Adiabaticity study tomography 15102019 Adiabaticity of longitudinal dynamics

Adiabaticity study & tomography 15/10/2019

Adiabaticity of longitudinal dynamics • R. Garoby, ”RF Gymnastics in Synchrotrons’ https: //arxiv. org/abs/1112. 3232 2

FETS ring v. FFA parameters Parameter Value Average radius 25/(2*pi) m Energy range 3 – 12 (17. 0) Me. V Harmonic 2 RF frequency range 1. 91 – 3. 8 (4. 5) MHz Injected bunch dp/p (6σ) +/- 0. 0075 [0. 045 Me. V] • VFFA has a fixed path length as in a RCS. 3

RF programme in v. FFA 1000 turn ramp 100 turn ramp • Linear increae phi_s from zero to a finite value in n turns and fix thereafter. • Maintain fixed bucket area. 4

Adiabaticity – dependence on ramp rate 100 turn ramp 1000 turn ramp Required RF voltage reduced if phi_s is ramped in fewer turns. However, the adiabaticity also increases. 5

Example RF programme in KURNS 1000 turn ramp 50 turn ramp • First accelerate to 30 Me. V with phi_s = 20 deg. • Linearly decrease phi_s from 20 deg to zero in n turns and fix thereafter. • Maintain fixed bucket area by reducing V 0 appropriately. 6

Adiabaticity – dependence on ramp rate 100 turn ramp 1000 turn ramp 7

Proposed Experiment Aim: Experimentally measure the dependence of longitudinal emittance growth on the adiabatic parameter. • Accelerate with usual settings until some point where beam has escaped foil and the emittance has reached an equilibrium. • Ramp to zero phi_s over a range of turns (1 – 3000 in steps of 500? ). • Maintain flattop for a few synchrotron oscillations. • Use raw bunch monitor data or tomography to measure emittance blow up if any. To do – Calculate emittance blow up in simulation to guide experiment. 8

RF parameter fitting C. Montag et al, PRST-AB 2002 • Tomography code by Montag allows RF parameters to be “measured” by adjusting the model until the difference between the reconstruction and data is minimized. • In RHIC rebucketing is performed to reduce bunch length after acceleration. It involves 28 MHz acceleration cavities (U 1) and 197 MHz bunching cavities U 2. • Voltages and phases of RF systems are free parameters to be found by minimising Δ. 9

• FFT of RF waveform over 1000 turns taken during accelerating phase and flattop phase. • There is a significant harmonic 3 component in both cases. • During the accelerating phase h 3/h 1 ~ 0. 1. During the flattop phase h 3/h 1~0. 06 in the cases examined. • Will the beam see this or is it an artefact of the measurement? Flattop phase Accelerating phase RF waveform: harmonic 3 component 10

Data from 20/6/2019 11

Hamiltonian with harmonic 3 • Hamiltonian in case of arbitrary waveform g(φ). Add harmonic 3 to potential term in Hamiltonian What is effect on synchronous phase and synchrotron period as a function of amplitude? 12

To do • Code updates • Allow additional RF harmonics to be included in code. • Longitudinal characterization – Attempt to use tomography to measure the harmonic content of the RF. Maybe the existing data is enough – this is to be determined. 13