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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

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Chapter 11

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  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

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