nuSTORM RFFAG solution JB. Lagrange, J. Pasternak Imperial College, - PowerPoint PPT Presentation

nuSTORM RFFAG solution JB. Lagrange, J. Pasternak Imperial College, UK/Fermilab, USA 1

Outline Doublet solution � Triplet solution � Injection � Improvements JB Lagrange - nuFACT 14 - August 2014 2

Outline Doublet solution � Triplet solution � Injection � Improvements JB Lagrange - nuFACT 14 - August 2014 3

Doublet solution Straight : 175 m, maximum scallop angle : 12 mrad 4 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Cell parameters Circular Matching Straight Section Section Section Type FDF FDF Doublet Cell radius/length [m] 17.6 36.2 5 Opening angle [deg] 30 15 5.5 m − 1 k-value/m-value 6.043 25.929 Packing factor 0.92 0.58 0.16 Maximum magnetic field [T] 2.5 3.3 1.5 horizontal excursion [m] 1.3 1.1 0.4 Full gap height [m] 0.45 0.45 0.45 Average dispersion /cell [m] 2.5 1.3 0.18 Number of cells /ring 4 × 2 4 × 2 35 × 2 5 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Magnetic field for P max (+16%) 3 2.5 2 1.5 1 0.5 Bz [T] 0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 0 50 100 150 200 250 s [m] 6 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Beta-functions at matching momentum 40 35 30 25 � [m] 20 15 10 5 0 0 50 100 150 200 250 s [m] Horizontal (plain red) and vertical (dotted purple) betafunctions for half of the ring. 7 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Dispersion function at matching momentum 2.5 2 � [m] 1.5 1 0.5 0 0 50 100 150 200 250 s [m] 8 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Tune diagram ∆ P = ± 16% P 5 5 5 5 5 5 5 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.6 4.6 4.6 4.6 4.6 4.6 4.6 Q z Q z Q z Q z Q z Q z Q z 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4 4 4 4 4 4 4 7 7 7 7 7 7 7 7.2 7.2 7.2 7.2 7.2 7.2 7.2 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.8 7.8 7.8 7.8 7.8 7.8 7.8 8 8 8 8 8 8 8 Q x Q x Q x Q x Q x Q x Q x 9 JB Lagrange - nuFACT 14 - August 2014

Doublet solution Transverse acceptance 8 8 6 6 4 4 x' [mrad] z' [mrad] 2 2 0 0 -2 -2 -4 -4 -6 -6 -8 -8 -200 -150 -100-50 0 50 100 150 200 -200 -100 0 100 200 z [mm] x [mm] Maximum horizontal stable Maximum vertical stable amplitude over 100 turns amplitude over 100 turns 10 JB Lagrange - nuFACT 14 - August 2014

Outline Doublet solution � Triplet solution � Injection � Improvements JB Lagrange - nuFACT 14 - August 2014 11

Motivations 1300 km decay scenario incompatible with scallop of the closed orbit. � � Doublet in the straight section cannot be used. Triplet in the straight section. 12 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Straight : 180 m, maximum scallop angle : 24 mrad 13 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Cell parameters Circular Matching Straight Section Section Section Type FDF FDF DFD Cell radius/length [m] 17.6 36.2 10 Opening angle [deg] 30 15 5.5 m − 1 k-value/m-value 6.057 26. Packing factor 0.92 0.58 0.24 Maximum magnetic field [T] 2.5 3.3 1.5 horizontal excursion [m] 1.3 1.1 0.6 Full gap height [m] 0.45 0.45 0.45 Average dispersion /cell [m] 2.5 1.3 0.18 Number of cells /ring 4 × 2 4 × 2 36 × 2 14 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Magnetic field for P max (+16%) 3 2.5 2 1.5 1 0.5 Bz [T] 0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 0 50 100 150 200 250 s [m] 15 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Beta-functions at matching momentum 40 35 30 25 � [m] 20 15 10 5 0 0 50 100 150 200 250 s [m] Horizontal (plain red) and vertical (dotted purple) betafunctions for half of the ring. 16 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Dispersion function at matching momentum 2.5 2 1.5 � [m] 1 0.5 0 0 50 100 150 200 250 s [m] 17 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Tune diagram ∆ P = ± 16% P 4 4 4 4 4 4 4 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.7 3.7 3.7 3.7 3.7 3.7 3.7 3.6 3.6 3.6 3.6 3.6 3.6 3.6 Q z Q z Q z Q z Q z Q z Q z 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.4 3.4 3.4 3.4 3.4 3.4 3.4 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3 3 3 3 3 3 3 6 6 6 6 6 6 6 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.8 6.8 6.8 6.8 6.8 6.8 6.8 7 7 7 7 7 7 7 Q x Q x Q x Q x Q x Q x Q x 18 JB Lagrange - nuFACT 14 - August 2014

Triplet solution Transverse acceptance 10 8 8 6 6 4 4 x' [mrad] z' [mrad] 2 2 0 0 -2 -2 -4 -4 -6 -6 -8 -10 -8 -400 -300 -200 -100 0 100 200 -200 -150 -100-50 0 50 100 150 200 x [mm] z [mm] Maximum horizontal stable Maximum vertical stable amplitude over 100 turns amplitude over 100 turns 19 JB Lagrange - nuFACT 14 - August 2014

Outline Doublet solution � Triplet solution � Injection � Improvements JB Lagrange - nuFACT 14 - August 2014 20

Preliminary Stochastic injection geometry (J. Pasternak) JB Lagrange - MAP meeting - May 14 21

Injection with matched ������������� �� dispersion Pions" Muons" (J. Pasternak) rad" JB Lagrange - MAP meeting - May 14 22

Injection parameters � with matched dispersion � Septum(field(1.4(T((room(temperature)( � Septum(thickness/length((~2cm/~72cm( � It(requires(SC(dipole/septum(of(4(T(and(6(cm( thickness(to(be(placed(upstream((72(cm(in( length)( � It(gives(20(cm(beam(clearance(at(the(upstream( FFAG(magnet.( � Alternatively(we(could(use(~2cm/164(cm(SC( septum(with(1.8T((results(are(pretty(the(same)( ( (J. Pasternak) JB Lagrange - MAP meeting - May 14 23

Zoom$in$ Pions$ rad$ (J. Pasternak) JB Lagrange - MAP meeting - May 14 24

Injection with no � dispersion (reversed direction) (note)the)inverse)direction)) Pions) Muons) rad) (J. Pasternak) JB Lagrange - MAP meeting - May 14 25

Injection parameters � with no dispersion � Septum(field(0.8(T((room(temperature)( � Septum(thickness/length((~2cm/~164cm( � It(gives(20(cm(beam(clearance(at(the(upstream( FFAG(magnet.( � The(pion(orbits(will(oscillate(in(the(decay( section.(We(need(to(evaluate,(how(this(affects( the(muon(collection(efficiency.( ( (J. Pasternak) JB Lagrange - MAP meeting - May 14 26

Outline Doublet solution � Triplet solution � Injection � Improvements JB Lagrange - nuFACT 14 - August 2014 27

Future improvements Small scallop angle in the straight: reduce the portion of the straight cell with scallop. � Larger DA: smaller gradient (m-value) in the straight section � Smaller magnets in the arcs: reduce the maximum dispersion in the arcs (> 1.3 m necessary for injection). � Neutrino flux estimation from pion & muon decay for doublet and triplet lattice, and comparison with FODO (see D. Adey’s talk). 28 JB Lagrange - nuFACT 14 - August 2014

Thank you for your attention 29 JB Lagrange - nuFACT 14 - August 2014