Simulations on the AGS horizontal tune jump mechanism Page: 3 of 5
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
SIMULATIONS ON THE AGS HORIZONTAL TUNE JUMP MECHANISM*
F.Lin, H.Huang, A.U.Luccio, T.Roser
Brookhaven National Laboratory, Upton, NY 11973, USAAbstract
A new horizontal tune jump mechanism has been pro-
posed to overcome the horizontal intrinsic resonances and
preserve the polarization of the proton beam in the Al-
ternating Gradient Synchrotron (AGS) during the energy
ramp. An adiabatic change of the AGS lattice is needed to
avoid the emittance growth in both horizontal and vertical
planes, as the emittance growth can deteriorate the polar-
ization of the proton beam. Two critical questions are nec-
essary to be answered: how fast can the lattice be changed
and how much emittance growth can be tolerated from both
optics and polarization points of view? Preliminary simu-
lations, using a realistic AGS lattice and acceleration rate,
have been carried out to give a first glance of this mech-
anism. Results with different optics are presented in this
paper.
INTRODUCTION
With two partial Siberian snakes[l]. the polarization of
proton beam can be maintained in the AGS during the ac-
celeration. The snakes cause the spin vector locally to pre-
cess by an angle of less than or equal to 1800 around an axis
in the horizontal plane. Two important types of spin reso-
nances, imperfection resonance happening at vs = Gy =
n and intrinsic resonance happening at Gy = kP v ,
are overcome by the two partial snakes. Here vs is the spin
tune, G = (g - 2)/2 1.7928 is the proton anomalous
gyromagnetic g-factor, + is the Lorentz energy factor, vy is
the vertical betatron tune, a and k are integers and P is the
super-periodicity of the machine lattice. 12 for AGS.
In the AGS, two partial helical dipole snakes, cold snake
(superconducting magnet) and warm snake (normal con-
ducting magnet), are intentionally separated by 1/3 of the
ring to eliminate the spin mismatching at the injection and
extraction energy. Hence, the spin tune is obtained as 121,7r
arecos (cos cos cos [ G-r] -
2 2
sin sin - os [G0),
2 2 39(1)
where Xy x, are the spin rotation angles caused by the
cold and warm snake, respectively. This leads to the spin
tune gap which limits the allowed range of tune values to
reach its maximum every G -- 3n (n is an integer). Since
the AGS has a super-periodicity of 12 and the vertical be-
tatron tune is close to integer 9, this feature provides the
'Work supported by DOE of United States under contract No. DE-
AC02-98CH0886. and with support of RIKEN(Japan))maximum space for placing the vertical betatron tune in
the prohibited region of spin tune at all the strong vertical
intrinsic resonances. The spin tune gaps (resonance free
space) at all other integers are large enough to avoid all
weak vertical spin resonances.
On the other hand, the stable spin direction[3], verti-
cal in a perfect planar accelerator, is titled away from the
vertical direction due to the two helical dipole snakes in
the AGS. The spin vector of polarized proton will pre-
cess around the non-vertical stable spin direction during
the acceleration. The interaction between the horizontal
displacement and the vertical magnetic field perturbs the
spin vector away from the stable spin direction and intro-
duces another type depolarizing resonance, horizontal in-
trinsic resonance, which happens when vs = k v, [4].
Here t, is the horizontal betatron tune, which is around
8.72 on the ramp in AGS. Therefore, the polarized proton
beam experiences 82 horizontal intrinsic resonances dur-
ing the whole energy ramp from 2.4GeV to 24 GeV in
the AGS. Realistic simulation and experiment results show
that 7 - 8% polarization loss due to those horizontal in-
trinsic resonances for the combination of 10% cold snake
and 5.9% warm snake, even worse for 15% cold snake and
5.9% warm snake, which tilt the stable spin direction fur-
ther away from the vertical direction and stronger horizon-
tal resonances are expected[5].
Different mechanism has been proposed to overcome the
horizontal intrinsic resonance [6]. An alternate practical
proposal is the horizontal tune jump at each resonance lo-
cation during the acceleration. The detail is described in
the following section.
HORIZONTAL TUNE JUMP MECHANISM
The scheme of horizontal tune jump is to accelerate a
spin horizontal intrinsic resonance crossing by varying the
betatron tune locally when the resonance condition is ap-
proaching to us = k + v, As given by the Froissart-Stora
Formula [7,P' -
' = 2e- - 1(2)
where P and Pf is the polarization before and after cross-
ing the resonance respectively, e is the resonance strength
and a = dOi is the resonance crossing rate. To
preserve the polarization, it requires either if I 0.056
(fast crossing) to maintain 99% polarization or cj >
1.81 (slow crossing) to attain -99% spin flip. Because in
the AGS those horizontal intrinsic resonances are mostly
weak, a fast crossing is a practical approach to overcome
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Lin,F.; Huang, H.; Luccio, A. U. & Roser, T. Simulations on the AGS horizontal tune jump mechanism, article, May 4, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc931309/m1/3/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.