Scaling FFAG lattices for muon acceleration T. Planche, Y. Mori, - - PowerPoint PPT Presentation

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Scaling FFAG lattices for muon acceleration T. Planche, Y. Mori, - - PowerPoint PPT Presentation

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Scaling FFAG lattices for muon acceleration T. Planche, Y. Mori, Kyoto University. Muon acceleration for a neutrino factory Constraints on the accelerating apparatus: (i) Fast acceleration requires static magnetic guide field and fixed rf

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Scaling FFAG lattices for muon acceleration

  • T. Planche, Y. Mori, Kyoto University.
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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Muon acceleration for a neutrino factory

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Constraints on the accelerating apparatus:

(i) Fast acceleration requires static magnetic guide field and fixed rf frequency acceleration. (ii) Muon beams have a huge transverse emittance, even after cooling (~ 30000 πmm.mrad in both horizontal and vertical planes).

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Muon acceleration for a neutrino factory

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Current status of the Cost/Performance balance:

Linac: expensive but cost-effective at low energy RLAs: less expensive than linac but limited number of passes, and need one arc per pass. NS-FFAG: the most cost effective, but the longitudinal amplitude growth with large transverse amplitude limits its use the the higher energy stage.

Figure 1 - Schematic diagram of the ISS baseline accelerator complex.

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Motivations

Find a better balance using scaling FFAG instead of RLA

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The amplitude dependance of the time of flight which limits the NS-FFAG acceptance is not an issue for scaling FFAG. We would like to show that is it possible to use scaling FFAG with constant rf frequency acceleration at lower energy than NS-FFAG. Using harmonic number jump acceleration Stationary bucket acceleration!

Two possible schemes

  • r
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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Contents

Part I - Scaling FFAGs for Stationary Bucket acceleration

1 - Principle 2 - Example of lattice parameters 3 - Acceptance study at fixed energy 4 - Full 6D simulation results 5 - Summary on SB acceleration

Part II - Scaling FFAGs for Harmonic Number Jump acceleration

1 - Principle and constraints of the HNJ acceleration 2 - FFAG ring with insertion based of FD doublet cells 3 - Use of dFDf quadruplet cells 4 - Summary on HNJ acceleration

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Scaling FFAG lattices for Stationary bucket acceleration

Part I

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Principle

With constant rf frequency scheme, accelerate particles following a pass from the bottom to the top of a stationary bucket.

Figure 2 - Longitudinal phase space showing a 6-turn acceleration cycle

  • f a muon beam (red), as well as

Hamiltonian contour (black lines)

7 20 40 60 80 100 120 0.2 0.4 0.6 0.8 1 ! rf phase/2"

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Example of lattice parameters

Stationary bucket acceleration for 3.6 to 12.6 GeV muon RF frequency = 200 MHz

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

158 159 160 161 162 163 164

  • 6
  • 4
  • 2

2 4 6 y [m] x [m]

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Lattice example for 3.6 to 12.6 GeV muon acceleration:

Table 1 - lattice parameters. Figure 3 - Scaling FFAG lattice for 3.6 to 12.6 GeV muon acceleration.

Example of lattice parameters

Lattice type scaling FFAG FDF Injection energy 3.6 GeV Extraction energy 12.6 GeV RF frequency 200 MHz Mean radius ∼ 161 m Synchronous energy (kinetic) 8.04 GeV Hormonic number h 675 Number of cells 225 Field index k 1390 RF peak voltage (per turn) 1.8 GV Number of turns 6 Bmax (at 12.6 GeV) 3.9 T Drift length ∼ 1.5 m Horizontal phase advance per cell 86.13 deg. Vertical phase advance per cell 37.90 deg. Excursion 14.3 cm

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50 100 150

  • 150-100 -50

50 100 150 y [m] x [m]

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

158 159 160 161 162 163 164

  • 6
  • 4
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2 4 6 y [m] x [m]

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Simultaneous acceleration of and beams:

Example of lattice parameters

In order to allow the simultaneous acceleration of and beams, the synchronous particle orbit length is adjusted to be equal to . The size of the long drift is design for two rf cavities with gaps distant of to be installed in it.

µ− µ+ 3βsλrf

1 2βsλrf

3βsλrf µ− µ+

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 5 - Horizontal (red) and vertical (purple) beta function at 3.6 Ge.

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  • 4
  • 3
  • 2
  • 1

1 2 3 4 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Bz [T] s [m] 2 4 6 8 10 12 14 16 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ! [m] s [m]

Figure 4 - Mid-plane field distribution along the closed orbits at 3.6, 8 and 12.6 GeV

We use step-wise particle tracking in geometrical field model to determine the lattice linear parameters and study the beam dynamics.

Example of lattice parameters

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Transverse acceptance at fixed energy

Figure 6 - (R, R') plane (@ middle of the long drift) showing a multi-turn tracking of 2 particles with different initial horizontal amplitudes, with an initial vertical displacement = 1 mm.

