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

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. 3 2a Acceleration in the cylindrical cavityT=0 (accelerating phase) z z E0E0 E(z) g (100 MHz)

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

5. 5 Analogy between cavity and oscillating circuit L R 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. C L R

6. 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. 8 From oscillating circuit to the cavity C L C 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. 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) g 2a z

10. 10 g 2a Acceleration in a cylindrical cavity z z E0E0 E(z)

11. 11 Cavity with rotational symmetry z gcgc The cavity parameter depend on the geometry and the material: Geometry => Frequency Material => Quality factor r0r0 Comes from Besselfunction (Solution of wave equation)

12. 12 Field strength for E 010 mode for a „pillbox cavity“ z r0r0

14. 14 Example for „Transit Time Factor“

15. 15 Illustration for the electric field in the RF cavity

16. 16 Superconducting RF cavity for Tesla and X-ray laser at DESY RF cavity with 9 cells

17. 17 Normal-conducting RF cavity for LEP

18. 18 Parameters for Cavities Shunt impedance (Definition for a circular accelerator) : Quality factor Q : For the DORIS Cavity : Q factor: 38000