PRISM WITH ADVANCED SCALING FFAG JB Lagrange, Y. Mori, Kyoto - PowerPoint PPT Presentation

PRISM WITH ADVANCED SCALING FFAG JB Lagrange, Y. Mori, Kyoto University Wednesday, September 23, 2009

CONSTRAINTS • Large transverse acceptance • horizontal: 20 000 π mm.mrad • vertical: 3 000 π mm.mrad • Momentum acceptance: 68MeV ±20% Wednesday, September 23, 2009

Original PRISM cell k 4.6 Average radius 6.5 m Phase advances: horizontal µ x 97 deg. vertical µ z 55 deg. Dispersion 1.16 m Figure 1: Original 10-cell PRISM ring Problem of Injection/Extraction Wednesday, September 23, 2009

Reduced-dispersion area wanted Dispersion suppressors Wednesday, September 23, 2009

DISPERSION SUPPRESSOR Bending: k 1 k 2 k 2 k 1 k 3 � n � � n � � n � � n � � n � Straight: ρ ρ ρ ρ ρ 1 3 1 2 2 5 Wednesday, September 23, 2009

DISPERSION SUPPRESSOR IN BENDING LINES R 2 − ( R 1 − R 2 ) = R 3 2 R 2 = R 1 + R 3 � P 1 � k +1 R = R 0 P 0 1st order 2 1 1 k 2 + 1 = k 1 + 1 + k 3 + 1 6 Wednesday, September 23, 2009

Dispersion suppressor cell FDF k 14.2 Average radius 13 m Phase advances: horizontal µ x 90 deg. vertical µ z 86 deg. Dispersion 1.16 m to 0.58 m Dispersion reduced areas Figure 2: PRISM ring with 4 dispersion suppressors and 6 original PRISM magnets. Wednesday, September 23, 2009

Figure 3: Change of working point in tune diagram. Wednesday, September 23, 2009

Horizontal Poincarre map Qx = 3.65, Qz = 3.54 Wednesday, September 23, 2009

2.2 sqrt(beta) [m**1/2] (red->H green->V) 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 s [m] Betafunctions of original PRISM cell. (red: horizontal, green: vertical) Wednesday, September 23, 2009

2.4 sqrt(beta) [m**1/2] (red->H green->V) 2.2 2 1.8 1.6 1.4 1.2 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 s [m] Betafunctions of a dispersion-suppressor cell (90 deg.) (red: horizontal, green: vertical) Wednesday, September 23, 2009

Betafunctions of PRISM ring with dispersion suppressor. (red: horizontal, green: vertical) Wednesday, September 23, 2009

SCALING STRAIGHT LINES Straight section = Bending section with infinite radius x � x r 0 k x � n ρ x � r � r 0 � r 0 �� � � k � 1 + x 1 + x n ρ x lim = lim = lim = e r 0 →∞ r 0 →∞ r 0 →∞ r 0 r 0 r 0 with r = x + r 0 k = r 0 ρ n ρ ( X − X 0 ) n � dB � B z = B 0 e n = ρ B dx z =0 13 Wednesday, September 23, 2009

ANOTHER LATTICE Bending cell k 6.5 Average radius 3.5 m Phase advances: horizontal µ x 90 deg. vertical µ z 87 deg. Dispersion 0.47 m Straight cell 2.14 m − 1 n/ ρ Length 3 m Phase advances: horizontal µ x 24 deg. vertical µ z 87 deg. Wednesday, September 23, 2009

Betafunctions of bending cell. (red: horizontal, green: vertical) Wednesday, September 23, 2009

Betafunctions of straight cell. (red: horizontal, green: vertical) Wednesday, September 23, 2009

Betafunctions of bending and straight cells (half ring) (red: horizontal, green: vertical) Wednesday, September 23, 2009

Horizontal Poincarre map Wednesday, September 23, 2009

STILL A LOT OF WORK TO DO... Wednesday, September 23, 2009

THANK YOU FOR YOUR ATTENTION Wednesday, September 23, 2009

APPLICATION: PRISM 21 Wednesday, September 23, 2009

CHANGE RADIUS R 1 − R 01 = R 2 − R 02 1st order � P R 01 = k 1 + 1 1 � k +1 R = R 0 R 02 k 2 + 1 P 0 22 Wednesday, September 23, 2009

MISMATCH BEND-STRAIGHT n/ ρ , X 0 k b , r 0 Straight cell: ρ s ( X − X 0 ) n B z = B 0 s e � r � k b Bending cell: B z = B 0 b r 0 Matching of P 0 : B 0 s ρ s = B 0 b ρ b � r � k b +1 n ρ ( X − X 0 ) = B 0 b ρ b Matching of P: B 0 s ρ s e r 0 1st order n = k b + 1 � r − r 0 � = 1 + n 1 + ( k b + 1) ( X − X 0 ) r 0 ρ s r 0 ρ s 23 Wednesday, September 23, 2009

DISPERSION SUPPRESSOR IN STRAIGHT LINES X 2 − ( X 1 − X 2 ) = X 3 2 X 2 = X 1 + X 3 n ln( P X = ρ ) P 0 2 ρ 2 = ρ 1 + ρ 3 n 2 n 1 n 3 24 Wednesday, September 23, 2009