1. 1 Muon Collider & Ionization Cooling Issues Y. Alexahin FERMI NATIONAL ACCELERATOR LABORATORY US DEPARTMENT OF ENERGY f FNAL Accelerator Advisory Committee meeting December 5, 2006

2. 2 Overview of basic ideas low emittance MC 6D ionization cooling PIC and REMEX Ongoing work Questions to answer FY07 plan FY08 plan and beyond Summary Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Plan of the talk

3. 3 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Muon Collider parameters Low Emitt. High Emitt. Energy (TeV) 0.75+0.75 (  =7098.4) Average Luminosity (1e34/cm^2/s)2.71 Average bending field (T)108.33 Mean radius (m)361.4363.8 Number of IPs4 (350m/2 each)2 (200m each) P-driver rep.rate (Hz)6560 Beam-beam parameter/IP,  0.0520.1  (cm)0.53 Bunch length (cm),  z 0.52 Number of bunches/beam, n b 101 Number of muons/bunch (1e11), N  112 Norm.transverse emittance (  m),   N 2.113 Energy spread (%)1 0.1 Norm.longitudinal emittance (m),  ||N 0.35 0.14 Total RF voltage (GV) at 800MHz406.6  10 3  c 0.26  10 3  c RF bucket height (%)23.90.6 Synchrotron tune0.723  10 3  c 0.02  10 3  c  +  - in collision / proton0.15 /20.15 8GeV proton beam power (MW)1.10.6  Low emittance option (advanced): owing to ideas by Yaroslav Derbenev (HCC, PIC) much lower 6D emittances seem to be feasible than previously thought of.  High emittance option (baseline): conceptually follows 1999 PRSTAB Muon Collider Collaboration report

4. 4 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Low emittance option for MC f  z /   “Hourglass factor” Low emittance pros: smaller  → smaller total number of particles n b N  →  relaxed coherent stability requirements  low proton driver power  low neutrino radiation Low emittance cons: bb-effect limits N  → larger n b is required → electrostatic separation or crossing angle smaller  → strong IR chromaticity → smaller  z is required →  small  c → strong arc cell chromaticity  higher  p /p for the same long. emittance problems with momentum acceptance

5. 5 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 The roadmap to low emittance Ionization cooling: very similar to SR cooling in e-damping rings The longitudinal damping partition number is naturally negative at p  <300MeV/c: How to make it positive – see next slide. The normalized equilibrium emittance (r.m.s.) so that to achieve   =2  m   <0.2mm is required (for  1). Is it feasible? Another possibility (D.Neuffer): decelerate muons to very low . With Z=4 (Be) and the natural value of g || <0 (the final cooling stage) (overestimation for H and He)

6. 6 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Basic 6D Cooling Two ways to get g || >0: generate large dispersion and use wedge absorbers; generate large momentum compaction  c >0 in a homogeneous absorber The first method is realized in two schemes: "Guggenheimed" RFOFO channel (helical or spiral with reducing radius), estimated emittances   N ~5  10 2  m,  || N ~1mm straight FOFO channel with tilted solenoids,   N ~5  10 2  m,  || N ~0.5mm The second method in: Helical Cooling Channel (HCC),   N ~2  10 2  m,  || N ~0.3mm; HCC is the most attractive scheme, however, it has inherent difficulties

7. 7 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 PIC & REMEX Basic idea of the Parametric resonance Ionization Cooling (Y. Derbenev): form a structure with ~180  phase advance/cell resonantly excite beta-beating with special lenses to obtain very small   at absorber plates Reverse EMittance EXchange: obtain very small   as described above enhance transverse damping by making g || <0 as large by the absolute value as possible by reversing the wedge angle and generating maximum dispersion at the wedges Lattice magnets and RF cavities not shown

8. 8 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 “Guggenheim” RFOFO structure (R.Palmer) - modification of the initially proposed by V.Balbekov RFOFO ring

9. 9 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 “Guggenheim” RFOFO cooling simulations (R.Palmer, A.Klier) Adding 804 MHz section would allow to achieve   N ~7.5  10 2  m, but: no matching section designed yet (may further increase losses surpassing 50% already) high magnetic field may drastically limit RF voltage (would GH 2 filling help?) shown reduction in emittances include both cooling and initial shaving the merit factor of the 2-stage RFOFO channel is just (N  /  6D ) fin / (N  /  6D ) ini = 800

10. 10 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 HCC Simulations (K.Yonehara) 6D cooling factor in the series of HCC is ~50,000 Initial proposal: RF cavities packed inside solenoid additional helical coils create rotating dipole and quadrupole fields As R.Palmer noted the transverse field on the coils would exceed 10 3 T at the last stage!

