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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