Design of RFQ Vane Tip to Minimize Sparking Problems

Abstract

Transverse and longitudinal focusing in radiofrequency quadrupole (RFQ) accelerators depends on V/Ro (the vane vol tage di vi ded by the mean radi al aperture). For maximum current carrying capacity, one generally designs for maximum V/Ro, which is limited by the peak surface electric field Es (= K (V/Ro)) that can be sustained without sparking. The val ue of the enhancement factor K depends on the pole geometry and can be minimized by choosing an appropriate pole shape. A computer program POTRFQ wi'll be described which derives the field potential f(r,0,z) and the vane tip contour, for a range of input parameters. The effects on the beam dynamics of the higher multipole components resultirig from the modified pole shapes will also be presented. Introducti onThe enhancement factor relates the peak surface electric field gradient on an RFQ vane to the V/ro. For a conventional geometry as used in the Los Alamos POP RFQI the enhancement factor is 1.355 for an unmodul ated vane, but for a modulated vane can be greater than 1.6. Accelerator perforriance can be opti'-mized by the proper choice of field gradient but in practical designs sparking between vanes prevents operation at this optimum. Improved performance is expected if the vane surfaces are shaped to reduce the enhancemenit factor and allow operation at higher fields. Intuitively what is wanted is to shave the vane tips to increase the minimum spacing between vanes without making the vanes sharp enough to increase the surface field. RFQ Vane Surfaces and the Potential From the viewpoint of bean particle dynanics any accelerator geormetry is considered acceptable if it is able to establish a suitable radiofrequency quadrupole electric field potential 1(r,e,z,t) in the vicinity of the beam axis. If the bean diameter is much less than the wavelength we can ignore rf magnetic fields near the beam axis and use a quasi-static approximation in which the tine dependence can be separated. flr,0,z,t) -= (r,6,z) sin(wt) Idealized vane surfaces have an asyrmmetri c quadrupole geometry with the asymmetry being periodic in the z-direction with period 2L. The potential has the following boundary and symmetry conditions: fp(r,e,z+2L) = p(r,o,z) ¢ (r,6+7T/2,z+L) = -P(r,0,z) f(-x,y,z) = f(x,y,z) (x,-y,z) = f(x,y,z) Db =_ az z=O A potential that satisfies these conditions can be expressed in the following series expansion 00 p(r,e,z) = z CO (kr) cos(xo) s=O + z cos(kmz) z C I (kmr) cos (x ) m=1 s=O ms X where k = 7r/L and x = 4s if m is odd = 4s + 2 if m is even I = a modified Bessel function of order X.If the Cms are known we can evaluate the potential and electric field anywhere. In partictilar, the equipotential suLrfaces which could define the vane tips and the electric field at any point on these surfaces can be found. POTRFQMathematically the simplest form of RFQ is one in which only the terms Coo and C1o are non-zero (the two-term potential). This is not a practicable device, however, because the vane surfaces required to give this potential would have a hyperbolic cro...

Beam dynamics and electromagnetic studies of a 3 MeV, 325 MHz radio frequency quadrupole accelerator

“…On the other hand, a lower value of r has the disadvantage that it will increase the contribution of higher order multipoles in the RFQ potential function. In reference [12], a value of r = 0.75r 0 is found to be an optimal choice, which we have followed in our design.…”