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Figure 7 - (Z, Z') plane (@ middle of the long drift) showing a multi-turn tracking of 2 particles with different initial horizontal amplitudes, with an initial vertical displacement = 1 mm.

Transverse normalized acceptance is greater than 40000 πmm.mrad in both horizontal and vertical planes.

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5 10 15

  • 120
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40 80 120 Z' [mrad] Z [mm]

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5 10 15 20 25 160.76 160.8 160.84 160.88 160.92 160.96 R' [mrad] R [m]

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Full acceleration cycle - 6D tracking

Figure 8, 9 and 10 - 6D tracking simulation results. Initial particle distribution is a homogeneous (Waterbag) distribution in the transverse 4D ellipsoidal phase space + homogeneous distribution in the 2D longitudinal phase

  • space. Initial transverse beam emittance is

30.000 πmm.mrad in both horizontal and vertical planes, and 0.17 eV.sec in longitudinal.

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3 4 5 6 7 8 9 10 11 12 13 0.2 0.4 0.6 0.8 1 Ekin [GeV] rf phase/2!

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5 10 15 160.8 160.9 161 161.1 R' [mrad] R [m]

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5 10 15

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40 80 Z' [mrad] Z [mm]

Initial (green) and final (red) particle distribution

  • f the particles in the horizontal (top figure),

and vertical (bottom figure) phase space.

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Summary on harmonic number jump

Works well!

* Very large transverse acceptance. * Large longitudinal acceptance @ 200 MHz. * No emittance degradation during acceleration! * Simultaneous acceleration of μ+ and μ- possible.

It is a good and robust alternative to RLAs for a Neutrino Factory!

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Summary on stationary bucket acceleration

It is a good and robust alternative to RLAs for a Neutrino Factory!

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50 100 150
  • 150-100 -50
50 100 150 y [m] x [m]

3.6-12.6 GeV scaling FFAG!

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Another way for constant frequency acceleration in scaling FFAG: The Harmonic Number Jump acceleration

Part II

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Principle and constraints of the HNJ acceleration

To jump one harmonic every turn: Energy gain per turn must follow:

Figure 11 - Revolution time as a function

  • f particle energy in the case of a 3 to

10 GeV scaling FFAG ring, with k = 145 and average radius = 120 m.

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∆Ei =

1 frf ·[ ∆T

∆E]Ei

Ti+1 − Ti = 1 frf

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Need for dispersion suppressor insertions:

Ti+1 − Ti = 1 fRF

Harmonic jump condition: In the same time:

∆Ci βc = Ti+1 − Ti

In case of highly relativistic particles:

average excursion = λRF · Nturns 2π ∆Ri ≈ c 2πfRF = λRF 2π

Need for excursion reduced areas!

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Principle and constraints of the HNJ acceleration

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Dispersion suppressor with FFAG magnets

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

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 20

Figure 13 - N cavities homogeneously distributed around the ring.

Assuming that the initial number of harmonic h0 is large we get(*):

fk ≈ f0(1 − 1 h0 · k N )

Every cavity working at a constant frequency fk but the frequency has to be tuned to a slightly different value! μ+ and μ- beams cannot be accelerated simultaneously if they circulated in opposite directions...

(*)look at the proceedings of

PAC’09 for all details.

Need for a double beam lattice:

Principle and constraints of the HNJ acceleration

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 21

A solution to circulate a particle and its antiparticle in the same direction in a scaling FFAG ring is to use a FD-symmetric lattice (T. Okawa):

Figure 14 - Double beam FFAG lattice (k = 145). Closed orbits of μ+ and μ− circulating in the same direction. Results are obtained from Runge-Kutta stepwise tracking in hard-edge field.

Need for a double beam lattice:

Principle and constraints of the HNJ acceleration

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

FFAG ring with insertion based of FD doublet cells

Figure 15 - Schematic view of a 3 to 10 GeV double beam muon FFAG ring with 4 excursion reduced insertions.

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Lattice type FD double beam Injection energy 3 GeV Extraction energy 10 GeV Bmax (at 10 GeV) 3 T Horizontal tune 23.52 deg. Vertical tune 7.12 deg.

Table 2 - Ring general parameters

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Table 3 - Ring main cells parameters

Mean radius 120 m Number of cells 4 × 11 Cell opening angle 4.5 deg. Field index k 145 Bmax 3 T

  • Horiz. phase adv. per cell

82.1 deg.

  • Vert. phase adv. per cell

31.8 deg.

Figure 15 - Schematic view of a 3 to 10 GeV double beam muon FFAG ring with 4 excursion reduced insertions.

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Table 4 - 1st dispersion suppressor

Mean radius 120 m Number of cells 4 × 4 Cell opening angle 4.3 deg. Field index k 183.6 Bmax 3 T

  • Horiz. phase adv. per cell

90 deg.

  • Vert. phase adv. per cell

27.6 deg.

