Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. The current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.
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PWA-CTM: An Extended Cell-Transmission Model based on Piecewise Affine Approximation of the Fundamental Diagram
Throughout the past decades, many different versions of the widely used first-order Cell-Transmission Model (CTM) have been proposed for optimal traffic control. Highway
traffic management techniques such as Ramp Metering (RM) are typically designed based on an optimization problem with nonlinear constraints originating in the flow-density relation of the Fundamental Diagram (FD). Most of the extended CTM versions are based on the trapezoidal approximation of the flow-density relation of the Fundamental Diagram (FD) in an attempt to simplify the optimization problem. However, this relation is naturally nonlinear, and crude approximations can greatly impact the efficiency of the optimization solution. In this study, we propose a class of extended CTMs that are based on piecewise affine approximations of the flow-density relation such that (a) the integrated squared error with respect to the true relation is greatly reduced in comparison to the trapezoidal approximation, and (b) the optimization problem remains tractable for real-time application of ramp metering optimal controllers. A two-step identification method is used to approximate the FD with piecewise affine functions resulting in what we refer to as PWA-CTMs. The proposed models are evaluated by the performance of the optimal ramp metering controllers, e.g. using the widely used PI-ALINEA approach, in complex highway traffic networks. Simulation results show that the optimization problems based on the PWA-CTMs require less computation time compared to other CTM extensions while
achieving higher accuracy of the flow and density evolution. Hence, the proposed PWA-CTMs constitute one of the best approximation approaches for first-order traffic flow models that can be used in more general and challenging modeling and control applications.
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- Award ID(s):
- 2127605
- NSF-PAR ID:
- 10381007
- Date Published:
- Journal Name:
- Proceedings of the 30th Mediterranean Conference on Control and Automation (MED 2022)
- Page Range / eLocation ID:
- 1059 to 1065
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/MED54222.2022.9837131
