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The Neutrino Factory is an important tool in the long-term neutrino physics program. Substantial effort is put internationally into designing this facility in order to achieve desired performance within the allotted budget. This accelerator is a secondary beam machine: neutrinos are produced by means of the decay of muons. Muons, in turn, are produced by the decay of pions, produced by hitting the target by a beam of accelerated protons suitable for acceleration. Due to the physics of this process, extra conditioning of the pion beam coming from the target is needed in order to effectively perform subsequent acceleration. The subsystem of the Neutrino Factory that performs this conditioning is called Front End, its main performance characteristic is the number of the produced muons.

Evolutionary Algorithms demonstrated themselves as a reliable and efficient tool for exploration, optimization and ultimately decision-making during the design process. In this work we describe the scenario for the Neutrino Factory Front End production optimization via the GATool Evolutionary Algorithm implemented in COSY Infinity and discuss the results of this optimization.

A brief review is given of the development of linacs, cyclotrons, synchrotrons (also accumulators) and FFAG accelerators for a variety of high power hadron beam applications.

The potential of muon beams for high energy physics applications is described along with the challenges of producing high quality muon beams. Two proposed approaches for delivering high intensity muon beams, a proton driver source and a positron driver source, are described and compared. The proton driver concepts are based on the studies from the Muon Accelerator Program (MAP). The MAP effort focused on a path to deliver muon-based facilities, ranging from neutrino factories to muon colliders, that could span research needs at both the intensity and energy frontiers. The Low EMittance Muon Accelerator (LEMMA) concept, which uses a positron-driven source, provides an attractive path to very high energy lepton colliders with improved particle backgrounds. The recent study of a 14-TeV muon collider in the LHC tunnel, which could leverage the existing CERN injectors and infrastructure and provide physics reach comparable to the 100TeV FCC-hh, at lower cost and with cleaner physics conditions, is also discussed. The present status of the design and R&D efforts towards each of these sources is described. A summary of important R&D required to establish a facility path for each concept is also presented.

The potential of muon beams for high energy physics applications is described along with the challenges of producing high quality muon beams. Two proposed approaches for delivering high intensity muon beams, a proton driver source and a positron driver source, are described and compared. The proton driver concepts are based on the studies from the Muon Accelerator Program (MAP). The MAP effort focused on a path to deliver muon-based facilities, ranging from neutrino factories to muon colliders, that could span research needs at both the intensity and energy frontiers. The Low EMittance Muon Accelerator (LEMMA) concept, which uses a positron-driven source, provides an attractive path to very high energy lepton colliders with improved particle backgrounds. The recent study of a 14-TeV muon collider in the LHC tunnel, which could leverage the existing CERN injectors and infrastructure and provide physics reach comparable to the 100TeV FCC-hh, at lower cost and with cleaner physics conditions, is also discussed. The present status of the design and R&D efforts towards each of these sources is described. A summary of important R&D required to establish a facility path for each concept is also presented.

The MICE experiment aims to demonstrate ionisation cooling for the first time experimentally. MICE is made up of a cooling channel, consisting of two RF linacs sandwiched between three absorbers, with instrumentation at either end. A detailed simulation of both the accelerator and detector elements of the experiment, called G4MICE, has been produced. This is required for both calibration of detectors and to provide a benchmark of whether the Monte Carlo is able to accurately reproduce cooling. This paper details the simulation of the components of the cooling channel and shows the cooling performance of MICE as simulated by G4MICE.

Muon Cooling is discussed, showing its importance both for a future Neutrino Factory and the Muon Collider. The physics cases are introduced and a comparison of the two facilities is done, which illustrates similarities and differences. R&D programs, with special emphasis on the presently starting cooling experiment MICE, are discussed.

A brief review is given of the development of linacs, cyclotrons, synchrotrons (also accumulators) and FFAG accelerators for a variety of high power hadron beam applications.

An accelerator complex that can produce ultra-intense beams of muons presents many opportunities to explore new physics. This facility is unique in that it can present a physics program that can be staged and thus move forward incrementally, addressing exciting new physics at each step. An intense cooled low-energy muon source can be used to perform extraordinarily precise lepton flavor violating experiments and these same muons can be accelerated to be used in a Neutrino Factory or energy-frontier Muon Collider. In this paper I will give an introduction to muon accelerator facilities and their physics capabilities and then will discuss some of the limiting technologies that must be developed in order to make these concepts a reality.

Sensitivity of a neutrino factory to various mixing angles in a scheme with one sterile neutrino is studied using ν_e → ν_μ, ν_μ → ν_μ, ν_e → ν_τ and ν_μ → ν_τ. While the "discovery-channel" ν_μ,→ ν_μ is neither useful in the standard three flavor scheme nor very powerful in the sensitivity study of sterile neutrino mixings, this channel is important to check unitarity and to probe the new CP phase in the scheme beyond the standard neutrino mixing framework.