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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Kwang-Je Kim & Chun-xi Wang
University of Chicago and Argonne National Laboratory
Cooling Theory/Simulation Day
Illinois Institute of Technology
February 5, 2002
Lab . Kwang-Je Kim
rotating frame with symmetric focusingHamiltonian Under Consideration
Solenoid + dipole + quadrupole + RF + absorber
Goal: theoretical framework and possible solution
In Larmor frame
Dispersion function decouples the betatron motion and dispersive effect
momentum gain . Kwang-Je Kim
Natural ionization energy loss is insufficient for longitudinal cooling
slope is too gentle for
Will be neglected
wedge . Kwang-Je KimModel for Ionization Processin Larmor Frame
: 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-