APPLICATION OF MOMENTS METHOD TO DYNAMICS OF MUON COOLING SYSTEM. Page: 4 of 6
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(&osh2aoz + ach2oioz)] (17)
R2 = 4a ) (ch2cxoz - 1) (18)
R3 = 1 + exp(-2az) sh2-o 1 - _ ch2z - 2 (19)
40 \ aof)
ao = a2 - Q2 (20)
If ao is imaginary, then
chaoz -* cosw1z
shcypz _ sin w, z w1 = SZ2 - a2 (21)
APPLICATIONS TO LONGITUDINAL COOLING
In this case y = z - zs. (zs is a coordinate of equilibrium particle),
d dE P
2a-mc232y dz ion Lo+ dK A/fA
d [(d) v] - 2a1+2a2+23 (22)
The first term in RHS describes longitudinal cooling due to wedges, the second
one damping due to change of longitudinal mass, and the third one - so
named "natural" cooling due to slope of the ionization losses curve . Here
o= _i" (23)
dX (dE' io
We see, that if (d) does not depend on X, the derivative is equal to zero,
and the first term in (22) disappears. Where X is a transverse coordinate.
Parameter A is defined by
A =R + (24)
R is a radius of curvature for ideal trajectory. Q is the synchrotron frequency
and in linear approximation may be written as
27rEac cos (27 zs) A
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PARSA,Z. & ZENKEVICH,P. APPLICATION OF MOMENTS METHOD TO DYNAMICS OF MUON COOLING SYSTEM., article, December 3, 1996; [Upton, New York]. (digital.library.unt.edu/ark:/67531/metadc892494/m1/4/: accessed September 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.