ICOOL: a simulation code for ionization cooling of muon beams

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Abstract
Current ideas (1,2) for designing a high luminosity muon collider require significant cooling of the phase space of the muon beams. The only known method that can cool the beams in a time comparable to the muon lifetime is ionization cooling (3,4). This method requires directing the particles in the beam at a large angle through a low Z absorber material in a strong focusing magnetic channel and then restoring the longitudinal momentum with an rf cavity. We have developed a new 3-D tracking code ICOOL for examining possible configurations for muon cooling. A cooling system is described in terms of a series of longitudinal regions with associated material and field properties. The tracking takes place in a coordinate system that follows a reference orbit through the system. The code takes into account decays and interactions of ~50-500 MeV/c muons in matter. Material geometry regions include cylinders and wedges. A number of analytic models are provided for describing the field configurations. Simple diagnostics are built into the code, including calculation of emittances and correlations, longitudinal traces, histograms and scatter plots. A number of auxiliary files can be generated for post-processing analysis by the user. 1. PROGRAM OVERVIEW A major part of the cooling simulation effort for the Muon Collider Collaboration has been directed toward the development of two programs. The first, ICOOL, provides the flexibility to quickly examine widely different ideas for implementing ionization cooling. For example, setting up desired field configurations is accomplished in ICOOL using predefined, analytic field models. This simplifies the adjustment of parameters for the field to obtain some desired result. The second program, DPGeant (5), is based on the GEANT code system (6). It is possible to describe very complicated 3-D problem geometries using DPGeant and to calculate quantities to greater accuracy than with ICOOL. DPGeant typically gets its field distributions from maps generated by other, more accurate field computation codes. In our experience the two codes have been quite complementary. One code is frequently used to check results from the other. ICOOL uses a command input file consisting of five parts: simulation control variables, beam definition, control of physics interactions, diagnostics, and region definition. Current ideas for ionization cooling make extensive use of solenoidal channels. For this reason we define a region to encompass a cylindrical volume which has a fixed length along the reference orbit. A region can be subdivided radially in up to 5 subregions. Each subregion has a field type, material type, and material geometry associated with it. Particles are allowed to pass back and forth between radial subregions. Wedge shaped material geometries are provided for reducing the momentum spread in dispersive regions. There is no practical limit on the number of regions in a problem. After validity checking, the region data are stored in a direct access disk file. The program tracks the particles to the end of a given region and generates any desired diagnostics. It then moves on to track the surviving particles to the end of the next region. This program structure was adopted to make it possible to eventually add space charge interactions. At present the code only has a very crude space charge model applicable in pillbox cavity regions. The region description language has two looping structures to aid in describing complicated, repetitive systems. A group of regions, such as rf cavity cells, may be repeated as often as desired using a REPEAT structure. Groups of REPEAT structures and isolated regions may be combined into a CELL structure, which may also be repeated as often as desired. In addition a CELL has its own field type associated with it. This allows applying a background solenoid field, for example, over a sequence of regions, each of which has its own local field. In addition to the physical regions described above, the user can insert "pseudoregions" into the command file at various locations to accomplish tasks, such as forcing diagnostic output, collimating the beam, transforming the beam with a TRANSPORT element, redefining the reference particle, etc. The program can initialize the phases of long strings of rf cavities by using an on-axis reference particle. The most commonly used algorithm tracks the reference particle through absorbers and other non-cavity regions, taking into account the mean energy lost there. The energy of the reference particle is increased in rf cavity

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