Stochastic cooling
Encyclopedia
Stochastic cooling is a form of particle beam cooling
Particle beam cooling
To be developed as a jump page related to particle acceleratorsCooling techniques are important for the control the emittance of particle beams in particle accelerators...

. It is used in some particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s and storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...

s to control the emittance
Beam emittance
The beam emittance of a particle accelerator is the extent occupied by the particles of the beam in space and momentum phase space as it travels. A low emittance particle beam is a beam where the particles are confined to a small distance and have nearly the same momentum...

 of the particle beam
Particle beam
A particle beam is a stream of charged or neutral particles which may be directed by magnets and focused by electrostatic lenses, although they may also be self-focusing ....

s in the machine. This process uses the electrical signals
Signal (electrical engineering)
In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity....

 that the individual charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

s generate in a feedback loop to reduce the tendency of individual particles to move away from the other particles in the beam. It is accurate to think of this as thermodynamic cooling, or the reduction of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

, in much the same way that a refrigerator
Refrigerator
A refrigerator is a common household appliance that consists of a thermally insulated compartment and a heat pump that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the ambient temperature of the room...

 or an air conditioner cools its contents.

The technique was invented and applied at the Intersecting Storage Rings
Intersecting Storage Rings
The ISR was a particle accelerator at CERN. It was the world's first hadron collider, and ran from 1971 to 1984, with a maximum center of mass energy of 62 GeV...

, and later the Super Proton Synchrotron
Super Proton Synchrotron
The Super Proton Synchrotron is a particle accelerator of the synchrotron type at CERN. It is housed in a circular tunnel, in circumference, straddling the border of France and Switzerland near Geneva, Switzerland. The SPS was designed by a team led by John Adams, director-general of what was...

, at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

 in Geneva, Switzerland by Simon van der Meer
Simon van der Meer
Simon van der Meer was a Dutch particle accelerator physicist who shared the Nobel Prize in Physics in 1984 with Carlo Rubbia for contributions to the CERN project which led to the discovery of the W and Z particles, two of the most fundamental constituents of matter.-Biography:One of four...

, a physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

 from the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

. It was used to collect and cool antiprotons--these particles were injected into the SPS with counter-rotating protons and collided at a particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

 experiment. For this work, van der Meer was awarded the Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...

 in 1984. He shared this prize with Carlo Rubbia
Carlo Rubbia
Carlo Rubbia Knight Grand Cross is an Italian particle physicist and inventor who shared the Nobel Prize in Physics in 1984 with Simon van der Meer for work leading to the discovery of the W and Z particles at CERN.-Biography:...

 of Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

, who conducted the physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 experiment that took advantage of this breakthrough. This experiment discovered the W and Z bosons
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...

, fundamental particles that carry the weak nuclear force.

Fermi National Accelerator Laboratory
Fermilab
Fermi National Accelerator Laboratory , located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics...

 continues to use stochastic cooling in its antiproton source. The accumulated antiprotons are used in the Tevatron
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...

 to collide with protons to create collisions at CDF
Collider Detector at Fermilab
The Collider Detector at Fermilab experimental collaboration studies high energy particle collisions at the Tevatron,the world's former highest-energy particle accelerator...

 and the D0 experiment
D0 experiment
The DØ experiment consists of a worldwide collaboration of scientists conducting research on the fundamental nature of matter...

.

Stochastic cooling in the Tevatron
Tevatron
The Tevatron is a circular particle accelerator in the United States, at the Fermi National Accelerator Laboratory , just east of Batavia, Illinois, and is the second highest energy particle collider in the world after the Large Hadron Collider...

 at Fermilab was attempted, but was not fully successful. The equipment was subsequently sold to Brookhaven National Laboratory
Brookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...

, where it was successfully employed in 2007, in the RHIC
Relativistic Heavy Ion Collider
The Relativistic Heavy Ion Collider is one of two existing heavy-ion colliders, and the only spin-polarized proton collider in the world. It is located at Brookhaven National Laboratory in Upton, New York and operated by an international team of researchers...

.

Technical details

This section needs to be edited for clarity by a stochastic cooling expert.

Stochastic cooling uses the electrical signals produced by individual particles in a group of particles (called a "bunch" of particles) to drive an electro-magnet device, usually an electric kicker, that will kick the bunch of particles to reduce the wayward momentum of that one particle. These individual kicks are applied continuously and over an extended time, the average tendency of the particles to have wayward momenta is reduced. These cooling times range from a second to several minutes, depending on the depth of the cooling that is required.

Stochastic cooling is used to reduce the transverse momentum spread within a bunch of charged particles in a storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...

 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
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

. 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
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

 the transverse motion of the particles is easily damped by synchrotron radiation
Synchrotron radiation
The electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers...

, 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
Free electron laser
A free-electron laser, or FEL, is a laser that shares the same optical properties as conventional lasers such as emitting a beam consisting of coherent electromagnetic radiation which can reach high power, but which uses some very different operating principles to form the beam...

).
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
      Klystron
      A klystron is a specialized linear-beam vacuum tube . Klystrons are used as amplifiers at microwave and radio frequencies to produce both low-power reference signals for superheterodyne radar receivers and to produce high-power carrier waves for communications and the driving force for modern...

       cavity
    • For transversal cooling the same devices are used as in an oscilloscope
      Oscilloscope
      An oscilloscope is a type of electronic test instrument that allows observation of constantly varying signal voltages, usually as a two-dimensional graph of one or more electrical potential differences using the vertical or 'Y' axis, plotted as a function of time,...

       or in a Streak camera
      Streak camera
      A streak camera is an instrument for measuring the variation in a pulse of light's intensity with time. They are used to measure the pulse duration of some ultrafast laser systems, and for applications such as time-resolved spectroscopy and LIDAR....

    • 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
        Traveling wave tube
        A traveling-wave tube is an electronic device used to amplify radio frequency signals to high power, usually in an electronic assembly known as a traveling-wave tube amplifier ....

      • undulator
        Undulator
        An undulator is an insertion device from high-energy physics and usually part of a largerinstallation, a synchrotron storage ring. It consists of a periodic structure of dipole magnets . The static magnetic field is alternating along the length of the undulator with a wavelength \lambda_u...

      • 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
      Cherenkov radiation
      Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...

      . The signals from multiple elements of the microstructure are added before being fed to the amplifier, reducing noise.
    • Multiple devices tuned (narrow 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 ring 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
Chirped pulse amplification
Chirped pulse amplification is a technique for amplifying an ultrashort laser pulse up to the petawatt level with the laser pulse being stretched out temporally and spectrally prior to amplification...

, compressor
Chirped pulse amplification
Chirped pulse amplification is a technique for amplifying an ultrashort laser pulse up to the petawatt level with the laser pulse being stretched out temporally and spectrally prior to amplification...

, or buncher, debuncher. (The links point to the equivalent devices for light pulses, so please note that the prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

s in the link are functionally replaced by dipole magnet
Dipole magnet
A dipole magnet, in particle accelerators, is a magnet constructed to create a homogeneous magnetic field over some distance. Particle motion in that field will be circular in a plane perpendicular to the field and collinear to the direction of particle motion and free in the direction orthogonal...

s 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.
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