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## Scholarly Works (163 results)

There is no clear path for building a particle accelerator at the energy frontier beyond the Large Hadron Collider (LHC). One option that is receiving attention is to use plasma wave wakefields driven by intense particle beams. Recent experiments conducted at the Stanford Linear Accelerator Center (SLAC) show that accelerating gradients in such wakefields in excess of 50 GeV/m can be sustained over meter scales. Based on this, a linear collider concept of staging one-meter long plasma cells together has been proposed. A facility at SLAC has been built to study the physics in one stage. In this dissertation we describe improvements and enhancements to a highly efficient simulation model for simulating current experiments at SLAC as well as parameters beyond the reach of current experiments. The model is the quasi-static particle-in-cell (PIC) code QuickPIC. A modified set of quasi-static field equations were developed, which reduced the number of predictor corrector iteration loops and an improved source deposit scheme was developed to reduce the parallel communication. These improvements led to a factor of 5 to 8 (depending on the simulation parameters) speedup compared with the previous set of field equations and deposition scheme. Several new modules were also added to QuickPIC, including the multiple field ionization and improved beam and plasma particle diagnostics. We also used QuickPIC to study the optimum plasma density for maximizing the acceleration field for fixed electron beam parameters. QuickPIC simulations were also used to study and design two-bunch PWFA experiments at SLAC including methods for mitigating the ionization-induced beam head erosion. The mitigation methods can enhance the energy gain in two-bunch PWFA experiments at SLAC by a factor of 10 for the same beam parameters. For beam parameters beyond SLAC but perhaps necessary for a future collider, QuickPIC was used to study how the ultra high electric fields of a tightly focused second electron bunch could lead to ion motion, which disrupts the focusing fields on the second bunch. The resulting nonlinearity in the transverse focusing force of the plasma wake will lead to emittance growth. We used QuickPIC to carry out the first fully self-consistent high resolution simulation on the effects of ion motion for PWFA linear collider problems. Preliminary results showed that the plasma-ion-motion-induced emittance growth was limited to less than a factor of 2. In addition to the electron beam driven PWFA, we also study how a short proton beam can excite a large plasma wake. Such short proton beams are currently not experimentally available. We therefore also study how long proton beams such as those at Fermi National Laboratory and CERN may drive a large plasma wake through a self-modulation instability. A linear theory for the self-modulation instability is presented under the wide beam limit. QuickPIC simulations show that the self-modulation of a long proton beam in a plasma may lead to the micro-bunching of the beam and excite a large plasma wake.

Accelerators at the energy frontier have been the tool of choice for nearly a century for unraveling the structure of matter, space, and time. Today's accelerators are the most complex and expensive tools for scientific discovery built by humans. The capability of these accelerators has increased at an exponential rate due to the development of new accelerator concepts and technology. The capability of existing accelerator technology has plateaued, so that a future accelerator at the energy frontier will be so large and expensive that it is not clear it will be built. On the other hand, plasma based acceleration has emerged as a possible alternative technology with much recent progress in theory, simulation, and experiment. In plasma based acceleration intense short-pulse laser, or particle beam excites a plasma wave wakefield as it propagates through long regions of plasma. When a laser is used it is called laser wakefield acceleration (LWFA), and when a particle beam is used it is called plasma wakefield acceleration (PWFA). Simulations have contribute greatly to the recent progress by providing guidance and insight for existing experiments, and for permitting the study of parameters beyond the current reach of experiments. However, these simulations require much computing resources. Therefore, alternative numerical techniques are desired, and in some cases are needed.

In this dissertation, we systematically explore the use of a simulation method for modeling LWFA using the particle-in-cell (PIC) method, called the Lorentz boosted frame technique. In the lab frame the plasma length is typically four orders of magnitude larger than the laser pulse length. Using this technique, simulations are performed in a Lorentz boosted frame in which the plasma length, which is Lorentz contracted, and the laser length, which is Lorentz expanded, are now comparable. This technique has the potential to reduce the computational needs of a LWFA simulation by more than four orders of magnitude, and is useful if there is no or negligible reflection of the laser in the lab frame.

