Chapter 11 RF cavities for particle accelerators Rdiger

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Chapter 11 RF cavities for particle accelerators Rüdiger Schmidt (CERN) – Darmstadt TU -

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

Accelerating structures in linear and circular accelerators • Acceleration cavity (cavity) • Analogy between

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

Acceleration in the cylindrical cavity. T=0 (accelerating phase) (100 MHz) 2 a z E(z)

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

Linear and circular accelerators Linear accelerator: Acceleration by traveling once through many RF Circular

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

Analogy between cavity and oscillating circuit C L R A simple RF accelerator would

Analogy between cavity and oscillating circuit C 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. L R 5

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

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

For a frequency of 100 MHz, a typical value for an accelerator, the inductance

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:

From oscillating circuit to the cavity C C L L The fields in the

From oscillating circuit to the cavity C C L L The fields in the cavity oscillate in TM 010 mode (no longitudinal magnetic field). There 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) 8

Parameter of a cylindrical cavity („pill-box“) 2 a z A cylindrical cavity with the

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

Acceleration in a cylindrical cavity 2 a z E(z) E 0 g z 10

Acceleration in a cylindrical cavity 2 a z E(z) E 0 g z 10

Cavity with rotational symmetry The cavity parameter depend on the geometry and the material:

Cavity with rotational symmetry The cavity parameter depend on the geometry and the material: • Geometry • Material => Frequency => Quality factor r 0 z gc Comes from Besselfunction (Solution of wave equation) 11

Field strength for E 010 mode for a „pillbox cavity“ r 0 z 12

Field strength for E 010 mode for a „pillbox cavity“ r 0 z 12

Example for „Transit Time Factor“ 14

Example for „Transit Time Factor“ 14

Illustration for the electric field in the RF cavity 15

Illustration for the electric field in the RF cavity 15

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

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

Normal-conducting RF cavity for LEP 17

Normal-conducting RF cavity for LEP 17

Parameters for Cavities Shunt impedance (Definition for a circular accelerator) : For the DORIS

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