Stochastic Cooling in RHIC
by Mike Blaskiewicz
During heavy ion operations a typical RHIC bunch contains about a billion particles. The individual particles undergo transverse focussing by the magnets and are kept longitudinally bunched by electric fields generated by radio frequency (RF) cavities. In the collision region a typical bunch has a radius of about 100 microns and a length of about a meter. During the course of a four hour store the bunch dimensions can double. In fact, the energy spread of the beam increases to the point that the RF can no longer keep all the particles bunched. This results in fewer collisions, reducing useful physics data.
The purpose of the stochastic cooling system is to keep the beam bunched. The basic idea is illustrated in the figure above. where only a few particles are shown to cut down on confusion. The red dots in the top panel show the energy errors of the particles and their arrival times with respect to the center of the bunch on one turn, while the blue dots show the energy errors and relative arrival times on the next turn. The change in relative arrival time is proportional to the energy error. More energetic particles take longer to go around the ring because the increased path length due to less effective magnetic focussing wins out over the slight increase in speed. The stochastic cooling system first measures the relative arrival time of particles on two subsequent turns. The red and blue traces in the bottom panel are model signals for the red and blue particles in the top panel. The signal from an individual particle is in the form of a doublet with the zero crossing centered on the particle's arrival time. Consider the rightmost particle, which requires a negative energy kick to cool it. By subtracting the blue pickup voltage from the red pickup voltage we obtain the black line for the kick in the upper panel. For the rightmost particle the kick is negative, correcting this particles positive energy error. For the three particles just to the left of this particle things are less straightforward but a negative kick certainly seems reasonable. It turns out that a kick proportional to (it's way too big) the black curve in the top trace will optimally cool the particles. The proportionality coefficient depends on the number of particles, going down as the number of particles goes up. This is why the system is designed to cool gold bunches with a billion particles, as opposed to proton bunches with about one hundred billion particles.
The RHIC cooling system is very similar to the one described above. The actual system involves many technical details and some fairly devious tricks. It worked as expected in a test using a special, low intensity proton bunch. Others have tried this before, without success. We plan on making the system operational over the course of the present gold run. Also, we are looking into the possibility of transverse stochastic cooling systems which would keep the bunches tight in the transverse directions as well.
"Successful Bunched Beam Stochastic Cooling in RHIC", J.M. Brennan, M. Blaskiewucz, F. Severino (PDF)