Approximation and Visualization of Pareto Frontier in the Framework of Classical Approach to Multi-Objective Optimization

This paper is devoted to a Pareto frontier generation technique, which is aimed at subsequent visualization of the Pareto frontier in an interaction with the user. This technique known as the Interactive Decision Maps technique was initiated about 30 years ago. Now it is applied for decision support in both convex and non-convex decision problems in various fields, from machinery design to environmental planning. The number of conflicting criteria explored with the help of the Interactive Decision Maps technique is usually between three and seven, but some users manage to apply the technique in the case of a larger number of criteria. Here we outline the main ideas of the technique, concentrating at nonlinear problems

Numerical Studies of Electron Acceleration Behind Self-Modulating Proton Beam in Plasma with a Density Gradient

Presently available high-energy proton beams in circular accelerators carry enough momentum to accelerate high-intensity electron and positron beams to the TeV energy scale over several hundred meters of the plasma with a density of about 1e15 1/cm^3. However, the plasma wavelength at this density is 100-1000 times shorter than the typical longitudinal size of the high-energy proton beam. Therefore the self-modulation instability (SMI) of a long (~10 cm) proton beam in the plasma should be used to create the train of micro-bunches which would then drive the plasma wake resonantly. Changing the plasma density profile offers a simple way to control the development of the SMI and the acceleration of particles during this process. We present simulations of the possible use of a plasma density gradient as a way to control the acceleration of the electron beam during the development of the SMI of a 400 GeV proton beam in a 10 m long plasma. This work is done in the context of the AWAKE project --- the proof-of-principle experiment on proton driven plasma wakefield acceleration at CERN.Comment: 4 pages, 5 figures

Long-term evolution of broken wakefields in finite radius plasmas

A novel effect of fast heating and charging a finite-radius plasma is discovered in the context of plasma wakefield acceleration. As the plasma wave breaks, the most of its energy is transferred to plasma electrons which create strong charge-separation electric field and azimuthal magnetic field around the plasma. The slowly varying field structure is preserved for hundreds of wakefield periods and contains (together with hot electrons) up to 80% of the initial wakefield energy.Comment: 5 pages, 6 figure

Self-modulation instability of a long proton bunch in plasmas

An analytical model for the self-modulation instability of a long relativistic proton bunch propagating in uniform plasmas is developed. The self-modulated proton bunch resonantly excites a large amplitude plasma wave (wake field), which can be used for acceleration of plasma electrons. Analytical expressions for the linear growth rate and the number of exponentiations are given. We use the full three-dimensional particle-in-cell (PIC) simulations to study the beam self-modulation and the transition to the nonlinear stage. It is shown that the self-modulation of the proton bunch competes with the hosing instability which tends to destroy the plasma wave. A method is proposed and studied through PIC simulations to circumvent this problem which relies on the seeding of the self-modulation instability in the bunch

Proton Beam Defocusing as a Result of Self-Modulation in Plasma

The AWAKE experiment will use a \SI{400}{GeV/c} proton beam with a longitudinal bunch length of $\sigma_z = 12\,\rm{cm}$ to create and sustain GV/m plasma wakefields over 10 meters . A 12 cm long bunch can only drive strong wakefields in a plasma with $n_{pe} = 7 \times 10^{14}\,\rm{electrons/cm}^3$ after the self-modulation instability (SMI) developed and microbunches formed, spaced at the plasma wavelength. The fields present during SMI focus and defocus the protons in the transverse plane \cite{SMI}. We show that by inserting two imaging screens downstream the plasma, we can measure the maximum defocusing angle of the defocused protons for plasma densities above $n_{pe} = 5 \times 10^{14}\,\rm{electrons/cm}^{-3}$. Measuring maximum defocusing angles around 1 mrad indirectly proves that SMI developed successfully and that GV/m plasma wakefields were created. In this paper we present numerical studies on how and when the wakefields defocus protons in plasma, the expected measurement results of the two screen diagnostics and the physics we can deduce from it.Comment: 3 pages, 2 figures, Conference Proceedings of NAPAC 201

High quality electron beam generation in a proton-driven hollow plasma wakefield accelerator

Simulations of proton-driven plasma wakefield accelerators have demonstrated substantially higher accelerating gradients compared to conventional accelerators and the viability of accelerating electrons to the energy frontier in a single plasma stage. However, due to the strong intrinsic transverse fields varying both radially and in time, the witness beam quality is still far from suitable for practical application in future colliders. Here we demonstrate efficient acceleration of electrons in proton-driven wakefields in a hollow plasma channel. In this regime, the witness bunch is positioned in the region with a strong accelerating field, free from plasma electrons and ions. We show that the electron beam carrying the charge of about 10% of 1 TeV proton driver charge can be accelerated to 0.6 TeV with preserved normalized emittance in a single channel of 700 m. This high quality and high charge beam may pave the way for the development of future plasma-based energy frontier colliders.Comment: 10 pages, 7 figure

Proton Driven Plasma Wakefield Acceleration

Plasma wakefield acceleration, either laser driven or electron-bunch driven, has been demonstrated to hold great potential. However, it is not obvious how to scale these approaches to bring particles up to the TeV regime. In this paper, we discuss the possibility of proton-bunch driven plasma wakefield acceleration, and show that high energy electron beams could potentially be produced in a single accelerating stage.Comment: 13 pages, 4 figure

A proposed experiment on the proton driven plasma wakefield acceleration

Simulations have shown that a high energy, short and intense proton beam can drive a large amplitude plasma wave and accelerate an electron beam to the energy frontier in a single plasma channel. To verify this novel idea, a proof-of-principle demonstration experiment is now being planned. The idea is to use the available high energy proton beams either from the Proton Synchrotron (PS) or the Super Proton Synchrotron (SPS) at CERN, to shoot the beam into a plasma cell and to excite the plasma wakefield. A strong density modulation due to the excited plasma wakefield is produced for a long drive beam and this modulated beam in turn produces a high electric field. The proposed experimental setup is introduced in this paper. The interactions between the plasma and the proton beam are simulated and the results are presented. The compression of an SPS bunch is also discussed.Comment: This paper is submitted to the proceedings of the first International Particle Accelerator Conference (IPAC10)in Kyoto, Japa

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Decision making in modern forest management planning is challenged by the need to recognize multiple ecosystem services and to address the preferences and goals of stakeholders. This research presents an innovative a posteriori preference modeling and multi-objective integer optimization (MOIP) approach encompassing integer programming models and a new technique for generation and interactive visualization of the Pareto frontier. Due to the complexity and size of our management problems, a decomposition approach was used to build the Pareto frontier of the general problem using the Pareto frontiers of its sub-problems. The emphasis was on the approximation of convex Edgeworth–Pareto hulls (EPHs) for the sub-problems by systems of linear inequalities; the generation of Edgeworth–Pareto hulls by the convex approximation of the Pareto frontier evinced a very small discrepancy from the real integer programming solutions. The results thus highlight the possibility of generating the Pareto frontiers of large multi-objective integer problems using our approach. This research innovated the generation of Pareto frontier methods using integer programming in order to address multiple objectives, locational specificity requirements and product even-flow constraints in landscape-level management planning problems. This may contribute to enhancing the analysis of tradeoffs between ecosystem services in large-scale problems and help forest managers address effectively the demand for forest products while sustaining the provision of services in participatory management planning processe