4-twist helix snake to maintain polarization in multi-GeV proton rings

Solenoid Siberian snakes have successfully maintained polarization in particle rings below 1 GeV, but never in multi-GeV rings, because the spin rotation by a solenoid is inversely proportional to the beam momentum. High energy rings, such as Brookhaven’s 255 GeV Relativistic Heavy Ion Collider (RHIC), use only odd multiples of pairs of transverse B-field Siberian snakes directly opposite each other. When it became impractical to use a pair of Siberian Snakes in Fermilab’s $120\mathrm{GeV}/\mathrm{c}$ Main Injector, we searched for a new type of single Siberian snake that could overcome all depolarizing resonances in the $8.9–120\mathrm{GeV}/\mathrm{c}$ range. We found that a snake made of one 4-twist helix and 2 dipoles could maintain the polarization. This snake design could solve the long-standing problem of significant polarization loss during acceleration of polarized protons from a few GeV to tens of GeV, such as in the AGS, before injecting them into multi-hundred GeV rings, such as RHIC.

Figure 1

(a) Horizontal and vertical field components for a Siberian Snake consisting of: 4-T–4-twist–5.653 m–long helical dipole, 4-T–0.203 m–long dipoles at each end and two 0.200 m-long gaps [2]. Vertical lines show the helix’s edges (solid black) and the dipoles’ edges (dashed blue). In the graphs, the curves are from a Python-based spin and excursion tracking program, the symbols are for analytic matrix calculations. (b) Horizontal and vertical orbit excursions. (c) Radial, vertical, and longitudinal spin components for a $8.9\mathrm{GeV}/\mathrm{c}$ beam. (d) Spin components for a $120\mathrm{GeV}/\mathrm{c}$ beam. Note that while numerical calculations can give us spin orientation anywhere inside the snake, the matrix calculations are only available for the end of each magnet. Note the much better agreement between our numerical and matrix calculation at $120\mathrm{GeV}/\mathrm{c}$ than at $8.9\mathrm{GeV}/\mathrm{c}$. Fortunately a polarized proton beam spends almost all of its time at or near its final energy; the depolarization near $8.9\mathrm{GeV}/\mathrm{c}$ should be much smaller.

Figure 2

Spin components at the exit of the snake as a function of time-step used for numerical calculations using Blewett-Chasman fields, for a $120\mathrm{GeV}/\mathrm{c}$ beam entering the snake on-axis with spin components $S_X$, $S_Z=0$ and $S_Y=1$.

Figure 3

Beam excursions and angles at the exit of the snake as a function of time-step used for numerical calculations using Blewett-Chasman fields, for a $120\mathrm{GeV}/\mathrm{c}$ beam entering the snake on-axis.