Variable voltage adjustment in a 2 m RFQ using tuning pistons

In 2 iterations of piston displacements, we set all the electromagnetic parameters of the specifications using tuning pistons in a 2-meter RFQ featuring a single electrode with a constant cross-section. The target voltage profile corresponds to that of the first 2 meters of the IPHI RFQ. In particular, at the end of tuning, the relative deviations of the 4 quadrant voltages from the target longitudinal voltage are less than 7.10^-3, compared with the 10^-2 required by the beam dynamics criteria. The conditions required for the convergence of a setting using pistons, which were defined during the constant profile setting tests, make it possible to set a variable tension profile in a very small number of iterations. 1 - Adjust the length of the dipolar tuning fingers to match the measured dipolar mode frequencies with those of the model. 2 - Select the most even possible longitudinal distribution of displaced tuning pistons. Theoretical depressions do not achieve the desired results. Whether applied to the raw RFQ or pre-balanced using our formalism; the resonant frequency of the accelerator mode is close to the target frequency, but the relative errors of all other parameters are above the required threshold. In particular, the relative deviations of the 4 quadrant voltages from the reference voltage Vp obtained are at least 5 times greater than the desired error threshold of ±10^-2 for all tests of theoretical depressions. Despite the good mechanical characteristics of the model, transverse defects cannot be neglected and predominate over the quality of the RFQ balance. Transverse and longitudinal couplings must be considered simultaneously. The final positions of the pistons in the RFQ set at 352.2 MHz differ from one quadrant to the next for the same transverse plane. The RFQ transfer function is non-linear, and large displacements are major disturbances which, in the context of our tuning formalism, degrade the bijective character of our control functions. Thus, the theoretically tested depressions constitute quadrupole control functions, yet their application increased the proportion of dipole components within the accelerating voltage