To realize the potential of Lorentz boosted frame simulations for LWFA, the first obstacle to overcome is a robust and violent numerical instability, called the Numerical Cerenkov Instability (NCI), that leads to unphysical energy exchange between relativistically drifting particles and their radiation. This leads to unphysical noise that dwarfs the real physical processes. In this dissertation, we first present a theoretical analysis of this instability, and show that the NCI comes from the unphysical coupling of the electromagnetic (EM) modes and Langmuir modes (both main and aliasing) of the relativistically drifting plasma. We then discuss the methods to eliminate them. In EM-PIC simulations of plasmas, Maxwell's equations are solved using a finite difference form for the derivatives in real space or using FFT's and solving the fields in wave number space. We show that the use of an FFT based solver has useful properties on the location and growth rate of the unstable NCI modes. We first show that the use of an FFT based solver permits the effective elimination of the NCI by both using a low pass filter in wave number space and by reducing the time step. We also show that because some NCI modes are very localized in wave number space, a modification of the numerical dispersion near these unstable modes can eliminate them. We next show that these strategies work just as well if the FFT is only used in the plasma drifting direction and propose a hybrid FFT/Finite Difference solver. This algorithm also includes a correction to the current from the standard charge conserving current deposit that ensures that Gauss's Law is satisfied for the FFT/Finite Difference divergence operator.

However, the use of FFTs can lead to parallel scalability issues when there are many more cells along the drifting direction than in the transverse direction(s). We then describe an algorithm that has the potential to address this issue by using a higher order finite difference operator for the derivative in the plasma drifting direction, while using the standard second order operators in the transverse direction(s). The NCI for this algorithm is analyzed, and it is shown that the NCI can be eliminated using the same strategies that were used for the hybrid FFT/Finite Difference solver. This scheme also requires a current correction and filtering which require FFTs. However, we show that in this case the FFTs can be done locally on each parallel partition.

We also describe how the use of the hybrid FFT/Finite Difference or the hybrid higher order finite difference/second order finite difference methods permit combining the Lorentz boosted frame simulation technique with another ``speed up'' technique, called the quasi-3D algorithm, to gain unprecedented speed up for the LWFA simulations. In the quasi-3D algorithm the fields and currents are defined on an $r-z$ PIC grid and expanded in azimuthal harmonics. The expansion is truncated with only a few modes so it has similar computational needs of a 2D $r-z$ PIC code. We show that NCI has similar properties in $r-z$ as in $z-x$ slab geometry and show that the same strategies for eliminating the NCI in Cartesian geometry can be effective for the quasi-3D algorithm leading to the possibility of unprecedented speed up.

We also describe a new code called UPIC-EMMA that is based on fully spectral (FFT) solver. The new code includes implementation of a moving antenna that can launch lasers in the boosted frame. We also describe how the new hybrid algorithms were implemented into OSIRIS. Examples of LWFA using the boosted frame using both UPIC-EMMA and OSIRIS are given, including the comparisons against the lab frame results. We also describe how to efficiently obtain the boosted frame simulations data that are needed to generate the transformed lab frame data, as well as how to use a moving window in the boosted frame.

The NCI is also a major issue for modeling relativistic shocks with PIC algorithm. In relativistic shock simulations two counter-propagating plasmas drifting at relativistic speeds are colliding against each other. We show that the strategies for eliminating the NCI developed in this dissertation are enabling such simulations being run for much longer simulation times, which should open a path for major advances in relativistic shock research.

This dissertation is composed of two chapters. Each chapter presents a study testing a theory from behavioral economics in a health economics setting using field data.

