1. Muon Collider Design & Simulations Plan Y. Alexahin FERMI NATIONAL ACCELERATOR LABORATORY US DEPARTMENT OF ENERGY f NF&MCC meeting, UCLA January 31- February 1, 2007

2. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 MCTF Accelerator Physics Studies Goals 2007: Choice of the baseline Ionization Cooling scheme Decision on prototyping the Helical Solenoid (6D MANX) Collider ring optics design, requirements to the magnets 2008: Choice of the proton driver and muon acceleration schemes Choice of the collider orientation and depth from radiological considerations Cost estimates Draft conceptual design report

3. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 Ionization Cooling Schemes Strawman LEMC PIC REMEX-2 HCC REMEX-1

4. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Palmer’s way 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 includes both cooling and initial shaving the merit factor of the 2-stage RFOFO channel is just (N  /  6D ) fin / (N  /  6D ) ini = 800 “Guggenheimed” RFOFO cooling simulations (R.Palmer, A.Klier)

5. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Palmer’s way Final 6D Cooling

6. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 Final 6D Cooling, R.Palmer’s way No field reversal in simulations? - trajectories are different which may affect transmission in nonlinear fields

7. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Palmer’s way REMEX in 50T solenoids

8. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Palmer’s way To choose this way would be helpful to know How to reduce the total length of the RFOFO channel? How to improve the transmission through the “Guggenheimed” RFOFO channel ? - Helical RFOFO? How the LiH container walls in Fernow’s new channel will contribute to the emittance? How field reversals will affect transmission through the new channel? Momentum acceptance in a channel with 50T solenoids with RF in and matching between the solenoids? Space charge effects in a bunch of 2  10 12 muons?

9. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Johnson’s way K.Yonehara obtained the 6D cooling factor in the series of HCC of ~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!

10. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 R.Johnson’s way “Slinky” helical solenoid (Vlad. Kashikhin) solves the problem with unrealistically high field, however, a number of problems remains: Is the helical solenoid with period of 15T technically feasible? How to fit the RF structure into the solenoid? Segmented HCC with RF cavities between solenoid sections was proposed but not demonstrated yet to work. PIC / REMEX The proposed scheme not demonstrated yet to work Previous efforts by V.Balbekov to implement the PIC idea failed due to strong nonlinear aberrations - is there understanding why the new scheme will be better?

11. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 How to make the choice? It would be wonderful to have end-to-end simulations with matching between all sections but may be not realistic due to time constraints may be not necessary since the different parts of the two schemes can be chosen and combined (e.g. HCC for 6D cooling and 50T solenoids for REMEX) new (or forgotten old) ideas may emerge and prove advantageous 2mm It would be enough to design and simulate two pieces of the channel with necessary matching, realistically placed RF, windows (if needed) for the two essential cooling ranges:   N 2.0 mm  0.4 mm (HCC, RFOFO, straight FOFO)  ||N 2.5 mm  0.5 mm   N 0.1 mm  25  m  ||N ?  <40 mm (50T solenoid), <40 mm / Nb (PIC), Nb= number of bunches to coalesce Important to check the results with the same software! Timeframe: end of August

12. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 Strawman Muon Collider parameters Low Emitt. High Emitt. Energy (TeV)0.75+0.75 (  =7098.4)1+1 Average Luminosity (1e34/cm^2/s)2.70.7 (corr)  1.4 Average bending field (T)105.18 Mean radius (m)361.4652.5 Number of IPs4 (350m for 2)? P-driver rep.rate (Hz)656 Beam-beam parameter/IP,  0.052 (corr) 0.043  0.086  (cm)0.50.3 Bunch length (cm),  z 0.50.3 Number of bunches/beam, n b 101 Number of muons/bunch (1e11), N  120 Norm.transverse emittance (  m),   N 2.150  25 Energy spread (%)1 0.12 Norm.longitudinal emittance (m),  ||N 0.35 0.036 Total RF voltage (GV) at 800MHz406.6  10 3  c - RF bucket height (%)23.9- Synchrotron tune0.723  10 3  c -  +  - in collision / proton0.15 /2- 8GeV proton beam power (MW)1.11.5  Low emittance option (Rol Johnson): owing to new ideas (HCC, PIC, gas-filled cavities) much lower 6D emittances seem to be feasible than previously thought of.  High emittance option (Bob Palmer): conceptually follows 1999 PRSTAB Muon Collider Collaboration report

13. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 LEMC Issues 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

14. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 Muon Collider Ring Design Carol’s design  * =3mm   max=150km,  c < 0, |  c |~ 10 -5 Eliana Gianfelice improved the momentum acceptance by a factor of 5, but at a cost of shifting the tunes to unfavorable for beam-beam effect values. Probably it can be increased further, but not too much. Alex Bogacz proposed a more conservative approach using 60º/60º FODO lattice and  * =1cm. However, he placed quads too close to IP (2m) and have not looked at chromatic aberrations (should not be a problem in his case though) Now we are trying FODO lattice in the arcs but with larger phase advance per cell, up to 108º (successfully tried in LEP in the horizontal plane) - no viable solution insofar

15. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 Requirements to the Muon Collider Ring Lattice Design So we may announce a competition for the lattice design with following properties:  *  1cm 2 IPs distance of the first quad from IP  6.5m (is really necessary for E=0.75TeV?) momentum compaction  c  10 -4 momentum acceptance  ± 0.5% transverse acceptance  10   (geo) (for high emittance)~ 60nm  a>4cm at  =25km possibility of electrostatic separation of 10 bunches/beam tunability in a wide particle energy range ( starting maybe from where LEP stopped ~100GeV) Have P.Snopok and C.Johnstone already done this? - Let’s ask Oprah for the prize! Timeframe: April, then Dynamic aperture study with realistic multipole field errors (long term tracking for the p-  option needed) Analysis of coherent instabilities Beam-beam simulations Beam collimation & energy deposition

16. Muon Collider Design & Simulations Plans - Y. Alexahin, FNAL February 1, 2007 MCTF Accelerator Physics Group FNAL: C.Ankenbrandt, Y.Alexahin, V.Balbekov, C.Bhat, A.Burov, A.Drozhdin, D.Finley, N.Gelfand, E.Gianfelice-Wendt, C.Johnstone, J.Johnstone, V.Lebedev, N.Mokhov, A.Moretti, D.Neuffer, K.-Y.Ng, M.Popovich, I.Rakhno, P.Spentsouris, A.Striganov, A.Valishev, A.Van Ginneken, K.Yonehara MuonsInc: R.Johnson, M.Cummings, S.Kahn, T.Roberts, R.Sah BNL: J.S.Berg, J.Gallardo, R.Gupta, H.Kirk, R.Palmer, R.Fernow Jlab: K.Beard, A.Bogacz, Y.-C.Chao, Y.Derbenev, B.Rimmer ANL: J.Norem My apologies for this list being obviously incomlete!