et al. [J. Comp. Phys. 228 (5) 2009] to model LWFA by expanding the fields and currents in azimuthal harmonics and truncating the expansion. 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 dissertation, we describe in detail the 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 (which we have subsequently coined the 'quasi-3D' method). 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. In almost all of the recent experiments progress on LWFA the plasma wave wake has been excited in the nonlinear blowout regime. A phenomenological description of this regime was given by Lu et al. [PRSTAB, 10 (061301) 2007]. This included matching conditions for the laser spot size and pulse length so that the laser evolution and wake excitation would be stable and the laser would self-guide. Scaling laws for the electron electron energy (self or externally injected) in terms of the laser and plasma parameters was also given. The parameters for the supporting simulations were limited due to the computational demands for such simulations particularly for higher electron energy. The recent implementation of the quasi-3D algorithm into OSIRIS including the charge conserving current deposit, now make it possible to study these scaling laws and examine how well they still hold for higher laser intensities and laser energies. We have studied in detail how well the nonlinear, self-guided regime works for existing and near term 15-100 Joule lasers. We demonstrate that the scaling laws do capture the key phenomenological characteristics LWFAs under a wide range of different laser and plasma parameters, but are not meant to give exact predictions for a choice of parameters. The simulations indicate that the self-injected particles reach slightly higher energies than estimated by the scaling laws, although the evolution of the maximum energy looks similar when scaled to the dephasing time. We also find that shape of the evolution of the energy, spot size, and wake amplitude scales if the normalized vector potential, and transverse and axial profile shapes remain fixed. If the normalized vector potential is changed then the scaling laws are still useful but the shape of energy evolution curve changes. We also used the scaling laws to optimize the energy gain for a fixed laser energy. We then use the quasi-3D OSIRIS code to study study in detail how to optimize the energy gain for fixed laser energy including how to optimize the axial laser profile. We find that shortening the pulse length and reducing the plasma density is effective in producing a higher energy beam with a low energy spread, given a fixed laser energy.