The first chapter studies the role of present bias in the choice of health insurance. I analyze the consequences of a policy change that removes deadlines for enrollment in high-quality (5-star) Medicare drug coverage plans (Part D), while maintaining existing deadlines for enrollment in all other plans. Although the goals of the policy were to increase enrollment in 5-star plans and to provide incentives for insurers to improve quality, the removal of deadlines might lead to the opposite. First, rational beneficiaries might wait to enroll in 5-star plans only when a negative health event occurs, which would both decrease enrollment and increase adverse selection. Second, without deadlines, present-biased beneficiaries might procrastinate, which would also lead to a drop in enrollment, driven by an overall increase in inertia. I develop a model to examine these different hypotheses and test its predictions using Medicare administrative micro data for the period of 2009-2012. I employ a difference-in-differences design within a differentiated-product discrete-choice demand framework. My identification strategy takes advantage of the fact that the policy did not actually change enrollment rules everywhere in the United States, as most counties were not within the coverage area of a 5-star provider in 2012, the year the policy was implemented. I have three main findings. First, the policy backfires: it decreases enrollment in the Part D program by 2.55pp from a baseline of 51.76\%, and decreases average market share of 5-star plans by 1.37pp from a baseline of 7.78\%. Second, the policy does not seem to impact adverse selection, suggesting the rational model might not fully account for the results. Third, the removal of deadlines leads to a drop in the probability that a previously enrolled beneficiary switches plans of 3.18pp (baseline 9.08\%), suggesting that at least some Medicare beneficiaries are present-biased.

The second chapter studies role of projection bias in mental health treatment decisions. Evidence from psychology suggests that on a bad-weather day, individuals may feel more depressed than usual. If people are not fully able to account for the effect of transient weather, they may take systematically biased treatment decisions. I derive a model of a person considering treatment for depression and show that when projection bias is present, transient weather might influence choice. I use detailed administrative medical records from the MarketScan \textregistered database and daily county-level meteorological data from the National Climatic Data Center. My period of analysis is 01/01/2003 through 12/31/2004. My main analysis focuses on patient behavior during a small interval of time after they have been seen by a physician. I look at how weather influences antidepressant filling decision within patient and only include appointments that involved a major diagnosis of a mental disease or disorder. I find that a one standard deviation increase in the amount of cloud coverage (2.73 oktas) leads to a 0.063 percentage point increase in the probability that a patient fills an antidepressant prescription on appointment day. That is a 1.04\% increase from the 6.07\% baseline. I also find effects associated with snow, rain, and temperature. All effects fade with time and are not significant within seven days of the appointment. Most of the impact of cloud coverage on antidepressant filling is due to an increase on the number of new prescriptions, not an increase in refills. Virtually all the effect happens at the pharmacy, not via mail order. Most regions have similar coefficients associated with cloud coverage, with stronger results in the Northeast and Upper Midwest. Finally, most of the impact happens during Winter.

Plasma wave wakes, which are the collective oscillatory response near the plasma frequency to the propagation of particles or electromagnetic waves through a plasma, play a critical role in many plasma processes. New results from backwards stimulated Raman scattering (BSRS), in which wakes with phase velocities much less than the speed of light are induced by the beating of counter-propagating light waves, and from electron beam stopping, in which the wakes are produced by the motion of relativistically propagating electrons through the dense plasma, are discussed. Both processes play important roles in Inertial Confinement Fusion (ICF). In BSRS, laser light is scattered backwards out of the plasma, decreasing the energy available to compress the ICF capsule and affecting the symmetry of where the laser energy hits the hohlraum wall in indirect drive ICF. The plasma wave wake can also generate superthermal electrons that can preheat the core and/or the ablator. Electron beam stopping plays a critical role in the Fast Ignition (FI) ICF concept, in which a beam of relativistic electrons is used to heat the target core to ignition temperatures after the compression stage. The beam stopping power determines the effectiveness of the heating process. This dissertation covers new discoveries on the importance of plasma wave wakes in both BSRS and electron beam stopping.

In the SRS studies, 1D particle-in-cell (PIC) simulations using OSIRIS are performed, which model a short-duration (~500/&omega_{0 FWHM) counter-propagating scattered light seed pulse in the presence of a constant pump laser with an intensity far below the absolute instability threshold for plasma waves undergoing Landau damping. The seed undergoes linear convective Raman amplification and dominates over the amplification of fluctuations due to particle discreteness. The simulation results are in good agreement with results from a coupled-mode solver when special relativity and the effects of finite size PIC simulation particles are accounted for. Linear gain spectra including both effects are discussed. Extending the PIC simulations past when the seed exits the simulation domain reveals bursts of large-amplitude scattering in many cases, which do not occur in simulations without the seed pulse. These bursts can have amplitudes several times greater than the amplified seed pulse, and an examination of the orbits of particles trapped in the wake illustrates that the bursts are caused by a reduction of Landau damping due to particle trapping. This large-amplitude scattering is caused by the seed inducing a wake earlier in the simulation, thus modifying the distribution function. Performing simulations with longer duration seeds leads to parts of the seeds reaching amplitudes several times more than the steady-state linear theory results, similarly caused by a reduction of Landau damping. Simulations with continuous seeds demonstrate that the onset of inflation depends on the seed wavelength and incident intensity, and oscillations in the reflectivity are observed at a frequency equal to the difference between the seed frequency and the frequency at which the inflationary SRS grows.}

