The Maxwell–Boltzmann distribution of a bunched charged particle beam is the state toward which every other distribution will relax. For beams with lifetimes much shorter than the time required for relaxation to equilibrium, it is the distribution at injection that minimizes the emittance growth due to relaxation toward equilibrium. Three-dimensional thermal distributions are found numerically for the case of linear external focusing forces acting on an axially symmetric bunched beam in a conducting pipe. Equations are derived for current loss into the conducting channel due to particle thermal motion in the equilibrium distribution. Relations between parameters such as perveance, emittance, space-charge tune depression, bunch radius, and bunch length are given over a wide range of conditions from short to long bunches and from space-charge dominated to emittance-dominated beams. Comparison is made with previous results of radial density profiles for unbunched beams and line-charge density profiles for bunched beams [Phys. Rev. Lett. 71, 2911 (1993)].

Modern data center applications have deep software stacks, with instruction footprints that are orders of magnitude larger than typical instruction cache (I-cache) sizes. To efficiently prefetch instructions into the I-cache despite large application footprints, modern server-class processors implement a decoupled frontend with Fetch Directed Instruction Prefetching (FDIP). In this work, we first characterize the limitations of a decoupled frontend processor with FDIP and find that FDIP suffers from significant Branch Target Buffer (BTB) misses. We also find that existing techniques (e.g., stream prefetchers and predecoders) are unable to mitigate these misses, as they rely on an incomplete understanding of a program's branching behavior.To address the shortcomings of existing BTB prefetching techniques, we propose Twig, a novel profile-guided BTB prefetching mechanism. Twig analyzes a production binary's execution profile to identify critical BTB misses and inject BTB prefetch instructions into code. Additionally, Twig coalesces multiple non-contiguous BTB prefetches to improve the BTB's locality. Twig exposes these techniques via new BTB prefetch instructions. Since Twig prefetches BTB entries without modifying the underlying BTB organization, it is easy to adopt in modern processors. We study Twig's behavior across nine widely-used data center applications, and demonstrate that it achieves an average 20.86% (up to 145%) performance speedup

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The Maxwell-Boltzmann ("thermal") distribution constitutes the natural thermodynamic equilibrium state for a charged particle beam, and knowledge of its properties is therefore of fundamental importance. The Boltzmann relation for the particle density has a nonanalytic form when the space-charge force is included. We use numerical integration to determine the transverse and longitudinal density profiles for a relativistic beam in a linear focusing system at different temperatures T± and 7V The calculated profiles are related to space-charge tune depression, rms width, perveance, and emittance of the beam.PACS numbers: 41.85.Ew, 52.25.Wz Many advanced charged particle beam experiments and applications, such as high-power microwave sources, free electron lasers, linear accelerators for heavy-ion inertial fusion, spallation neutron sources, radioactive waste transmutation, high-energy colliders, and other uses, require very high beam intensity so that the beam dynamics depend strongly on the particle density profile. It is therefore of fundamental interest to know the equilibrium state of the charged particle beam for a given situation. Thermodynamically, this equilibrium state is best described by a Maxwell-Boltzmann ("thermal") distribution with different transverse and longitudinal temperatures (T ± and T\\) since in practice many beams are not equipartitioned. Many effects lead to coupling between T± and T\\ [1]; we deal here with cases where the coupling is small. When space-charge forces are significant the equilibrium density profiles have a nonanalytic form and must be found numerically, which explains why the thermal distribution has received less attention in the literature on beam theory than it deserves. Lawson [2] has published numerical results for the radial density profiles of a continuous nonrelativistic thermal beam in a linear focusing channel. In our work reported here we extend Lawson's results by including the relativistic factor y 2 , correcting an error, and correlating the density profiles with space-charge tune depression, perveance, and emittance of the rms equivalent uniform (K-V) beam. In addition, we determine the line-charge density profiles for a bunched beam with linear longitudinal focusing forces for different longitudinal temperatures and relate the results to the tune depression and other parameters of the rms equivalent parabolic bunch.The equilibrium distribution /of a group of charged particles in a focusing channel can be found from the Vlasov equation. We assume that the potential can be written as the sum of a transverse potential ±(r) and a longitudinal potential \\(z) in cylindrical coordinates, and that the beam and focusing system are uniform, or "smooth." Each of these potentials is the sum of a selfcomponent [0j_ 5 (r) and \\ s (z)] and an external focusing component [(/>± e (r) and (j>\\ e (z)].The Maxwell-Boltzmann distribution has the form f^foQxpi -H/kBT), where H is the single-particle Hamiltonian, kg is Boltzmann's constant, and T is the temperature. I...

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