Field tuning and rf measurement of the four-vane radio frequency quadrupole with piecewise linear intervane voltage

This paper presents the results of the beam dynamics design, radio frequency (rf) structure design, and rf field tuning of a 108 MHz four-vane radio frequency quadrupole (RFQ) with a piecewise linear intervane voltage. Typically, a constant or a linearly ramped intervane voltage is employed in the beam dynamics design of RFQ accelerators. However, to enhance the acceleration gradient of the RFQ, we apply a linearly increasing intervane voltage configuration in the initial part of the RFQ. Furthermore, we adopt a constant intervane voltage design in the subsequent part of the RFQ to lower the peak surface electric field. A transition section between the constant and linearly increasing voltage regions is specially designed to ensure a smooth second derivative of the voltage. The beam dynamics design indicates that the RFQ cavity measures 3.27 m in length and is capable of accelerating <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>Bi</a:mi> <a:mrow> <a:mn>32</a:mn> <a:mo>+</a:mo> </a:mrow> </a:msup> </a:math> ions with a peak current of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>50</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>eμA</c:mi> </c:mrow> </c:math> from 4 keV/u to 0.4 MeV/u, achieving a transmission efficiency of 95.9%. During the rf structure design, the vane base width is tailored as a function of longitudinal position to maintain the desired local frequency. It is revealed that measuring the magnetic field near the cavity wall makes it challenging to guarantee the intervane voltage distribution of the RFQ. This difficulty arises from a localized dip in the magnetic field within the transition section because of the localized dip of the vane base width, together with the additional disturbance effect of the nearby tuners on the field. As a result, establishing a voltage baseline in the transition section is not feasible. Instead, the electric field near the vane tip was measured and the field was tuned by adjusting the insertion depths of 48 tuners after the RFQ cavity was machined and assembled. After tuning, the relative error between the measured field distribution and the designed curve for the operating quadrupole mode is within <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mo>±</e:mo> <e:mn>1</e:mn> <e:mo>%</e:mo> </e:math> , and the dipole components are within <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mo>±</g:mo> <g:mn>2</g:mn> <g:mo>%</g:mo> </g:math> of the quadrupole mode. The unloaded quality factor of the RFQ cavity was measured to be 13,179, which is 83% of the value predicted by the software.