In the electron beam stopping studies, 3D PIC simulations are performed of relativistic electrons with a momentum of 10m_{ec propagating in a cold FI core plasma. Some of the simulations use one simulation particle per real particle, and particle sizes much smaller than the interparitcle spacing. The wake made by a single electron is compared against that calculated using cold fluid theory assuming the phase velocity of the wake is near the speed of light. The results agree for the first wavelength of the wake. However, the shape of the wake changes for succeeding wavelengths and depends on the background plasma temperature, with the concavity pointing in the direction the electron is moving in cold plasmas and in the opposite direction as the plasma temperature increases. In the warm plasma the curvature is described by electrostatic Vlasov theory (for vparticle >> vth) and is due to the diffraction of the wave, while for cold plasmas the curvature is due to nonlinear radial oscillations of background electrons. Beams with multiple electrons exhibit correlation effects caused by electrons interacting through their wakes. Non-divergent beams are simulated, and a significant time-dependent increase in the stopping power is observed when the average electron spacing is 2c/&omegape or less. This increase is caused by beam-plasma-like instabilities including self-focusing and/or filamentation and the beam-plasma-like instability. The stopping power growth rate and peak value depend on the beam size and density. For long beams with dimensions of 10c/&omegape × 10c/&omegape × 80c/&omegape and an inter-particle separation of 0.25c/&omegape (nb/n0 ≈ 4× 10-3), the peak stopping power averaged over the electrons is (1 ± 3) × 103 times that of an uncorrelated electron. These results indicate that an enhanced energy-independent or weakly dependent correlated stopping may occur for Fast Ignition scenarios, even for interparticle spacings when discreteness effects are important. The dependence of correlation effects on beam electron separation in terms of c/&omegape also indicates that Fast Ignition may be possible with core densities below those designed using single-electron stopping powers. Target optimization to exploit correlated stopping in the target core may be possible once the effects of angular spread and energy spread are understood. Furthermore, this work begins to allow a connection from the discrete wakes effect to collective instabilities as the interparticle spacing is decreased relative to the size of the wake due to the use of denser beams, lower plasma densities, and the filamentation/self-focusing of the beam.}

The continued development of the chirped pulse amplification technique has allowed for the development of lasers with powers of in excess of $10^{15}W$, for pulse lengths with durations of between .01 and 10 picoseconds, and which can be focused to energy densities greater than 100 giga-atmospheres. When such lasers are focused onto material targets, the possibility of creating particle beams with energy fluxes of comparable parameters arises. Such interactions have a number of theorized applications. For instance, in the Fast Ignition concept for Inertial Confinement Fusion \cite{Tabak:1994vx}, a high-intensity laser efficiently transfers its energy into an electron beam with an appropriate spectra which is then transported into a compressed target and initiate a fusion reaction. Another possible use is the so called Radiation Pressure Acceleration mechanism, in which a high-intensity, circularly polarized laser is used to create a mono-energetic ion beam which could then be used for medical imaging and treatment, among other applications. For this latter application, it is important that the laser energy is transferred to the ions and not to the electrons. However the physics of such high energy-density laser-matter interactions is highly kinetic and non-linear, and presently not fully understood.

