Possible CCR Arc designs S.V. Benson, February 15, 2018 On behalf of the Cooling Ring Design Team

LERF Readiness Review 9/30/15 Outline CCR specifications Simple Arc Axially Asymmetric/Symmetric Match Arc FFFAG Arc Dispersive Arc Other arc designs Project E arc Curved, tilted solenoid Figure 8 LERF Readiness Review 9/30/15

Circulating Cooler Ring Specifications Bunched beam electron cooling on JLEIC requires a high repetition rate and a large charge. This is incompatible with any available electron source technology (state-of-the-art = 65 mA for one shift). The proposed solution is to use a Circulating Cooling Ring (CCR) to provide high current in the cooler (~1 A) without requiring such high current in the electron source. The CCR has the following requirements: Isochronous. Need RF compensation to counter SC and CSR Local axial symmetry? Local isochronicity small compaction oscillations (for µBI) Achromatic? Local dispersion suppression High periodicity with rational tune Moderate size We would also like the ring to use conventional magnet and vacuum chamber technology as far as possible. Should take advantage of CSR shielding.

CSR Shielding Shielding of CSR is effective when the full aperture size is less than 𝑅 1 3 𝜋 𝜎 𝑧 2 3 where R is the bend radius and sz is the rms bunch length For example, for the simple arc R = 0.53 m and sz = 5.8* mm and the (full) aperture needs to be less than 2.2 inches (5.6 cm) note, previous analysis using Project-E arc had R=1.5 m  allowance for larger aperture *where s of flattop is taken as 𝐹𝑊 2 3

Initial Beam Distribution uniform transverse (horizontal and vertical) distribution temporally, flattop distribution with Gaussian edges sDE/E = 3×10-4 sz = 2 cm (full) enx=eny= 36.87 mm-mrad

Simple Arc Layout design by D. Douglas sextupole quadrupole dipole

Lattice Functions

Microbunching Gain using C.Y. Tsai Code set up to run on fel-sim4 have computing power required to run large mesh numbers can now include transient CSR impedance (along with steady-state, csrdrift and LSC) mBI gain is ≤ unity needs to be less than unity for multiple passes (gain grows exponentially)

Bmad with CSR and Shielding with CSR + shielding

Bmad – Multiturn Tracking with CSR shielding

Longitudinal Phase Space Comparison: After 10-Turns elegant – Stupakov + RF correction elegant – without csrdrifts Bmad – with shielding

Axially Asymmetric Match Arc sextupoles added to force T166, T266 and T566 to zero other minor changes include (dipole bend radii, drift lengths)

Comparison to “Simple Arc” R56, T566 and T544 of “Simple Arc” (red) and new AAM arc (black)

Microbunching Gain microbunching gain is moderate (still unacceptably large for the CCR) for a single arc traversal gain explodes when adding a second traversal (i.e. one full turn of the CCR)! 2 arc traversals (1 full-turn) gain ~ 450 1 arc traversal gain ~ 3

Tracking Simulations preliminary tracking in elegant shows that the microbunching gain is indeed very large physical phase space at the exit of the first 6 passes of the CCR “ring” longitudinal phase space at the exit of the first 6 passes of the CCR “ring” pass 6 enx,drift > 300 mm-mrad

FFFAG Design Requirements Try to meet all specifications Use nothing but “misaligned quads” – i.e., symmetric entry/exit rectangular bends with n ~ ½. Fear no 3D effects – just trust that all that FFAG stuff works at the field control level needed for ERLs Unlike “real” FFAGs, there is no need to cram stuff together: only one energy of beam is in the machine, and it will notionally have the same trajectory on each turn in the CCR This actually simplifies life; the magnets can be (and it turns out must be, to get enough phase advance…) separated enough to avoid cross-talk, unlike in FFAGs, where fully 3D magnets interact with each other, making them not just 3D, but 3D-der…

Lattice Functions Layout

Beam Envelopes

Geometric Aberrations

Dispersive CCR layout Horizontal dispersion trek: Compensated CS (two contrary solenoids with the helicity flip in between) Expanders (ES) of the beam size to match with long beta in arcs Constant dispersion in CS (not necessarily horizontal) /associated with the drift space/ Outcome (after ES) dispersion 𝑫 horizontal, 𝑫 ′ vertical Arcs: constant bends, weak symmetric focusing, no coupling Connecting straight: specific matching with arcs to provide zero compaction factor of each arc Helicity flip in the connecting straight Dispersion associated with the drift degree of freedom in cooling solenoid

LERF Readiness Review 9/30/15 Other Ideas Project E arc. µBI gain was small for this arc and we can make it globally symmetric. It is rather large and the fields will be low at 20 MeV. Bent solenoid arc Use solenoids with bent coils to transport beam around bends. How do we make achromatic? Figure 8 solenoid Stays with the JLEIC theme of figure 8s. Each half of the arc can be non-isochronous. Each half cancels out the other to make the ring isochronous. Old figure 8 design had fatal µBI. How to stop with this design? LERF Readiness Review 9/30/15

Conclusions Simple arc looks good for a single pass but still fails for 11 passes. µBI looks very good. So far, AAM and ASM arc designs are worse. Still need to analyze FFFAG, Project E arc. Have to look at lower charge behavior. Should also look at longer bunches Have a potential solution if we want a dispersive cooler but this idea has many potential problems that have not yet been addressed.

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