49th ICFA Advanced Beam Dynamics Workshop Electron cloud Induced Instabilities, Non-Linear Beam Dynamics, and Emittance Growth G. Dugan, Cornell University ECLOUD’10 WORKSHOP 10/8/10 10/13/2010
Electron clouds and particle beams 49th ICFA Advanced Beam Dynamics Workshop • You have heard about how electron clouds are formed and can build up in the vacuum chambers of accelerators. • The high-energy particle beam in the accelerator has to share the “vacuum” chamber with the electron cloud, and does not like it. • Note that the dominant effects are present for positively charged beams (e.g., protons, positrons), since in these cases charged beams (e.g., protons, positrons), since in these cases the beam attracts the electron cloud and can be strongly influenced by it. • In this talk, we will discuss the effects that electron clouds can have on the dynamics of particle beams in accelerators. The emphasis will be on positron beams and experiments at CESR. 10/13/2010
Accelerators 49th ICFA Advanced Beam Dynamics Workshop • An accelerator is a device used to produce a beam of high-energy particles September 24, 2010 ECLOUD`10 - Cornell University 3
Cornell Electron Storage Ring 49th ICFA Advanced Beam Dynamics Workshop • The Cornell Electron Storage Ring (CESR) is a circular accelerator of a type called a “synchrotron”. • The particles in the beam (positrons) travel at very close to light speed in roughly circular orbits of circumference about 760 m. •The bending magnets (dipoles) provide the bending needed for a circular orbits. •The focusing magnets •The focusing magnets (quadrupoles) provide the restoring forces needed for stable oscillations. •The RF cavity provides energy to the beam. September 24, 2010 ECLOUD`10 - Cornell University 4
Particle beam oscillations 49th ICFA Advanced Beam Dynamics Workshop • The particles in the beam (positrons), traveling in approximately plane circular orbits within a vacuum chamber, execute small-amplitude oscillations about the plane: Beam particle Circular orbit (~ 760 m in CESR) Vacuum chamber not shown Oscillation (amplitude << 1 mm) In the accelerator, the focusing forces which provide the stability for the oscillations are provided by the quadrupole magnets, arranged in a “lattice”. 10/13/2010
Particle beam dynamics 49th ICFA Advanced Beam Dynamics Workshop • Here is a very simple analogy for the transverse motion of a beam particle: a particle in a quadratic potential well. • A beam particle oscillates in the potential well. The total energy of the particle, together with the curvature of the potential energy function, determines the amplitude of the determines the amplitude of the oscillation. • The (linear) forces responsible for the quadratic potential energy are provided by quadrupole magnets in the accelerator. • The frequency of the oscillations is called the “tune”. 10/13/2010
Phase space and emittance 49th ICFA Advanced Beam Dynamics Workshop • A plot of the position vs. velocity of the particle as measured at some point in the ring, on subsequent turns, is called a “phase space” plot. • Over many cycles of the oscillation, if the forces are linear, the particle will trace out an ellipse in phase space. • The area contained within the ellipse is related to the amplitude of the oscillations, and is called the “emittance”. At different points in the ring, the orientation and shape of the ellipse • will be different, but the area will always be the same. will be different, but the area will always be the same. Phase plot Beam particle at point A Area=emittance A Dots represent the position and velocity of a beam particle at point A in the ring, on each turn September 24, 2010 ECLOUD`10 - Cornell University 7
Beam quality: emittance 49th ICFA Advanced Beam Dynamics Workshop • When we have a collection of beam particles with different Phase plot emittances in the accelerator, at point A the projection of the collection’s points onto the position axis is the beam position distribution at that point in the ring. It is determined by the average emittance. For many applications, the beam • • For many applications, the beam size should be kept as small as possible: hence the average emittance should be as low as possible. Beam size at point A • The most important reason to control the electron cloud in accelerators is to prevent any growth in the emittance. Beam distribution at point A 10/13/2010
