A Diffusive Model for Radio-Frequency Knock-Out Slow Extraction

TL;DR

This paper introduces an analytical model for radio-frequency knock-out slow extraction in synchrotrons, enabling precise spill calculations and a method to flatten beam delivery for uniform particle extraction.

Contribution

It provides explicit analytical formulas for spill prediction and a semi-analytical approach to optimize amplitude modulation for uniform beam extraction.

Findings

Derived analytical expressions for spill calculation

Developed a semi-analytical method for spill flattening

Enhanced control over beam uniformity

Abstract

Slow resonant extraction from synchrotrons via radio-frequency knock-out is a well-established technique to deliver charged particle beams for various applications. In this contribution, we present explicit analytical expressions for calculating the number of particles slowly extracted over time, commonly referred to as spills. The proposed formulation enables the semi-analytical determination of an amplitude modulation curve to be applied to the radio-frequency exciter, which flattens the spill macrostructure, a feature of high relevance to all users requiring uniform beam delivery.