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

What do we electromagnetically tune ? 1. Resonance Frequency fQ : 352.21 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)|< 10-2 |uT(z)/uQ(z) |< 10-2 4. Closest dipole modes frequencies f +D - fQ = fQ - f -D

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

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

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

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

Comparison measurements / model / 3d simulations 2 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

Slug tuners : fast simultaneous convergence uQ(z) [u.a.] uT(z) [u.a.] uS(z) [u.a.] fQ 0 350,62 MHz 2 352,22 MHz 1 352,18 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

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

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

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

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).