1 / 18

Chapter 11

Chapter 11. RF cavities for particle accelerators. Rüdiger Schmidt (CERN) – Darmstadt TU - 2011 –Version E2.2. Accelerating structures in linear and circular accelerators . Acceleration cavity (cavity) A nalogy between oscillating circuit and cavity Cylindrical cavity

tory
Download Presentation

Chapter 11

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. Chapter 11 RF cavities for particle accelerators Rüdiger Schmidt (CERN) – Darmstadt TU - 2011 –Version E2.2

  2. Accelerating structures in linear and circular accelerators • Acceleration cavity (cavity) • Analogy between oscillating circuit and cavity • Cylindrical cavity • Shunt impedance and quality factor

  3. Acceleration in the cylindrical cavityT=0 (acceleratingphase) (100 MHz) 2a z E(z) g E0 z

  4. Linear and circular accelerators Linear accelerator: Acceleration by traveling once through many RF Circular accelerator: Acceleration by travelling many times through few RF cavities

  5. Analogy between cavity and oscillating circuit C L R L A simple RF accelerator would work with a capacitor (with an opening for the beam) and a coil in parallel to the capacitor. The energy oscillates between electric and magnetic field. R

  6. Analogy between cavity and oscillating circuit Oscillating circuit with capacitor, coil and resistance. C L R

  7. For a frequency of 100 MHz, a typical value for an accelerator, the inductance of the coil and the capacity of the condenser must be chosen very small. Example:

  8. From oscillating circuit to the cavity C C L L The fields in the cavity oscillate in TM010 mode (no longitudinal magnetic field). There are an infinite number of oscilllation modes, but only a few are used for cavities (calculation from Maxwells equations, application for waveguides, for example K.Wille)

  9. Parameter of a cylindrical cavity („pill-box“) • A cylindrical cavity with the • length of g, the aperture • 2*a and the field of E(t) 2a z g

  10. Acceleration in a cylindrical cavity 2a z g E(z) E0 z

  11. Cavity with rotational symmetry • The cavity parameter depend on the • geometry and the material: • Geometry => Frequency • Material => Quality factor r0 z gc • Comes from Besselfunction (Solution of wave equation)

  12. Field strength for E010 mode for a „pillbox cavity“ r0 z

  13. Example for „Transit Time Factor“

  14. Illustration for the electric field in the RF cavity

  15. Superconducting RF cavity for Tesla and X-ray laser at DESY RF cavitywith 9 cells

  16. Normal-conducting RF cavity for LEP

  17. Parameters for Cavities Shunt impedance (Definition for a circular accelerator) : Quality factor Q : For the DORIS Cavity : Q factor: 38000

More Related