Figure 15 - Schematic view of a 3 to 10 GeV double beam muon FFAG ring with 4 excursion reduced insertions.

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Table 5 - 2nd dispersion suppressor

Mean radius 120 m Number of cells 4 × 4 Cell opening angle 3.34 deg. Field index k 307.7 Bmax 3 T

  • Horiz. phase adv. per cell

90 deg.

  • Vert. phase adv. per cell

20.4 deg.

Figure 15 - Schematic view of a 3 to 10 GeV double beam muon FFAG ring with 4 excursion reduced insertions.

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Table 6 - dispersion suppressed area

Mean radius 350 m Number of cells 4 × 8 Cell opening angle 1.2425 deg. Field index k 1168.6 Bmax 3 T

  • Horiz. phase adv. per cell

64.6 deg.

  • Vert. phase adv. per cell

12.6 deg.

Figure 15 - Schematic view of a 3 to 10 GeV double beam muon FFAG ring with 4 excursion reduced insertions.

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 16 - μ- closed orbits at 3, 6 and 10 GeV.

k=145 k=183.6 k=307.7 k=1168.6

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 17 - μ- (red) and μ+ (green) closed orbits at 3, 6 and 10 GeV.

k=145 k=183.6 k=307.7 k=1168.6

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

k=145 k=183.6 k=307.7 k=1168.6

Perfectly symmetrical behavior broken by the choice of the matching point!

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Study of linear parameters using Runge-Kutta stepwise tracking in soft edge field model:

Figure 18 - μ- Tune variation between 3 and 10 GeV in the lattice with insertions (from stepwise tracking in a soft edge field model). Figure 19 - μ+ Tune variation between 3 and 10 GeV in the lattice with insertions (from stepwise tracking in a soft edge field model).

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 20 - μ- : Longitudinal phase space showing a 6 turns acceleration cycle from 3 to 10 GeV with an initial beam 4D emittance of 0.2 eV.sec × 30 000 π.mm.mrad. Figure 21 - μ- : Horizontal phase space showing the injected beam profile (red) and the same beam after a 6 turns acceleration cycle (green) with (4D emittance

  • f 0.2 eV.sec × 30 000 π.mm.mrad).

μ- beam: 4D tracking results: RF frequency = 400 MHz, peak voltage 2GV/turn.

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

μ+ beam: 4D tracking results: RF frequency = 400 MHz, peak voltage 2GV/ turn.

Tried 3 to 10 GeV acceleration cycle

(with RF frequency = 400 Hz, peak voltage 2GV/turn)

Particle lost on collimator even for small transverse emittance...

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FFAG ring with insertion based of FD doublet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Use of dFDf quadruplet cells

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Figure 22 - Horizontal beta function for μ+(red) and μ− (green) in a double beam doublet cell. Figure 23 - Horizontal beta function for μ+ (red) and μ− (green) in a double beam quadruplet cell.

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 24 - Schematic view of a 3 to 10 GeV double beam (quadruplets) muon FFAG ring with 4 excursion reduced insertions.

Ring all made of quadruplet cells. Here dispersion is reduced by a factor 2 (not 3 as before):

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Lattice type FD double beam Injection energy

  • 3. GeV

Extraction energy 10 GeV Bmax (at 10 GeV) 3 T Horizontal tune 21.6 deg. Vertical tune 11.4 deg.

Use of dFDf quadruplet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 25 - μ+ Tune variation between 3 and 10 GeV (from stepwise tracking in a soft edge field model). Figure 26 - μ- Tune variation between 3 and 10 GeV (from stepwise tracking in a soft edge field model).

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Use of dFDf quadruplet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Figure 27 - μ+ - transverse phase space showing a 25 000 π.mm.mrad normalized transverse acceptance at 3 GeV (tracking done with small vertical motion). Figure 28 - μ- - transverse phase space showing a 25 000 π.mm.mrad normalized transverse acceptance at 3 GeV (tracking done with small vertical motion).

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Use of dFDf quadruplet cells

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Summary on harmonic number jump

Encouraging results

* Large transverse acceptance. * Large longitudinal acceptance, and no emittance degradation during acceleration. * Excursion reduction of a factor 3 has been shown with doublet lattice. * Possible with RF frequency in the 200 MHz to 400 MHz range.

Possible to accelerate μ+ and μ- in the same time!... Although it is a very challenging scheme.

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* Energy range of 3.6 to 12.6 GeV has to be try to fit with the latest neutrino factory design study. * More work has to be done on the quadruplet cells, better lattice design, 6D tracking...

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

General Summary

I - The Stationary Bucket acceleration in scaling FFAG rings is suitable for muon acceleration. It is a robust and cost- effective alternative to RLAs.

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II - Encouraging results have been obtained for the Harmonic Number Jump acceleration of muons. Zero- chromatic FFAG lattices with insertions have successfully been developed. Further study are ongoing...

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Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche

Thank you!