Demonstrating 6D Cooling. Guggenheim Channel Simulations Pavel Snopok IIT/Fermilab March 1, 2011 1
1 Introduction 2 Wedge absorber in MICE 3 Tapered Guggenheim simulation 4 6D cooling demonstration strategy 2
Introduction Ionization cooling The only efficient technique to cool within a muon lifetime. Passing through material reduces all three components of momentum, only the longitudinal is restored, transverse cooling. Need emittance exchange to cool in 6D. 3
Introduction 6D cooling Transverse part: will be demonstrated in MICE. 6D cooling (via transverse cooling + emittance exchange): Initial test using a wedge absorber in MICE (emittance exchange). Down-selection of the cooling channel. 6D experiment planning and design (implementation is not part of MAP). 4
Wedge absorber in MICE Wedge absorber in MICE Step IV 5
Wedge absorber in MICE MICE layout µ Spectrometer Solenoid 1 Matching Coils 1.1&1.2 Focus Coils 1 Coupling Coils 1&2 Focus Coils 2 Focus Coils 3 Matching Coils 2.1&2.2 Spectrometer Solenoid 2 Incident muon beam Beam PID: TOF 0 Cherenkovs TOF 1 Adjustable Diffuser RF Cavities 1 RF Cavities 2 Liquid Hydrogen Absorbers 1,2,3 Downstream PID: TOF 2 KL Calorimeer e-µ Ranger Trackers 1&2 (emittance measurement in & out) MICE layout scheme 6
Wedge absorber in MICE MICE step-wise implementation MICE implementation schedule. Now it looks like Step II/III might be skipped due to spectrometer solenoid issues (see Kaplan s talk on MICE). 7
Wedge absorber in MICE Emittance exchange Incident Muon Beam Dipole magnet Wedge absorber Δp/p Based on the image by Muons, Inc. Introduce dispersion (in MICE: by careful beam selection). Let particles pass through a wedge absorber in such a way that particles with larger momentum lose more energy. Longitudinal emittance is reduced at the expense of deliberately increasing transverse emittance (emittance exchange). 8
Wedge absorber in MICE MICE Step IV with wedge Top: MICE Step IV with a liquid hydrogen absorber. MICE is a 4D cooling experiment: transverse emittance is reduced while longitudinal emittance stays the same or increases slightly due to stochastic processes in the energy loss. Bottom: LH 2 absorber is replaced with a solid wedge absorber. This way emittance exchange can be observed if the beam is properly matched (dispersion is introduced). 9
Wedge absorber in MICE Wedge schematic Wedge absorber = cylinder intersected with a triangular prism. Opening angle = 90, on-axis length = 75.4 mm (corresp. to 12 MeV energy loss at p=200 MeV/c), radius=225 mm, gap=187.3 mm. 10
Wedge absorber in MICE LiH wedge beam 90 LiH wedge ordered (consisting of two parts, only one part is shown). 90 wedge provides best longitudinal cooling / emittance exchange. 45 half-wedge needs to be simulated. In addition to the LiH wedge a set (90, 60, and 30 ) of plastic wedges would be useful to test properties of different materials (time permitting). Wedge support design is underway. 11
Wedge absorber in MICE Cooling performance 90 ϵ // [mm] ϵ 6D ϵ [mm] // 88 86 84 82 80 78 76 74 No wedge LiH 30 LiH 60 LiH 90-1.5-1 -0.5 0 0.5 1 1.5 2 z [m] 5.8 5.7 5.6 5.5 5.4 ϵ 6D [mm 3 ] 3000 2900 2800 2700 2600 2500 2400 2300 No wedge o LiH 30 o LiH 60 o LiH 90-1.5-1 -0.5 0 0.5 1 1.5 2 z [m] Cooling effect observed for different angles (red 30, blue 60, green 90 ) 5.3 5.2 5.1 5 No wedge LiH 30 LiH 60 LiH 90-1.5-1 -0.5 0 0.5 1 1.5 2 z [m] ɛ = c m det(v(ct, E)), 3 ɛ 6D = c m det(v(ct, E, x, px, y, p y)), V covar. matrix of the specified space. 12
Wedge absorber in MICE Concern: 6D emittance change with no material With no material in the channel the system is Hamiltonian. According to the graph, the 6D emittance changes. Is Liouville safe? ϵ 6D [mm 3 ] 3000 2900 2800 2700 2600 2500 2400 2300 No wedge o LiH 30 o LiH 60 o LiH 90-1.5-1 -0.5 0 0.5 1 1.5 2 z [m] 13
Wedge absorber in MICE Phase volume conservation Hamiltonian system: det(jac(m)) = 1, where Jac(M) is the Jacobian of the transformation of phase space: M( q, p) = ( Q, P), (q, p) are phase space coordinates before the transformation, (Q, P) after the transformation. Let S 1 be a subset of phase space, S 2 = M(S 1 ). Then, V 2 = S 2 d n Qd n P = S 1 det(jac(m))d n qd n p = S 1 d n qd n p = V 1. V 2 = V 1 = const. Need to check that the determinant in question is indeed equal to 1. 14
Wedge absorber in MICE COSY Infinity analysis Implemented MICE magnets in COSY, compared to g4beamline, very good agreement. Calculated a high-order transformation map. Obtained the determinant of the Jacobian as a high-order polynomial. det(jac(m)) = 1, deviation from 1 in (x,y) is shown on right. B [T] 4.5 4 3.5 3 2.5 2 1.5 1 0.5 Magnetic field comparison g4beamline COSY Infinity 0 0 0.5 1 1.5 2 2.5 3 3.5 z [m] 0-2 -4 x 10-11 0.3 0.2 0.1 Deviation of det(jac(m)) from 1, ninth order 0-0.1-0.2 x [m] 0 0.1 0.2 0.3 y [m] -0.2-0.1 x 10-11 0-1 -2-3 -4 15
