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Introduction to Radio Frequency Quadrupoles Ajit Kurup 9 th December 2004 z = distance moved by particle in one oscillation + -

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Page 2 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Basic Description Resonant structure used to focus, bunch and accelerate a continuous stream of ions. 4-rod rfq 4-vane rfq

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Page 3 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Some Basics About Resonance A resonant cavity is analogous to a simple parallel LCR circuit. The impedance of the reactive part is infinite at the resonant frequency 0. Optimal energy transfer from voltage source to the load ( R ) at the resonant frequency reactive components idid igig

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Page 4 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Cylindrical Cavity Example Need to solve Maxwell’s equations to determine the field shapes. Boundary conditions: field along axis is non- zero, field in z direction at r = R 0 is zero. Only certain solutions are allowed specific resonant modes. R0R0 d z

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Page 5 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Resonant Modes TM0n0 modes are useful for particle acceleration Resonant frequency depends on R 0 TM 010 TM 020

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Page 6 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Resonant Modes 2 Can also have TE modes which are not useful for acceleration Resonant frequency of TE modes depend on R 0 and d. TM 010 TE 111

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Page 7 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Mode Degeneracy TM 010 TM 020 TE 011 TE 111

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Page 8 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup Power Transfer and Losses RF power from the coaxial cable is often magnetically coupled to RFQs via a copper loop. Real resonant structures contain resistances which can be simplified as a resistor ( R l ) in series with the inductor. If there is no beam (i.e. R B =0) power is still required to maintain oscillations in the cavity. coupling loop RBRB RLRL coaxial cable cavity L C

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Page 9 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup The Quality Factor i d = displacement current i g = current from generator High Q-value gives bigger amplitude oscillations but the bandwidth is narrower

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Page 10 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup The RFQ Quadrupole Field Focuses in one direction and defocuses in the other. Since fields vary in time, the focusing and defocusing directions swap.

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Page 11 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup The RFQ Accelerating Field Electrodes are sinusoidally modulated to give an electric field in the z direction. + - z = distance moved by particle in one oscillation + -

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Page 12 Introduction to Radio Frequency Quadrupoles 9th December 2004Ajit Kurup The Front End Test Stand RFQ 4-rod RFQ capable of accelerating mA beam from 65KeV to 2MeV Needs to be about 4m long Frequency still to be decided but will probably be either 200MHz or 352MHz Artists impression of possible new design ! 4m

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