In this dissertation, we use the Particle-in-Cell code OSIRIS \cite{Fonseca:2002, Hemker:1999} to explore the generation and transport of relativistic particle beams created by high intensity lasers focused onto solid density matter at normal incidence. To explore the generation of relativistic electrons by such interactions, we use primarily one-dimensional (1D) and two-dimensional (2D), and a few three-dimensional simulations (3D). We initially examine the idealized case of normal incidence of relatively short, plane-wave lasers on flat, sharp interfaces. We find that in 1D the results are highly dependent on the initial temperature of the plasma, with significant absorption into relativistic electrons only possible when the temperature is high in the direction parallel to the electric field of the laser. In multi-dimensions, absorption into relativistic electrons arises independent of the initial temperature for both fixed and mobile ions, although the absorption is higher for mobile ions. In most cases however, absorption remains at $10's$ of percent, and as such a standing wave structure from the incoming and reflected wave is setup in front of the plasma surface. The peak momentum of the accelerated electrons is found to be $2 a_0 m_e c$, where $a_0 \equiv e A_0/m_e c^2$ is the normalized vector potential of the laser in vacuum, $e$ is the electron charge, $m_e$ is the electron mass, and $c$ is the speed of light. We consider cases for which $a_0>1$. We therefore call this the $2 a_0$ acceleration process. Using particle tracking, we identify the detailed physics behind the $2 a_0$ process and find it is related to the standing wave structure of the fields. We observe that the particles which gain energy do so by interacting with the laser electric field within a quarter wavelength of the surface where it is at an anti-node (it is a node at the surface). We find that only particles with high initial momentum -- in particular high transverse momentum -- are able to navigate through the laser magnetic field as its magnitude decreases in time each half laser cycle (it is an anti-node at the surface) to penetrate a quarter wavelength into the vacuum where the laser electric field is large. For a circularly polarized laser the magnetic field amplitude never decreases at the surface, instead its direction simply rotates. This prevents electrons from leaving the plasma and they therefore cannot gain energy from the electric field.

For pulses with longer durations ($\gtrsim 250fs$), or for plasmas which do not have initially sharp interfaces, we discover that in addition to the $2 a_0$ acceleration at the surface, relativistic particles are also generated in an underdense region in front of the target. These particles have energies without a sharp upper bound. Although accelerating these particles removes energy from the incoming laser, and although the surface of the plasma does not stay perfectly flat and so the standing wave structure becomes modified, we find in most cases, the $2 a_0$ acceleration mechanism occurs similarly at the surface and that it still dominates the overall absorption of the laser.

To explore the generation of relativistic electrons at a solid surface and transport of the heat flux of these electrons in cold or warm dense matter, we compare OSIRIS simulations with results from an experiment performed on the OMEGA laser system at the University of Rochester. In that experiment, a thin layer of gold placed on a slab of plastic is illuminated by an intense laser. A greater than order-of-magnitude decrease in the fluence of hot electrons is observed when those electrons are transported through a plasma created from a shock-heated plastic foam, as compared to transport through cold matter (unshocked plastic foam) at somewhat higher density. Our simulations indicate two reasons for the experimental result, both related to the magnetic field. The primary effect is the generation of a collimating B-field around the electron beam in the cold plastic foam, caused by the resistivity of the plastic. We use a Monte Carlo collision algorithm implemented in OSIRIS to model the experiment. The incoming relativistic electrons generate a return current. This generates a resistive electric field which then generates a magnetic field from Faraday's law. This magnetic field collimates the forward moving relativistic electrons. The collisionality of both the plastic and the gold are likely to be greater in the experiment than the 2D simulations where we used a lower density for the gold (to make the simulations possible) which heats up more. In addition, the use of 2D simulations also causes the plastic to heat up more than expected. We compensated for this by increasing the collisionality of the plasma in the simulations and this led to better agreement. The second effect is the growth of a strong, reflecting B-field at the edge of the plastic region in the shock heated material, created by the convective transport of this field back towards the beam source due to the neutralizing return current. Both effects appear to be caused primarily by the difference is density in the two cases. Owing to its higher heat capacity, the higher density material does not heat up as much from the heat flux coming from the gold, which leads to a larger resistivity.

