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Introduction to Radio Frequency Quadrupoles = distance moved by particle in one oscillation - z + Ajit Kurup 9th December 2004 Introduction to Radio Frequency Quadrupoles 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 Page 2 Introduction to Radio Frequency Quadrupoles Some Basics About Resonance reactive components Z ig id 0 j L 1 2 LC 1 LC • 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 9th December 2004 Ajit Kurup Page 3 Introduction to Radio Frequency Quadrupoles Cylindrical Cavity Example R0 z d • Need to solve Maxwell’s equations to determine the field shapes. • Boundary conditions: field along axis is nonzero, field in z direction at r = R0 is zero. • Only certain solutions are allowed specific resonant modes. 9th December 2004 Ajit Kurup Page 4 Introduction to Radio Frequency Quadrupoles Resonant Modes TM010 • TM0n0 modes are useful for particle acceleration • Resonant frequency depends on R0 TM020 9th December 2004 Ajit Kurup Page 5 Introduction to Radio Frequency Quadrupoles Resonant Modes 2 9th December 2004 TM010 • Can also have TE modes which are not useful for acceleration TE111 • Resonant frequency of TE modes depend on R0 and d. Ajit Kurup Page 6 Introduction to Radio Frequency Quadrupoles Mode Degeneracy TM020 R0 TE011 c TM010 TE111 d 9th December 2004 R0 Ajit Kurup Page 7 Introduction to Radio Frequency Quadrupoles Power Transfer and Losses • RF power from the coaxial cable is often magnetically coupled to RFQs via a copper loop. RL C coaxial cable RB 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. L coupling loop cavity 9th December 2004 Ajit Kurup Page 8 Introduction to Radio Frequency Quadrupoles The Quality Factor Q energy stored in the resonant circuit energy lost per half cycle 1 R L Q LC 0 id i g id i g High Q-value gives bigger amplitude oscillations but the bandwidth is narrower id = displacement current ig = current from generator 0 9th December 2004 0 Ajit Kurup Page 9 Introduction to Radio Frequency Quadrupoles 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 Page 10 Introduction to Radio Frequency Quadrupoles The RFQ Accelerating Field • Electrodes are sinusoidally modulated to give an electric field in the z direction. - + = distance moved by particle in one oscillation - z + 9th December 2004 Ajit Kurup Page 11 Introduction to Radio Frequency Quadrupoles The Front End Test Stand RFQ • 4-rod RFQ capable of accelerating 3570mA 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 Page 12