First Thoughts on IDS G H Rees, RAL

Topics 1.Two-way, μ ± injection chicane for the dog-bone RLA. 2.Injection energy & efficiency for a first dog-bone RLA. 3. Injection and extraction efficiency for an FFAG.

Evolution of NF Muon Acceleration Linac Energy RLA stages FFAG stages 3.0 GeV 2 Racetracks None (3-11 & GeV) 1.5 GeV 1 Dog-bone (chicane) 2 (5-10 & GeV) 0.9 GeV 2 Dog-bones (chicane) 1 (12.5 to 25 GeV) Q. How does 2-way chicane allow such a low injection energy?

Two-way, μ ± injection chicane. μˉ μ + μ+Dμ+D μˉ θ θ 1 ≈ 5θ/8 1.5 GeV 0.9 GeV ℓ

Approximate Data for a Two-way Chicane Dipoles ≈ 2/3 m, sep’ns ≈ 2 m, β ≈ 4 m, ε n ≈ 30 mm, Δ ≈ ± 7% D (μ + deflection shown) = 2 tan θ + 2 (1- cos θ)/3θ ≈ 2 tan θ 1 + (1- cos θ 1 )/θ √βε + 2 Δ(tan θ + tan θ 1 + θ/3) + ℓ Central, two-way dipole (B) cannot be a septum magnet. Solutions then require D > 4 m, θ > 60° and B > 11 T. Practical solutions don’t seem possible for the 6 m chicane, nor for a longer chicane, with an added septum and x 2 μ ± cooling.

Consequences of not using a Chicane 1. Injection of μ ± into upstream end of the RLA straight 2. A higher energy injector is required for the first RLA 3. There is a half-turn gain of acceleration in the RLA 4. Different μ ± injection and μ ± transfer lines required 5.Reassessment of pros & cons of dog-bones & racetracks 6. There is no longer a base line NF design

Pros & cons of dog-bones & racetracks 5-pass Dog-bone RLA 4½-turn Racetrack RLA 2 x 2 droplets (4 x °) 2 x 4 arcs (8 x 180°) 1 long linac, energy E 2 short linacs, energy E/2 total energy gain = 5 E total energy gain = 4.5 E sep’n 2E in arcs/spreaders sep’n E in arcs/spreaders same μ ± beam focusing different μ ± beam focusing crossing of droplet orbits no crossing of orbits On balance, the dog-bone RLA is still the favoured choice

Energy Range of Revised Dog-bone RLAs An earlier, 3½ pass dog-bone RLA had energies 1½ to 5 GeV. The first, full energy pass through linac was from 2 to 3 GeV. So, assume a first full energy linac pass from 2 to 3 GeV and four further linac passes of 1 GeV to reach 7 GeV. There are then many options, eg, RLA + RLA, 2RLA + FFAG A five pass, RLA with 3.6 GeV per pass could reach 25 GeV. Fast ejection (as in racetrack) prob. not needed for dog-bone. Q. If 50 GeV needs 2 RLAs, why does 25 GeV need 3 accels?

Injection Energy for the First RLA Choice of the energy depends on the μ ± injection efficiency. Carol Johnstone required a racetrack at 3 GeV for ε n = 15 mm. Chicane design assumes dog-bone at 0.9 GeV for ε n = 30 mm. No-chicane, dog-bone, Δφ-s req. is ≈ 2.0 GeV for ε n = 30 mm. No-chicane, dog-bone, efficient injection req. may be > 2 GeV Spreader injection involves 3 (5) orbits for dogbone (racetrack). Spreader injection study is needed to decide injection energy.

Further Evolution of μ ± Acceleration? Linac Energy RLA stages FFAG stages 3.0 GeV 2 Racetrack None (3-11 & GeV) 1.5 GeV 1 Dog-bone (chic) 2 (5-10 & GeV) 0.9 GeV 2 Dog-bones (chic) 1 (12.5 to 25 GeV) 2.25 GeV? 2 Dog-bones (no chic) None, or ( & 7-25 GeV) 1 (25 to 50 GeV)

Injection & Extraction for FFAGs Kicker-septum systems: pulsed power scales approx. as ( ε n ) 2. Kickers only: pulsed power is F (ε n, w (cryostat dimension)) and the extraction is more difficult than injection. At 25 GeV: a 1.46 m, 1 T septum unit bends the beam by 1° and displaces it < w (septum, shield & vac. wall). So, there is no advantage in such a septum unit. Decay ring: 20 GeV,  k = 6.47 mr, 24 m kicker, 44 m straights, 7, shorted, 3m, 10 Ω delay line, push pull K with 14 x (50 kV PFN, 5 kA pulsers & 10 Ω feeders)/ring FFAG ring; 25 GeV,  k ≈ 30 mr, 1.2 m kicker, B field x100

FFAG Injection and Extraction………. Pulsed powers for kickers ≈ 20 x that of state of the art kickers. Deflecting fields in kickers ≈ 40 x that of state of the art kickers. Induction linac modulators are able to produce the pulse power, when driving cavities with toroidal B fields, longitudinal E fields. Different drive arrangements allow different impedance levels. Short, transverse deflection kickers do not have many options: push-pull, 1-turn windings, each with a low Z, matched feeder. Difficult to transform from the low Z and the very high current. To see if such short kickers are feasible, R and D is needed in collaboration with an experienced, induction linac group.

Injection & Extraction Efficiency Most, existing fast injection and extraction systems use: zero dispersion straight sections, linear focusing regions, low beam emittances and a low beam momentum spread. None of these conditions apply to the GeV FFAG. Linear, n-sc, FFAGs now consider adding sextupole comps. Special wide aperture magnets are needed for inj(ej) channels. Study needed of effect on in(out)put matching and efficiencies. Racetrack RLAs needed fast extraction, but not fast injection. Hopefully, the dog-bone RLAs will not need any fast system.

Summary  A 2-way, 0.9 GeV injection chicane may not be feasible, so injection at ≥ 2 GeV may be needed for a first dog-bone RLA  A possible, μ ± acceleration scenario could then consist of: 5-pass, dog-bone RLAs at 2.25 to 7 GeV and 7 to 25 GeV  This would defer choice between a dog-bone and an FFAG accelerator to the higher energy range from 25 to 50 GeV  A 3 orbit, reverse beam spreader design is needed for dog- bone RLAs, and estimates made of the injection efficiencies