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Introduction to Radio Frequency Quadrupoles
Ajit Kurup
9th December 2004
z
= distance moved by particle in one oscillation
+
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9th December 2004 Ajit Kurup Page 2
Introduction to Radio Frequency Quadrupoles
Basic Description
• Resonant structure used to focus, bunch and accelerate a continuous stream of ions.
4-rodrfq
4-vane rfq
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Introduction to Radio Frequency Quadrupoles
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
LC
LjZ
21
LC
10
id
ig
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Introduction to Radio Frequency Quadrupoles
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
d
z
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Introduction to Radio Frequency Quadrupoles
Resonant Modes
• TM0n0 modes are useful for particle acceleration
• Resonant frequency depends on R0
TM010
TM020
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Introduction to Radio Frequency Quadrupoles
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
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Introduction to Radio Frequency Quadrupoles
Mode Degeneracy
c
R0
0Rd
TM010
TM020
TE011
TE111
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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.
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.
coupling loop
RB
RL
coaxial cable
cavity
L
C
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Introduction to Radio Frequency Quadrupoles
The Quality Factor
cycle halfper lost energy
circuitresonant in the storedenergy Q
0
1
LC
R
QL
gd iigd ii
0 0
id = displacement current
ig = current from generator
High Q-value gives bigger amplitude oscillations but the bandwidth is narrower
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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.
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Introduction to Radio Frequency Quadrupoles
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 Page 12
Introduction to Radio Frequency Quadrupoles
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 possiblenew design !
4m
