Linear Theory of Ionization Cooling in 6D. Kwang-Je Kim & Chun-xi Wang University of Chicago and Argonne National Laboratory Cooling Theory/Simulation Day Illinois Institute of Technology February 5, 2002. Theory development . . . . . . . . . . . . . . . . . . .Kwang-Je Kim
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Linear Theory of Ionization Cooling in 6D
Kwang-Je Kim & Chun-xi Wang
University of Chicago and Argonne National Laboratory
Cooling Theory/Simulation Day
Illinois Institute of Technology
February 5, 2002
rotating frame with symmetric focusing
Solenoid + dipole + quadrupole + RF + absorber
Goal: theoretical framework and possible solution
In Larmor frame
Dispersion function decouples the betatron motion and dispersive effect
Natural ionization energy loss is insufficient for longitudinal cooling
slope is too gentle for
Will be neglected
: Average loss replenished by RF
I is a quadratic invariant with periodic coefficients.
(, , ), (z, z , z); Twist parameters for and ||
These are complete set!
These are the inverses of Eq. (a).
s = -(-ec-) s+ec+a+es+xy+bL+s,
a = -(-ec-) a+ec+s+ a,
xy = -(-ec-) xy+es+s+ xy,
L = -(-ec-) L+bs+ L,
z = -(+2ec-) z+ z,
C± = cos(qD-qw), s± = sin(qD ±qw), s- = sin (qD-qw)
b = xb + aes- + bes-