Stochastic cooling

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Stochastic cooling is a technique to reduce the transverse momentum spread within a bunch of charged particles in a storage ring by detecting fluctuations in the momentum of the bunches and applying a correction (a "steering pulse" or "kick"). This is an application of negative feedback. This is known as "cooling" as the bunch can be thought of as containing an internal temperature. If the average momentum of the bunch were to be subtracted from the momentum of each particle, then the charged particles would appear to move randomly, much like the molecules in a gas. The more vigorous the motion, the "hotter" the bunch is -- again, just like the molecules in a gas.

The charged particles travel in bunches in potential wells, and the oscillation of the center of mass of each bunch is easily damped using standard RF techniques. However, the internal momentum spread of each bunch is not affected by this damping. The key to stochastic cooling is to address individual particles within each bunch using electromagnetic radiation.

The bunches pass a wideband optical scanner, which detects the position of the individual particles. In a synchrotron the transverse motion of the particles is easily damped by synchrotron radiation, which has a short pulse length and wide bandwidth, but the longitudinal motion can only be increased by simple devices (see for example Free electron laser). To achieve cooling the position information is fed-back into the particle bunches (using, for example, a fast kicker magnet), producing a negative feedback loop.

• Micro-structure of the coupler.
  • Klystron cavity
  • For transversal cooling the same devices are used as in an oscilloscope or in a Streak camera
  • directional couplers, that integrate measurement and steering adjustment (in this context often called kicking) in one device. Coupled energy increases with the square of the length of the structure due to reapplying the field to the particle. The particles travel near but not exactly at light-speed, so the devices are need to slow down the light.
    • traveling wave tube
    • undulator
    • For transverse cooling multiple steering plates and coils connected to form a delay line can be used
• Macro-structure for the pickup. Coupled energy increases lineary with of the length of the structure.
  • Cherenkov radiation. The signals from multiple elements of the microstructure are added before being fed to the amplifier, reducing noise.
  • Multiple devices tuned (narow band=lower noise) to different frequencies are used, so that about 20 GHz can be covered.

The bunches are focused through a small hole between the electrode structure, so that the devices have access to the near-field of the radiation. Additionally the current impinging on the electrode is measured and based on this information the electrodes are centered around the beam and moved together while the beams cools and gets smaller.

The word “stochastic” in the title stems from the fact that usually only some of the particles can unambiguously be addressed at once. Instead, small groups of particles are addressed within each bunch, and the adjustment or kick applies to the average momentum of each group. Thus they cannot be cooled down all at once but instead it requires multiple steps. The smaller the group of particles which can be detected and adjusted at once (requiring higher bandwidth), the faster the cooling.

As the particles in the storage ringe travel at nearly the speed of light, the feedback loop, in general, has to wait until the bunch returns to make the correction. The detector and the kicker can be placed on different positions on the ring with appropriately chosen delays to match the eigenfrequencies of the ring.

The cooling is more efficient for long bunches, as the position spread between particles is longer. Optimally bunches are as short as possible in the accelerators of the ring and as long as possible in the coolers. Devices which do this are intuitively called stretcher, compressor, or buncher, debuncher. (The links point to the equivalent devices for light pulses, so please note that the prisms in the link are functionally replaced by dipole magnets in a particle accelerator.)

In low energy rings the bunches can be overlapped with freshly created and thus cool (1000 K) electron bunches from a linac. This is a direct coupling to a lower temperature bath, which also cools the beam. Afterwards the electrons can also be analyzed and stochasitic cooling applied.