Lastly, we explored a numerical effect which has particular relevance to these simulations, due to their high energy and plasma densities. This effect is caused by the use of macro particles (which represent many real particles) which have the correct charge to mass ratio but higher charge. Therefore, any physics of a single charge that scales as $q^2/m$ will be artificially high. Physics that involves scales smaller than the macro-particle size can be mitigated through the use of finite size particles. However, for relativistic particles the spatial scale that matters is the skin depth and the cell sizes and particle sizes are both smaller than this. This allows the wakes created by these particles to be artificially high which causes them to slow down much faster than a single electron. We studied this macro-particle stopping power theoretically and in OSIRIS simulations. We also proposed a solution in which particles are split in to smaller particles as they gain energy. We call this effect Macro Particle Stopping. Although this effect can be mitigated by using more particles, this is not always computationally efficient. We show how it can also be mitigated by using high-order particle shapes, and/or by using a particle-splitting method which reduces the charge of only the most energetic electrons.

This dissertation concerns the development and use of numerical simulation techniques for studying nonlinear plasma systems in which accurate representations of the electron distribution function are required. The kinetic description of the electrons is accomplished via two different simulation modalities: the code OSHUN, which directly solves the Vlasov-Fokker-Planck (VFP) partial differential equation, and the code OSIRIS, which uses the particle-in-cell (PIC) method including an option for a separate Monte Carlo collision model.

The dissertation consists of ten chapters that are based on reprints of refereed publications that describe the development and use of OSHUN and OSIRIS. The increasing complexity of today’s computers necessitates an increase in the complexity of software to take full advantage of the available computing resources. This requires that software be engineered properly to ensure correct functioning and to enable more developers to contribute. The dissertation includes examples of the creation --- that is, combining new and novel algorithms with software engineering techniques --- and novel usage of simulation software packages capable of exploiting the power of today's computers to enable new capability and discovery.

OSHUN includes relativistic corrections to the Vlasov equation but uses a non-relativistic description for the collision operator. The fields can be advanced in time using the full set of Maxwell’s equations explicitly, just the electrostatic fields, or an implicit set of equations that includes Ampere’s law without the displacement current. An arbitrary number of spherical harmonics can be included permitting efficient studies of physics when the distribution function is nearly in or far from equilibrium. This can drastically reduce the computational cost when only a few spherical harmonics are required. OSHUN was tested against a variety of problems spanning collisional and collisionless systems including Landau Damping, the two stream instability, Spitzer-Harm, and Epperlein-Haines heat flow coefficients in warm magnetized and unmagnetized plasmas. It was also used to explore how the heat flow in the laser entrance hole could modify Stimulated Raman Backscatter in Inertial Confinement Fusion relevant plasmas.

New numerical/algorithmic techniques where implemented in the PIC code OSIRIS. In particular, new software engineering techniques facilitated the addition of an algorithm which uses PIC in the r-z coordinates system with a gridless description in the azimuthal angle \phi. The fields, equations, and current are decomposed into an azimuthal mode, m, expansion. This Quasi-3D description permits 3D simulations at a drastically lower computational cost (approaching the cost of 2D simulations) in systems that exhibit nearly azimuthal (cylindrical) symmetry. This capability was used to

examine laser wakefield acceleration (LWFA). It was used to verify scaling laws for LWFA in a nonlinear, self-guide regime. The Quasi-3D algorithm was coupled to an independently developed module in OSIRIS that allows simulation of LWFA in a Lorentz-boosted frame. Doing the calculations in this frame yields a computational savings that scales as gamma^2 (where gamma is the Lorentz boost factor) which typically ranges from 100 to 100,000 in the systems under consideration. These modules required the development of novel field solvers and current deposition algorithms to eliminate a numerical instability called the Numerical Cerenkov Instability (NCI). These were added to OSIRIS using the new software engineering techniques now possible with Fortran 2003.

OSIRIS was updated to utilize the Graphics Processing Units (GPUs) present in exascale systems like the Summit supercomputer recently built at the Oak Ridge National Laboratory. A GPU version of OSIRIS was used to examine the interactions of Laser Speckles from Stimulated Raman Scattering (SRS). It was found that speckles can mutually interact via scattering light, plasma waves, or non-thermal electrons transporting from speckles above threshold from SRS. This can trigger SRS in speckles that were below threshold.

Efforts towards the ultimate (and ongoing) goal of fully integrating the Quasi-3D, Lorentz-boosted frame, and GPU modules is described. When combined, these modules have the potential speed up 3D laser-plasma simulations by immense factors of a million or more.