1 Monday Week 1 Lecture Jeff Eldred Longitudinal
- Slides: 34
1 Monday Week 1 Lecture Jeff Eldred Longitudinal Dynamics, RF manipulations
2 Jeffrey Eldred (TA) • Graduated with Ph. D December 2015 • Indiana University working with Shyh-Yuan Lee • Worked at Fermilab on PIP-II upgrade • Slip-stacking and Electron Cloud. Postdoc at Fermilab on IOTA experiment Nonlinear transverse dynamics, Landau damping, space-charge compensation, modern ring-design Kilean Hwang (grader) • Graduating with Ph. D this semester • Indiana University working with Shyh-Yuan Lee • Dipole fringe fields • Electrostatic storage rings using EDM.
3 Overview 1. 2. 3. 4. 5. RF Cavities Longitudinal Dynamics RF bucket phase-space RF acceleration Other RF dynamics
4 Longitudinal Motion of Particle Beams
5 Credit: FNAL Rookie Book
6 Numerically Calc. Eigenmodes Credit: University of Rostock
7 Credit: Q. Wu, S. Belomestnykh W. Xu
8 Energy in one pass through cavity
9 Change in Momentum Fractional Momentum: RF Acc. Per Pass: Change Momentum per unit time: Sinesoidal potential:
10 Phase-Slip Factor η The arrival time of the particle depends on the momentum: Higher momentum particles may arrive earlier or later than lower momentum particles: We can write the change in phase per unit time using the phase-slip factor:
11 Longitudinal Focusing
12 Phase-space Motion
13 Hamiltonian & Separatrix Hamiltonian: Separatrix: Stable Phase-space Area:
14 Perturbation of Synchrotron Motion
15 Stable Beams
16 Perturbation of Stable Beams
17 Slipping Beams
18 Perturbation of Slipping Beams
19 Accelerating Buckets
20 RF Acceleration • A fixed frequency beam longitudinally focuses the beam into a several beam “bunches” in individual RF “buckets”. • Particles in the bucket can be accelerated by adiabatically changing the RF frequency, the other particles are lost.
21 Credit: X. Kang SY. Lee
22 0 15 30 45
23 Stable Phase-space Area as a function of φs
24 Other Examples of Longitudinal RF Dynamics
25 Transition Crossing
26 Phase-Focusing & Acceleration
27 Phase-space at Transition
28 RF + Harmonic RF Cavities
29 Harmonic RF 2 nd Harmonic RF: In general you could imagine:
30 Harmonic RF for H- injection Credit: JPARC
31 Harmonic RF for Ph-Sp Dilution Credit: A. Pham
32 Bunch Rotation by Quadrupole Resonance
33
34 Credit: X. Yang
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