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

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

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PRISM WITH ADVANCED SCALING FFAG JB Lagrange, Y. Mori, Kyoto University Wednesday, September 23, 2009 CONSTRAINTS Large transverse acceptance horizontal: 20 000 mm.mrad vertical: 3 000 mm.mrad Momentum acceptance: 68MeV

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SLIDE 1

PRISM WITH ADVANCED SCALING FFAG

JB Lagrange, Y. Mori, Kyoto University

Wednesday, September 23, 2009

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SLIDE 2

CONSTRAINTS

  • Large transverse acceptance
  • horizontal: 20 000π mm.mrad
  • vertical: 3 000π mm.mrad
  • Momentum acceptance: 68MeV ±20%

Wednesday, September 23, 2009

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SLIDE 3

Figure 1: Original 10-cell PRISM ring Problem of Injection/Extraction

Original PRISM cell k 4.6 Average radius 6.5 m Phase advances: horizontal µx 97 deg. vertical µz 55 deg. Dispersion 1.16 m

Wednesday, September 23, 2009

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SLIDE 4

Reduced-dispersion area wanted Dispersion suppressors

Wednesday, September 23, 2009

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SLIDE 5

DISPERSION SUPPRESSOR

5

Bending:

k1 k2 k3 k2 k1

Straight:

n ρ

  • 1

n ρ

  • 2

n ρ

  • 3

n ρ

  • 1

n ρ

  • 2

Wednesday, September 23, 2009

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SLIDE 6

DISPERSION SUPPRESSOR IN BENDING LINES

6

R = R0 P P0

  • 1

k+1

1st order

2 k2 + 1 = 1 k1 + 1 + 1 k3 + 1

2R2 = R1 + R3

R2 − (R1 − R2) = R3

Wednesday, September 23, 2009

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SLIDE 7

Figure 2: PRISM ring with 4 dispersion suppressors and 6 original PRISM magnets.

Dispersion reduced areas

Dispersion suppressor cell FDF k 14.2 Average radius 13 m Phase advances: horizontal µx 90 deg. vertical µz 86 deg. Dispersion 1.16 m to 0.58 m

Wednesday, September 23, 2009

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SLIDE 8

Figure 3: Change of working point in tune diagram.

Wednesday, September 23, 2009

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SLIDE 9

Horizontal Poincarre map Qx = 3.65, Qz = 3.54

Wednesday, September 23, 2009

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SLIDE 10

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sqrt(beta) [m**1/2] (red->H green->V) s [m]

Betafunctions of original PRISM cell. (red: horizontal, green: vertical)

Wednesday, September 23, 2009

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SLIDE 11

1 1.2 1.4 1.6 1.8 2 2.2 2.4 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sqrt(beta) [m**1/2] (red->H green->V) s [m]

Betafunctions of a dispersion-suppressor cell (90 deg.) (red: horizontal, green: vertical)

Wednesday, September 23, 2009

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SLIDE 12

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

Wednesday, September 23, 2009

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SLIDE 13

SCALING STRAIGHT LINES

Straight section = Bending section with infinite radius

13

Bz = B0e

n ρ (X−X0)

lim

r0→∞

r r0 k = lim

r0→∞

  • 1 + x

r0 r0

x x r0 k

=

  • lim

r0→∞

  • 1 + x

r0 r0

x n ρ x

= e

n ρ x

k = r0 ρ n

n = ρ B dB dx

  • z=0

r = x + r0

with

Wednesday, September 23, 2009

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SLIDE 14

ANOTHER LATTICE

Straight cell n/ρ 2.14 m−1 Length 3 m Phase advances: horizontal µx 24 deg. vertical µz 87 deg.

Bending cell k 6.5 Average radius 3.5 m Phase advances: horizontal µx 90 deg. vertical µz 87 deg. Dispersion 0.47 m

Wednesday, September 23, 2009

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SLIDE 15

Betafunctions of bending cell. (red: horizontal, green: vertical)

Wednesday, September 23, 2009

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SLIDE 16

Betafunctions of straight cell. (red: horizontal, green: vertical)

Wednesday, September 23, 2009

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SLIDE 17

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

Wednesday, September 23, 2009

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SLIDE 18

Horizontal Poincarre map

Wednesday, September 23, 2009

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SLIDE 19

STILL A LOT OF WORK TO DO...

Wednesday, September 23, 2009

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SLIDE 20

THANK YOU FOR YOUR ATTENTION

Wednesday, September 23, 2009

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SLIDE 21

APPLICATION: PRISM

21

Wednesday, September 23, 2009

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SLIDE 22

CHANGE RADIUS

22

R1 − R01 = R2 − R02

R = R0 P P0

  • 1

k+1

1st order

R01 R02 = k1 + 1 k2 + 1

Wednesday, September 23, 2009

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SLIDE 23

MISMATCH BEND-STRAIGHT

23

n/ρ, X0

Matching of P0: Straight cell: Bending cell: Matching of P: 1st order

1 + (kb + 1) r − r0 r0

  • = 1 + n

ρs (X − X0)

B0sρs = B0bρb B0sρse

n ρ (X−X0) = B0bρb

r r0 kb+1 kb, r0 Bz = B0b r r0 kb n ρs = kb + 1 r0 Bz = B0se

n ρs (X−X0)

Wednesday, September 23, 2009

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SLIDE 24

DISPERSION SUPPRESSOR IN STRAIGHT LINES

24

X = ρ n ln( P P0 )

2X2 = X1 + X3

X2 − (X1 − X2) = X3

2 ρ2 n2 = ρ1 n1 + ρ3 n3

Wednesday, September 23, 2009