Dipole stabilizing rods system for a four-vane RFQ: Modeling and measurement on the TRASCO RFQ aluminum model at LNL

The Dipole Stabilizing Rods (DSR's) are devices used in order to reduce a priori the effect of perturbation on the operating mode of a four-vane RFQ caused by neighbouring dipole modes by increasing the frequency spacing between the TE210 mode and dipole modes, without, in principle, affecting the quadrupole TE210 mode. They have proven to be particularly useful in the case of coupled RFQ's whose overall length is significantly greater than the operating wavelength. In this article we present a circuit model of such DSR's, that, used in combination with a transmission line model of a four vane RFQ, has allowed us to predict the dimensioning of the DSR's in the case of the aluminium model of TRASCO RFQ. The DSR parameters and, in general, the accuracy of the model have been also confirmed by HFSS simulations and by RF measurements on the above-mentioned model. INTRODUCTION The effect of a perturbation (e.g. due to mechanical errors and/or misalignments) on the nominal geometry in a four-vane RFQ provokes a mixing of the operating TE210 mode with neighbouring quadrupole TE21n and TE11n dipole modes. If the overall length L of the RFQ is significantly greater than the wavelength, the neighbouring modes can be very close to the operational one, thus enhancing the effect of perturbations. This is an issue for high intensity machine, as the case of TRASCOSPES RFQ in construction at LNL [1], where high field uniformity is required in order to minimize beam losses. TRASCO-SPES RFQ operates at 352.2 MHz and is L=7.13 m = 8.4 λ long. The segmentation of the RFQ[2] adopted in TRASCO-SPES RFQ by means of coupling cells (two in this case, located at L/3 and 2L/3 positions) can reduce the effect of TE21n perturbative terms. Therefore, a chain of N coupled RFQ’s can be represented for the TE21 (quadrupole) and TE11 (dipole) modes by a system of N coupled transmission lines terminated by resonant loads, called end-cells tuned at the quadrupole frequency (Fig. 1)[3,4]. Figure. 1: The equivalent transmission line for N=3 coupled RFQ’s. It has to be pointed out that the segmentation of the RFQ’s is not effective with the dipole perturbations. Moreover, the insertion of end cells raises the f110 frequency, shifting it closer to the operational one [4]. Therefore dedicated stabilizing systems for dipole modes are needed. The usage of DSR’s to be inserted in correspondence of the end-cells and coupling cells is a solution typically used for high power RFQ’s [5,6,7]. THE PRINCIPLE OF DIPOLE STABILIZATION Dipole Stabilizing Rods are conductive bars departing from the end and coupling plates and protruding into each RFQ quadrant. If they are located at a height hb on the axis of a RFQ transverse section in which electric and magnetic energy densities balance at the f210 frequency, they almost do not affect the TE210 mode. Moreover they couple their coaxial modes (“bar mode”) with the dipole modes (Fig. 2), thus shifting the dipole band. In fact in the quadrants 1 and 3 an electric field from the bar to the electrodes appear and a magnetic field wraps around the bars. Figure 2: The coaxial bar mode coupling effect on the dipole mode: E field (left) and H field (right). Therefore one can think of modelling the bar as a parallel inductance Lb and parallel capacitance Cb depending on bar length lbar added in the end and coupling cell sides the equivalent transmission line for TE11 modes (Figure 3). Figure 3: The equivalent circuit for TE11n modes of the RFQ in correspondence of the undercuts when bar are inserted Now, if lbar is such that the equivalent admittance eq bar e b e b Y ( , l ) j (C C ) 1/( j (L L )) ω = ω + + ω + vanishes at hb Proceedings of EPAC 2006, Edinburgh, Scotland TUPCH123 07 Accelerator Technology T06 Room Temperature RF 1301 the 2D dipole frequency, not only the TE110 frequency becomes equal to the 2D value, but the dipole free region width around the quadrupole mode is maximized. Therefore the optimization of DSR’s could be accomplished by simply tuning the TE110 frequency to its original 2D value. Due to the TEM nature of the bar mode inside the quadrants, an unambiguous voltage Vb between the bar and the electrode can be calculated. Moreover, the capacitance per unit length can be evaluated in this part, where almost all the electric energy is concentrated, according to the relationship 2 b eb b bar end cell b bar end cell C (4w / V )(l l ) c (l l ) − − = − = − web being the electric energy per unit length. On the other hand, the knowledge of the frequency of the bar mode allows to evaluate the inductance Lb. It is worth noticing that due to the field configuration in the End Cells, there is an excess of inductance with respect to the uniform coaxial line, and then an optimal bar length less than λ/4 is to be expected. RESULTS OF SIMULATIONS ON THE ALUMINUM MODEL The dimensioning and design of DSR’s has been also verified with HFSS simulations on the aluminum model of the RFQ, installed at LNL, Its overall length is L=3.044 and it consists of three coupled segments. For such RFQ, calculations have given the following values for the main parameters of interest. Table 1: Main parameters for the aluminum model of the RFQ. f110 (2D) [MHz] 339.289 f210 (2D) [MHz] 350.613