1. RFQ Tuning Method last results
CEA/DSM/DAPNIA/SACM
IPHI-SPL collaboration meeting - CERN 28 & 29 /04/2003

2. What do we electromagnetically tune ?
1. Resonance Frequency fQ :
MHz
V [kV]
z [m]
2. Accelerating voltage profile : Vp(z)
|(uQ(z)-Vp(z))/Vp(z)|< 10-2
3. Dipole components presence within the accelerating mode
|uS(z)/uQ(z)|< |uT(z)/uQ(z) |< 10-2
4. Closest dipole modes frequencies
f +D - fQ = fQ - f -D

3. … Quadripole Mode dipole Modes Mode S et T (ST) distribution S Mode Q
 focalisation
 Kpq = 352,2 MHz …

4. What do we mechanically tune ?
End regions
Central region
1. Slug tuners
2. « dipole » rods
3. Plate thickness

5. The tuning tools that we have developed
Diagnosis
Treatment
1. Model
What is the
ideal RFQ ?
2. Test bench
e.l.m. parameters
of the real RFQ
e.l.m. parameters  mechanical devices
5. Mathematical formalism
3. Spectral analysis
Frequencies
Field distribution
1. Slug tuners
2. Dipole rods
3. End plates 
4. Cold-model
 Defaults real RFQ / ideal RFQ
 Fast tuning
 High accuracy

6. Our model & the associated spectral analysis
Coupled, inhomogeneous,
4-wire line equivalent circuit
Central region
d2U/dz2 – A U = - (/c)2 U
End regions
Boundary conditions
M = hermetian operator (tM=M)
Eigen values (R+) = resonance frequencies fQi, fSj, fTk
Eigen functions (orthogonal basis)
= { vQi(z), vSj(z), vTk(z) }
voltage base functions
Refer to :
A. France, F. Simoens, “Theoretical Analysis of a Real-life RFQ Using a 4-Wire Line Model and the Spectral Theory of Differential Operators.”, EPAC2002 Conference (Paris), June 2002

7. Comparison measurements / model / 3d simulations2 4 L1 C1 L2 L3 C3 L4 C4
Model
3d simulations
Refer to : F. Simoens, A. France, O. Delferrière, “An Equivalent 4-Wire Line Theoretical Model of Real RFQ based on the Spectral Differential Theory”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

8. Slug tuners : fast simultaneous convergence
uQ(z) [u.a.]
uT(z) [u.a.]
uS(z) [u.a.] fQ
,62 MHz
,22 MHz
,18 MHz
RFQ 2x1m
-6,4.10-2<(uQ-Vp)/Vp<3,4.10-2
-9,2.10-2<uD/uQ<10,6.10-2
-0,2.10-2<(uQ-Vp)/Vp<0,2.10-2
-0,4.10-2<uD/uQ<0,4.10-2
Ref: F. Simoens, A. France, J. Gaiffier, “A New RFQ Model applied to the Longitudinal Tuning of a Segmented, Inhomogeneous RFQ with Highly Irregularly Spaced Tuners”, EPAC2002 Conference (Paris), June 2002

9. Dipole rods length adjustment
A new tuning criteria : ‘quadratic shift frequency’
 Matching of the equivalent end loads
When
df(n)real RFQ  df(n)ideal RFQ
 Good correspondence between the measured
and the ‘ideal’ dipole mode frequencies
Voltage profiles of the first dipole mode
steep slopes
before dipole rods tuning
straightened slopes
after dipole rods tuning
Refer to :
F. Simoens, A. France, “Tuning procedure of the 5 MeV IPHI RFQ”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

10. End plate thickness adjustment
 = L x  f [m.MHz]
L = RFQ half-length
f = (mismatched resonance freq.) - (nominal cut-off freq.)
End region mismatch characterization :  parameter
Nominal mid-position thickness
   0 m.MHz
Example of the IPHI RFQ cold-model end region
adjustment range [-0,24 m.MHz , +0,33 m.MHz]
Refer to :
F. Simoens, A. France, “Tuning procedure of the 5 MeV IPHI RFQ”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

11. End plate thickness adjustment
 Parameter extraction from measurements
End #2
End #1
Slugs are moved at some distance of the end being tuned
i.e. for end#1, in planes #6, 7 and 8 of segment #1
= set of different voltage excitations
Spectral analysis
end#1 plate thickness
 Average [m.MHz]
Std. Dev. [m.MHz]
-0.120
0.032 10
0.001
0.055 20
+0.300
0.086
 The nominal plate thickness is well-adjusted,
Refer to :
F. Simoens, A. France, “Tuning procedure of the 5 MeV IPHI RFQ”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

12. Conclusion Last results
The agreement between measurements, 3d simulations and our model validates our mathematical formalism.
The tuning procedures of the different mechanical devices have been developed and experimentally validated.
In a 2-m long RFQ, we have achieved relative voltage error lower than 10-2 within 3 steps of slug tuners displacements.
For the dipole rods adjustments, a new practical tuning criteria has been introduced, that ensures the convergence of tuning.
The end region mismatch can be characterized from a set different voltage excitations and directly related to the end plate thickness.
Studies in progress
Chronology of the different tuning procedures in the context of the RFQ machining and assembling steps.
RF power coupling (iris / loop).