Wedge absorber in MICE COSY analysis summary 6D emittance is conserved. Change in emittance observed is due to approximation: ɛ 6D = c m det(v(ct, E, x, px, y, p y )), V covar. matrix of the specified space. Need a better 6D emittance estimate. Two ideas: find 6D phase space volume using Voronoi tesselation (computationally challenging in 6D); reconstruct emittance immediately upstream and downstream of the wedge from tracker measurements. 16
Tapered Guggenheim simulation Tapered Guggenheim simulations (step towards down-selection) 17
Tapered Guggenheim simulation From Bob Palmer s talk in April 2010: Simulation using matrix emittance exchange Full simulation of tapered Guggenheim requires coil tilting for dipole fields and wedge absorbers will be time consuming But required dipole field << solenoid fields (eg:.125 vs 3 T) focusing betas are almost identical to those in a linear channel resulting emittance exchange is close to ideal It is easier and faster to simulate a linear channel Adding exchange by a matrix acting on (x, x, y, y, σ z, σ p /p) 1 0 0 0 0 0 0 1 + δ 0 0 0 0 0 0 1 0 0 0 0 0 0 1 + δ 0 0 0 0 0 0 1 0 0 0 0 0 0 1-2δ Comparisons with full simulation of an un-tapered lattice are close 18
Tapered Guggenheim simulation From Bob Palmer s talk in April: Emittances vs length 10 2 8 6 50.6 % 4 2 Qmax=23 10.0 8 < Q >=12.5 6 4 2 long 1.24 (mm) 1.0 8 6 perp 0.45 4 0 100 200 300 400 length (m) No transverse emittance growth at matches is observed Initial Q is better than in un-tapered lattice (23 vs. 15) Final Q is better than in un-tapered lattice (12 vs. 8) 19
Tapered Guggenheim simulation G4beamline simulation For each step: Earlier studies show that simulation results for the helix and the ring are very similar. Hence, I simulate a set of rings rather than the helix. This allows for staged simulations, and reduces the complexity of the model. Results will be more realistic than simulating a linear channel + linear emittance exchange map. 20
Tapered Guggenheim simulation G4beamline simulation For each stage: 1 Coil tilting (to generate bending field). 2 Coil displacement (to minimize vertical orbit excursion). 3 Geomety issues (placement along the arc rather than a straight line). 4 Wedge absorbers (size, position, tilt, edge cut). 5 Closed orbit. 21
Tapered Guggenheim simulation Transverse emittance, [mm] 12 10 8 6 4 2 Transverse emittance Untapered Guggenheim Tapered Guggenheim 0 0 50 100 150 200 250 300 350 400 450 500 z [m] 22
Tapered Guggenheim simulation Longitudinal emittance, [mm] 20 18 16 14 12 10 8 6 Longitudinal emittance Untapered Guggenheim Tapered Guggenheim 4 0 50 100 150 200 250 300 350 400 450 500 z [m] 23
Tapered Guggenheim simulation 10 4 6D emittance Untapered Guggenheim Tapered Guggenheim 6D emittance, [mm 3 ] 10 3 10 2 10 1 0 50 100 150 200 250 300 350 400 450 500 z [m] 24
Tapered Guggenheim simulation 100 80 Transmission Untapered Guggenheim Tapered Guggenheim Transmission, [%] 60 40 20 0 0 50 100 150 200 250 300 350 400 450 z [m] 25
Tapered Guggenheim simulation 30 25 20 15 Q factor Untapered Guggenheim Tapered Guggenheim Q 10 5 0 5 10 0 50 100 150 200 250 300 350 400 450 500 z [m] Q = dɛn 6D /ds dn/ds N(s) ɛ N (s), ɛn 6D (s) normalized six-dimensional emittance 6D of the beam, N(s) number of surviving particles. Q factor compares the rate of change of emittance to the particle loss. 26
6D cooling demonstration strategy 6D demo strategy 27
6D cooling demonstration strategy MICE is both technology demo and beam experiment. Once MICE demonstrates transverse cooling and emittance exchange, most of remaining 6D-cooling-channel risk is believed to be technological (i.e., can we build and operate the channel as designed). Bench test: cooling channel section should be long enough to address key integration issues (cavities in B field, spatial compatibility issue, Bench-tested channel section may be different than that needed for a beam test (but try to maintain compatibility). 28
6D cooling demonstration strategy Cooling experiment design: Simulations to clarify appropriate performance + needed precision. Diagnostics/detector study to determine how to measure the muon beam to required precision. Design/integration study to specify and lay out experiment: coordinate to ensure bench-test hardware also suitable for beam test, find suitable location, design needed muon beam line (unless MICE hall and beam suitable and available). Many details undefined until baseline channel is selected. 29
6D cooling demonstration strategy Thank You! 30