1 / 11

Tuesday Week 2 Lecture

1. Tuesday Week 2 Lecture. Jeff Eldred Wakefield Impedances. 2. Wakefield Impedance. Wake Functions. Decaying cosine-like. Decaying sine-like. From Panofsky Wenzel:. Impedance Analogy to EE. Impedances as a force per current:. Impedances as a Fourier decomposition of Wake functions:.

claudiam
Download Presentation

Tuesday Week 2 Lecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1 Tuesday Week 2 Lecture Jeff Eldred Wakefield Impedances

  2. 2 Wakefield Impedance

  3. Wake Functions Decaying cosine-like Decaying sine-like From Panofsky Wenzel:

  4. Impedance Analogy to EE Impedances as a force per current: Impedances as a Fourier decomposition of Wake functions:

  5. Tabulated Impedances Many common sources of wakefield impedances – space-charge, resistive wall, RF cavities, BPMs, beampipe transitions, etc. – have been already been calculated. MAFIA, CST are able to perform simulations for more complicated scenarios.

  6. Broad vs. Narrow Impedances

  7. Impedance Compensation Impedance from one source can be compensated by impedances from another source. Some impedances are capacitive and others are reactive and consequently the imaginary part of the impedance can be canceled in the complex plane. Example: IMPEDANCE CALCULATION FOR FERRITE INSERTS Ferrite inserts to compensate space-charge driven impedances without introducing undesired new impedances.

  8. Toy Model: Oscillator with Feedback The real part is a tune-shift, the imaginary part is an exponential growth/damping term. Different sources of impedance can actually be used to cancel each other out.

  9. It’s More Complicated than that • The wakefields drive the motion of the beam, but there is only a feedback loop if the motion of the particles in the beam adds up coherently. If the beam is focused nonlinearly then Landau damping will counteract the instability. • Should be modeled as set of independently moving oscillators driven by a collective force.

  10. Multipole Expansion

  11. It’s More Complicated than that K.Y. Ng’s • Next USPAS Chao and Stupakov are teaching a 2-week course on collective effects. Chao’s

More Related