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

2. 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

3. 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

4. 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

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

6. 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

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

8. 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

9. 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

10. 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

11. 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

12. 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