Effects of the electron cloud-I 49th ICFA Advanced Beam Dynamics Workshop • The electron cloud constitutes a charge distribution which can exert forces on the beam. This changes the effective potential energy curve. • If these forces are linear with displacement, the change is reflected in a change in the oscillation frequency, but no change in the emittance. change in the emittance. If the forces are non-linear, the • shape of the potential well is distorted, chaotic motion ensues, and the beam emittance increases. • This source of emittance growth is usually small, but it could be important for future accelerators which require very low emittance beams. 10/13/2010
Effects of the electron cloud-II 49th ICFA Advanced Beam Dynamics Workshop • The electron cloud can move under the influence of the fields of the beam, so that the beam and the cloud interact dynamically. • The beam-cloud interaction will result in each system undergoing oscillations driven by the other system. • If this mutual interaction is strong • If this mutual interaction is strong enough, unstable motion of the beam can result, increasing its emittance and possibly even driving it into the vacuum chamber walls. • In plasma physics terminology, this is called a “two-stream instability”. 10/13/2010
Effects of the electron cloud 49th ICFA Advanced Beam Dynamics Workshop Summarizing the effects of the electron cloud on the beam: 1. At low cloud densities, the linear forces exerted by the cloud change the oscillation frequency (tune) of the beam. 2. At higher densities, the smaller non-linear forces can cause chaotic motion of the beam particles, leading to growth in the emittance (and size) of the beam. 3. At still higher densities, the mutual dynamic interaction between the beam and the cloud can cause the beam’s motion to become unstable, leading to very large growth in the emittance and possibly also loss of the beam from the large growth in the emittance and possibly also loss of the beam from the vacuum chamber. • Effect 2 can be observed by precise measurements of the beam size in the presence of the cloud. • We will look a little more closely at effects 1 and 3, and how they can be measured in CESR-TA. 10/13/2010
Bunches and trains 49th ICFA Advanced Beam Dynamics Workshop • It is important to understand how the beam is “formatted” in CESR. • The circulating beam is a string of “bunches” Bunch length which form a “train”. Each bunch is a collection of around 10 10 beam particles. The length of a bunch is about 2 cm (~ 0.1 x 10 -9 s), and they are typically separated by about 4.2 m (14 x 10 -9 s). • • The bunches can be “loaded” to form trains of from 1 to ~ 500 bunches. • In a given experiment, the number of particles in z a bunch, the bunch spacing, and the number of bunches in a train can be varied. • In the experiments I will describe at CESR, the length of the train is much less than the Bunches in the train circumference, so there is a big “gap” after each train. 10/13/2010
Electron cloud build-up 49th ICFA Advanced Beam Dynamics Workshop • As you have heard from previous speakers, each bunch emits synchrotron radiation in each bunch emits synchrotron radiation in the bending magnets, which strikes the vacuum chamber wall, creating photoelectrons. • These photoelectrons, together with secondary electrons they produce, form the electron cloud. The cloud from each bunch decays as • electrons are absorbed on the vacuum chamber walls. Bunch Bunch 10/13/2010
Electron cloud build-up 49th ICFA Advanced Beam Dynamics Workshop • If the bunches are closer together than the cloud decay time, the electron cloud builds up along the train, so that each later bunch in the train sees the electron cloud generated by previous generated by previous Bunches bunches. • The change in oscillation • Hence the effects of the cloud frequency (“tune shift”) due on the beam are greater for to the electron cloud is bunches later in the train, related to the cloud density, than for earlier bunches. and it will increase for each later bunch in the train. 10/13/2010
Measurement of the tune-I 49th ICFA Advanced Beam Dynamics Workshop To measure the frequency of oscillation of a bunch, we “kick” the bunch (give it an initial vertical oscillation amplitude using a time-varying magnetic field) and then observe its subsequent oscillations by looking at its vertical position at one point in the ring on subsequent turns: Measurement point KICK Bunch vertical position at measurement point vs. turn number after “kick” 10/13/2010
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