11. 11 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 HCC issues Vladimir Kashikhin found a brilliant solution: helical solenoid! Magically, the dipole and quadrupole components have the right values, while the orbit goes through the centers of the coils! Still a number of problems to be solved: how far down this helix can be scaled? Is helix period of ~ 20cm (with Bs~15T) technically feasible? a principal solution for the RF structure which can fit inside the HCC has yet to be found; segmented HCC with RF cavities between solenoid sections was proposed but not demonstrated to provide adequate cooling

12. 12 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 REMEX with HTS solenoids (R.Palmer) It is possible to obtain   N ~10  m in a solenoidal focusing channel with LH 2 absorber: Simulations of cooling in a channel with 6 solenoids (no RF yet) gave   N =25  m. To achieve emittances for the low emittance MC option this channel must be followed by a stronger focusing channel with short solid absorbers.

13. 13 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Mixed Lattice for PIC/REMEX channels (A.Bogacz) 10T solenoidquadsdipoles absorber This mixed quadrupole-solenoid focusing lattice provides   =1.4cm at the absorber center. Large dispersion function gives the possibility of chromatic correction (not demonstrated yet). By reducing dimensions and increasing field strength one may hope to get   in the mm range.

14. 14 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Questions to answer Collider ring: correction of chromatic perturbations (chromatic beta-beating, nonlinear chromaticity and momentum compaction factor); radiation shielding necessary to protect the superconducting magnets and detectors at specific for the particular design beam intensity and sizes ; field quality of the magnets which have the required aperture and field strength (magnets being developed for the LHC luminosity upgrade is a good first approximation); dynamic aperture with realistic field and alignment errors; beam-beam effects; suppression of coherent instabilities at given bunch intensity, length, momentum compaction and lattice functions. 6D cooling channel: scalability of the proposed by V.Kashikhin HCC technical solution to the helix period of ~ 20cm (with Bs~15T); principal solution for the RF structure which can fit inside the HCC;

15. 15 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Questions to answer 6D cooling channel (continued) ability of gas-filled cavities to support high-gradient RF field in the presence of ionizing beam; end-to-end simulation of the "Guggenheimed" RFOFO channel to prove its competitiveness; proof-of-principle study of the FOFO channel with tilted solenoids followed by cooling simulations. PIC / REMEX optics design for different stages (solenoidal vs quadrupole and mixed focusing) compensation of chromatic and spherical aberrations; space charge effects Proton driver, Pion production, Muon RF capture, Bunch coalescing, Acceleration There is little doubt in feasibility of these elements of the complex, there are a number of options for each of them which should be studied and compared, but only after the principal solution for the collider ring and the cooling channel is chosen.

16. 16 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 FY07 plan Physics analysis and computer simulations of different schemes for the basic 6D cooling channel and PIC/REMEX channel. Side-by-side comparison of the obtained results with the aim of choosing the 6D cooling channel baseline scheme compatible with the chosen collider option. Analysis of implications of different options for the muon collider (low emittance vs. high emittance, electrostatic separation in one ring vs. double ring) resulting in a presumably optimal choice of parameters. Collider ring optics design for the chosen option. Preliminary analysis of the technical feasibility and physical validity of the proposed design (momentum acceptance, medium-term dynamic aperture, coherent stability). Formulating requirements to the proton driver and other systems of the complex. Consistent scheme(s) of the muon collider complex.

17. 17 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 FY08 plan and beyond Upgrade of the muon production and RF capture systems design Analysis, selection and preliminary design of muon acceleration systems (RLA vs. FFAG for the first stage, RLA vs. fast ramping synchrotrons for subsequent stages) Extensive simulation studies and design optimization of all essential systems of the collider complex. Analysis of radiological issues for appropriate choice of the collider orientation and depth Cost estimates Draft conceptual design report Optimistically, the conceptual design will be finished in 2009

18. 18 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Summary  The Muon Collider for c.o.m. energy 1.5-2TeV seems doable with present day technology and can be accomodated on the Fermilab site  Extensive design and simulation work is necessary for all parts of the complex with the 1999 PRSTAB Muon Collider Collaboration report being a good first approximation  The requested funding for this work seems adequate taking into account heavy contribution from other labs especially BNL, JLab and MuonsInc.

19. 19 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Backup slides – Emittance diagram Emittance evolution in R.Palmer’s muon cooling scheme

20. 20 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Backup slides – straight FOFO channel (Y.Alexahin)  straight solenoids tilted solenoids RF cavities Closed orbit at  = 0.01 (dispersion follows the same pattern) y/L z/L x/L Phase advance over the 4-solenoid period is above 2  → resonant dispersion generation Cooling by combination of GH 2 and Li wedges in high-dispersion locations for damping repartition The scheme requires RF cavities operation in high magnetic field (hopefully GH 2 will help)

21. 21 Muon Collider & Ionization Cooling Issues - Y. Alexahin, FNAL December 5, 2006 Backup slides – collider ring optics Two optics designs so far: prepared for 1999 PRSTAB Muon Collider Collaboration report by Carol Johnstone et al.:  * = 3mm, peak  max =1.5  10 5 m,  c = - 9.2  10 -5. Requires further work on chromatic correction, the momentum acceptance is just (- 1.2  10 -4, 1.6  10 -4 ). more conventional design by A.Bogacz:  * = 1cm, peak  max =4.8  10 3 m (but with the distance from IP to the first quad just ~2m),  c = 2  10 -4 IR and a few arc cells in the design by A.Bogacz