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1
**Introduction to Radio Frequency Quadrupoles**

= distance moved by particle in one oscillation - z + Ajit Kurup 9th December 2004

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

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**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 ig id 9th December 2004 Ajit Kurup

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**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 = R0 is zero. Only certain solutions are allowed specific resonant modes. R0 z d 9th December 2004 Ajit Kurup

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Resonant Modes TM0n0 modes are useful for particle acceleration Resonant frequency depends on R0 TM010 TM020 9th December 2004 Ajit Kurup

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Resonant Modes 2 Can also have TE modes which are not useful for acceleration Resonant frequency of TE modes depend on R0 and d. TM010 TE111 9th December 2004 Ajit Kurup

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Mode Degeneracy TM020 TE011 TM010 TE111 9th December 2004 Ajit Kurup

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**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 (Rl) in series with the inductor. If there is no beam (i.e. RB=0) power is still required to maintain oscillations in the cavity. RL coaxial cable C RB L coupling loop cavity 9th December 2004 Ajit Kurup

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The Quality Factor High Q-value gives bigger amplitude oscillations but the bandwidth is narrower id = displacement current ig = current from generator 9th December 2004 Ajit Kurup

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**The RFQ Quadrupole Field**

Focuses in one direction and defocuses in the other. Since fields vary in time, the focusing and defocusing directions swap. 9th December 2004 Ajit Kurup

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**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 + - 9th December 2004 Ajit Kurup

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**The Front End Test Stand RFQ**

4-rod RFQ capable of accelerating 35-70mA 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 9th December 2004 Ajit Kurup

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