  This paper describes a new way to reconstruct and identify muons with high
efficiency and high pion rejection. Since muons at the ILC are often produced
with or in jets, for many of the physics channels of interest[1], an efficient
algorithm to deal with the identification and separation of particles within
jets is important. The algorithm at the core of the method accounts for the
effects of the magnetic field and for the loss of energy by charged particles
due to ionization in the detector. We have chosen to develop the analysis
within the setup of one of the Linear Collider Concept Detectors adopted by the
US. Within b-pair production jets, particles cover a wide range in momenta;
however ~ 80% of the particles have a momentum below 30 GeV[2]. Our study,
focused on bbar-b jets, is preceded by a careful analysis of single energy
particles between 2 and 50 GeV. As medium energy particles are a substantial
component of the jets, many of the particles lose part of their energy in the
calorimeters and the solenoid coil before reaching the muon detector where they
may have energy below 2 GeV. To deal with this problem we have implemented a
Runge-Kutta correction of the calculated trajectory to better handle these
lower energy particles. The multiple scattering and other stochastic processes,
more important at lower energy, is addressed by a Kalman-filter integrated into
the reconstruction algorithm. The algorithm provides a unique and powerful
separation of muons from pions. The 5 Tesla magnetic field from a solenoid
surrounds the hadron calorimeter and allows the reconstruction and precision
momentum measurement down to a few GeV.
