Muon cooling channels Page: 1 of 20
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Fermilab FERMILAB-TM-2196 March 2003
Muon Cooling Channels*
Eberhard Keil
November 26, 2002
Abstract
A procedure uses the equations that govern ionization cooling, and leads to the most im-
portant parameters of a muon cooling channel that achieves assumed performance parameters.
First, purely transverse cooling is considered, followed by both transverse and longitudinal
cooling in quadrupole and solenoid channels. Similarities and differences in the results are
discussed in detail, and a common notation is developed. Procedure and notation are applied to
a few published cooling channels. The parameters of the cooling channels are derived step by
step, starting from assumed values of the initial, final and equilibrium emittances, both trans-
verse and longitudinal, the length of the cooling channel, and the material properties of the
absorber. The results obtained include cooling lengths and partition numbers, amplitude func-
tions and limits on the dispersion at the absorber, length, aperture and spacing of the absorber,
parameters of the RF system that achieve the longitudinal amplitude function and bucket area
needed. Finally, I compute the merit factor that describes the enhancement of the density in 6D
phase space. The consequences of changes in the input parameters are discussed. The lattice
parameters needed to achieve the assumed performance are summarised. The design proper
of such a lattice, i.e. finding the precise arrangement of magnets, RF cavities, absorbers, etc.,
which has these properties is well beyond the scope of this document.
1 INTRODUCTION
In this document, I develop a procedure in the form of a Mathematica notebook, which leads to the
most important parameters of a muon cooling channel that achieves assumed performance param-
eters. I first assemble the equations that govern ionization cooling. In Chapter 2, I consider purely
transverse cooling, following [1]. In Chapter 3, I treat both transverse and longitudinal cooling
in styles due to Neuffer [2] and Wang and Kim [3]. I discuss the similarities and discrepancies
in their results in detail, and develop my own notation. In Chapter 4, I apply my procedure and
notation to a few published cooling channels. In Chapter 5, I derive the parameters of the cooling
channels step by step. I start from assumed values of the initial, final and equilibrium emittances,
both transverse and longitudinal, the length of the cooling channel, and the material properties of
the absorber. I obtain cooling lengths and partition numbers, amplitude functions and limits on the
*Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United
States Department of Energy.1
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Keil, Eberhard K. Muon cooling channels, report, March 10, 2003; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc738095/m1/1/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.