Second Harmonic capture in the IPNS RCS: Transition from SH to fundamental rf operation during the acceleration cycle using CAPTURE_SPC Jeff Dooling Presented at The Ninth Second Harmonic RF/Low Output-Impedance Amplifier Collaboration Meeting Argonne National Laboratory, June 14-15, 2004

Motivation Currently, we believe our ferrite will not allow second harmonic (SH) rf operation up to the maximum acceleration frequency— 5.15 MHz x 2 = MHz Most loss occurs at injection Can we run SH early in cycle using the new 3 rd cavity, switching to fundamental later and still realize a net increase in current?

Guide field, , and V rf

Frequency and energy vs. time

Bucket Area in the RCS

Fundamental and SH voltage and current profiles from Hofmann-Pedersen elliptical distributions

Maximum bucket area vs. maximum bunching factor

Capture Efficiency and Fundamental-SH phase angle, 

Goal: Full SH rf for the full acceleration cycle (the following animation includes the phase ramp)

Potential benefit

Modify CAPTURE to include  (t) * CALL CPfield( tn, evol, fnuS, omegaS, & flagrf, Nrfpoints, rf_time, rf_evol, & rf_sh_phase, Imax, secHarmPhase ) * * CALL CPfield( tn, evol, fnuS, omegaS, & flagrf, Nrfpoints, rf_time, rf_evol, & rf_sh_phase, rf_sh_ampl, Imax, & secHarmPhase, secHarmFactor ) *

Two cases CASE 1: Run SH at d=0.55 for the first 4 ms Ramp SH to 0 between 4 and 5 ms Leave V rf unchanged CASE 2: Run SH at d=0.55 for the first 4 ms Ramp SH to 0 between 4 and 5 ms Ramp V rf to 1.55*V rf between 5 and 6 ms

Ramping Vrf up after 5 ms

Second Harmonic rf early,  =0.55 ramping off between 4 and 5 ms

Second Harmonic rf early,  =0.55; ramping off between 4 and 5 ms; ramping back on in the fundamental between 5 and 6 ms (to 1.55*V rf )

Transmission efficiency and loss rate

Observations Transmission efficiency improves with SH rf even when no further rf is applied Ramping back on V rf shuts off the loss by increasing the bucket size Timing is important—implied in these simulations is the fact that the third cavity is being made to go from full SH voltage to full fundamental voltage in 2 ms. May not need to go to full 1.55*V rf in the fundamental to gain efficiency

Why does SH early improve capture efficiency when no additional rf is applied According to Chao, the limiting tune shift is, One way to look at this is to say that SH effectively moves injection to higher energy --A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, New York, 1993, p. 14.

Conclusions Third cavity, even with limited SH capability, will allow for important capture studies. Also, the 3 rd cavity may provide a modest improvement in RCS beam current limit.

Acknowledgement This work would not be possible without the dedication and hard work of the IPNS Accelerator Operations Group.