The preservation of beam quality in a plasma wakefield accelerator driven by ultrahigh intensity and ultralow emittance beams, characteristic of future particle colliders, is a challenge. The electric field of these beams leads to plasma ions motion, resulting in a nonlinear focusing force and emittance growth of the beam. We propose to use an adiabatic matching section consisting of a short plasma section with a decreasing ion mass to allow for the beam to remain matched to the focusing force. We use analytical models and numerical simulations to show that the emittance growth can be significantly reduced.

We study the effect of plasma temperature on ion motion in a plasma wakefield accelerator with parameters typical of a future high-energy accelerator. We show that the collapse of the plasma ions caused by the extremely high fields of ultradense electron bunches can be prevented only by a very high plasma ion temperature. DOI: 10.1103/PhysRevSTAB.14.021303 PACS numbers: 52.40. Mj, 52.75.Di, 29.27.Àa Plasmas are capable of sustaining extremely high amplitude electric fields that can be used to accelerate particles to high energies, in distances orders of magnitude shorter than in conventional accelerators. In fact, in a recent experiment at the SLAC National Accelerator Laboratory, the energy of 42 GeV trailing electrons was doubled in only 85 cm of lithium plasma [1].In a beam driven plasma-based particle accelerator or plasma wakefield accelerator (PWFA) [2], a high-density relativistic drive electron bunch expels the plasma electrons off its path [ Fig. 1(a)] [1]. In order to reach large accelerating fields, the electron bunch must be short, and the plasma density such that the wavelength of the relativistic plasma wave pe is on the order of the bunch length z :pe ¼ 2c=! pe $ z . The plasma angular frequency in a plasma with electron density n e is ! pe ¼ ð2n e e 2 =m e Þ 1=2 . When the beam density n b is larger than the plasma density (n b > n e ), all the plasma electrons are displaced on a time scale given by the electron plasma frequency ( e $ 2 ! pe ) to a distance on the order of the bunch neutralization radius: r e $ ðn b =n e Þ 1=2 r , where r is the bunch radius. Typically, the ions respond and move on a much longer time scale given by the ion plasma frequency. Therefore the ions (usually assumed cold, T i ¼ 0) can be considered immobile and the ion column density uniform [ Fig. 2(a)] since the wake generation and particle acceleration processes are over after a time $ e . Gauss' law dictates that the uniformly distributed ions create a transverse electric field that increases linearly with radius r: E r ¼ 2n i er [n i ¼ n e for the neutral plasma, Fig. 2(b)], which focuses a following witness bunch. This field also pulls back to the axis the expelled plasma electrons that sustain the accelerating structure [ Fig. 1(a)]. The intense longitudinal component of the wakefield accelerates the witness bunch when injected at the proper position behind the drive bunch [ Fig. 1(b)]. Energy is therefore transferred from the drive bunch to the witness bunch through the plasma wake.The ion column also acts as a focusing channel that prevents the two bunches from expanding because of their finite transverse emittances thus allowing for acceleration over long distances ($ 1 m) [1]. In the case of a uniform column density with linear focusing force [Figs. 2(a) and 2(b)], the emittance of the witness bunch is preserved upon propagation and acceleration [4]. However, in the case of an ultradense (drive or witness) electron bunch with n b ) n e , the electric field of the bunch is so intense that the cold ions ar...

Optimal distribution substation placement is one of the major components of optimal distribution system planning projects. This paper proposes the application of an Imperialist Competitive Algorithm (ICA) for the optimal expansion planning of large distribution network, solving the optimal sizing, siting and timing of medium voltage substation, using related fixed and variable costs subject to any operating and optimization constraints. A step by step expansion design and planning is proposed to consider dynamic behavior of the load forecasting uncertainty, asset management and geographical constraints. In order to reach the global solution, an effective coding for the ICA parameter is developed. The value of loads' density in every site is determined by mid and long-term load forecasting program. The results show the efficiency and capability of the proposed method which has been tested on a large-scale real size distribution network.

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Plasma wakefield accelerator is examined in the extreme regime of nanometer transverse beam sizes, typical of designs in the multi-TeV range. We find that ion motion, synchrotron radiation, nuclear scattering and particle trapping constrain the design parameters in which high beam quality and efficiency can be maintained. For a particular example relevant to an ILC Afterburner, the analysis suggests that an intermediate mass ion such as Argon may best satisfy the constraints.