First Look at the Non-Scaling PRISM J. Pasternak Imperial College London/RAL STFC

1. First Look at the Non-Scaling PRISM J. Pasternak Imperial College London/RAL STFC J. Pasternak

2. Outline • Introduction and motivation • Non-scaling FFAG lattice – preliminary design • Beam dynamics • Phase rotation for large amplitude particles • Summary and future plans J. Pasternak

3. Possible PRISM Task Force Design Strategy Option 1: Adopt current design and work out injection/extraction, and hardware Option 2: Find a new design They should be evaluated in parallel and finaly confronted with the figure of merit (FOM) (number of muons delivered to target/cost). Requirements for a new design: • High transverse acceptance (at least 38h/5.7v [Pi mm] or more). • High momentum acceptance (at least ± 20% or more). • Small orbit excursion. • Compact ring size (this needs to be discussed). • Relaxed or at least conserved the level of technical difficulties. for hardware (kickers, RF) with respect to the current design. J. Pasternak

4. Ring Design Options R Scaling FFAG Options: • standard lattice, • periodic with extended cell (for example 5 magnets per cell), • superperiodic (proposed by S. Machida) • advanced (proposed by Y. Mori and collaborators, see J-P.Lagrange’s lattice) Non-Scaling FFAG Main motivation for Non-Scaling design is a possibility to obtain „infinite” DA! Problems to be addressed: • confirmation of a large DA • currently no insertion scheme, • very difficult injection • TOF with amplitude J. Pasternak

5. Basic constraints • Energy acceptance depends on RF voltage and harmonic number. Observation: if we want to go for h=2, we need a factor of 2 more RF! • Synchrotron tune tells us about number of turns needed for phase rotation. Observation: for h=2 phase rotation is twice as fast (3turns). • If we want to lower the central momentum (keeping momentum acceptance), RF voltage goes down, but bucket starts to be more asymmetric (A. Sato proposed to look at 40 MeV/c). • Changing central momentum increases revolution time. This is good for kickers, but you need to be within the frequency range of MA cavities. C. Ohmori Harmonic number can be 1 or 2! J. Pasternak

6. First look at Non-Scaling Design Short Drift 0.376 m Short Drift 0.376 m Long Drift 1.1 m Long Drift 1.1 m F Quad, 0.376 m B from -0.07 to 0.1 T Defocusing RBend, 0.376 m B from 0.34 to 0.31 T • Some parameters: • Lattice Symmetric FDF triplet • N 10 • p0 68 MeV/c • Circunference 40.84 m • (QH, QV)/cell at p0 (0.276, 0.189) • Drif length 2.2 m Ring with „PAMELA” -like magnet geometry J. Pasternak

7. Orbit in NS-PRISM prototype lattice p0 +20% p0 p0 p0 -20% p0 m • Orbit excursion 0.38 m • Orbit is very linear with momentum MeV/c J. Pasternak

8. Tunes Tune/cell QH QV MeV/c • Chromaticity is relatively flat in horizontal plane. • Vertical tune excursion is large – edge focusing. • Tunes cross – potential problem! J. Pasternak

9. Dynamical aperture tests xp,rad • Tracking of large amplitude particles shows • no strong distortion • Tracking is done with hard-edge • approximation, tracking with soft edges • needs to be done. x, m yp,rad y, m J. Pasternak

10. First phase rotation simulations Red- particles at injection Black- no transverse amplitude Blue – large horizontal amplitude Pink – large vertical amplitude • Phase rotation performed with non ideal „sawtooth” RF voltage • ToF variation with amplitude introduces a small additional energy spread, • but it can be accepted . J. Pasternak

11. Summary and future plans • First non-scaling PRISM lattice was tried. • Tune crossing can be a potential problem and should be eliminated. • TOF with amplitude seems not to be a problem, but more studies are needed. • Demonstration of the expected large DA should be studied. • Injection/extraction and matching seem to be very difficult. • There is a lot of space for more work and inventions! J. Pasternak