decay ring design - cern · decay ring design a. chancÉ cea saclay irfu/sacm 20th october 2011...

Decay Ring Design

A. CHANCÉ

CEA Saclay IRFU/SACM

20th October 2011

Beta-Beam meeting, Napoli, Decay ring design 20th October 2011 1 / 20

Why a new lattice?

High fluxes of (anti) neutrinos imply high intensities tostore (several hundreds of Amps peak!)Collective effects (space charge, beam loading,wake fields...) must be investigated.The head tail effects (excitation of the tail of thebeam by the head due to tranversal fields) are oneof the big issues for the stability in the decay ring.Two solutions have been under study to mitigate thiseffect:

a new lattice with a smaller transition gamma;making an amplitude detuning with octupoles,which sometimes enables to push the intensity limit.For the decay ring, we will see the impact of thissolution on the optics.


How to decrease the transition gamma

The momentum compaction αP is defined by:

αP =1γ2

T

=1L

∮Dx(s)ds

ρ

L is the total length, Dx the horizontal dispersion and ρthe curvature radius. αP can be increased by:

increasing the average dispersion in the dipoles.Larger apertures.Few degrees of freedom.Difficult to significantly change the value of αP .

increasing the integration length.“Wiggler” scheme: the sign of the curvature radiusalternates with the dispersion.The integrate

∮ Dx (s) dsρ increases.

We have chosen the second solution.


An injection out of the arc

The injection is out of the arcs.

, Simpler arcs: FODO lattices., More compact arcs: enlarged duty factor (39 %)./ More dipoles needed (208 against 172 before).

General:Layout:


An injection out of the arc

The injection is out of the arcs.

, Simpler arcs: FODO lattices., More compact arcs: enlarged duty factor (39 %)./ More dipoles needed (208 against 172 before).

Injection chicane:Layout:


Optical functions in the decay ring

Straight section length: 2706 m.Total length: 2200 π m.Dipoles of 7.46 T (for 6He2+) with an angle of π/84 rad.


Optical functions in the injection chicane

Optical functions at the center of the chicane:

Dx = 11 m.βx = 22 m.βy = 7.3 m.


Optical functions in the arcs

Phase advance of π/2 in both planes per FODOperiod.

⇒ Cancels some non linearities brought by thesextupoles.


Dynamic aperture

rms beam sizes:σx = 1.83 mmσy = 0.76 mm.

Advantages of the new lattice:

Very simple arcs.Two sextupole families to cancel the chromaticity.Large dynamic aperture in the momentum range ofthe beam.


Tracking with PTC_MADX and δ = 0

Initial position:(x = nσx ,Px = y = Py = 0)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40 -30 -20 -10 0 10 20 30 40

Px

[10-3

]

x [mm]

Initial position:(y = nσy , x = Px = Py = 0)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-20 -15 -10 -5 0 5 10 15 20

Py

[10-3

]

y [mm]

Step of 1 for n

Beam sizes: σx = 1.83 mm and σy = 0.76 mm.The beam stays elliptic up to 10 σx .Small non linearities.


Summary of the new lattice

The transition gamma γT for the new lattice is 18.7(to compare with the old value of 27).The value of the average betatron functions are :< βx >= 125 m (against 134 m before)< βy >= 160 m (against 175 m before).The fractional part of the tune is kept equal to theone of the reference lattice. We have then:

Qx = 22.228 and Qy = 19.16

The arcs are more compact and much simpler.The dynamic aperture is still large (more than 20σ inboth planes) and the tracking shows that the beamkeeps an elliptic shape for the first 10 sigmas.


Amplitude detuning for the decay ring

The intensity limit has been pushed by changing thetransition gamma.BUT the aimed intensities are still over this limit (morethan twice).A studied solution is to add octupoles in the latticeto make an amplitude detuning. The expectedamplitude detuning are:

∂Qx

∂εx= 425 m−1,

∂Qx

∂εy= −878 m−1,

∂Qy

∂εy= 1155 m−1

How to make the amplitude detuning?Where to put the octupoles?Which strength?Which impact on the dynamic aperture?


Location of the octupoles

The intensity limit is mostly sensitive to the derivative ∂Qy∂εy

.The two other derivatives are less relevant (possibility tooptimize their value with optical reasons).We will use two octupole families. Two locations werestudied:

The arcs. The phase advance in the FODO latticesin the arcs is π/2 rad. The octupoles can becompensated and their contribution to thedynamic aperture should be small. The integratedoctupole strengthes are 360 T/m2 and 1000 T/m2.The long straight section. There is plenty of place toinsert them there. Larger betatron functions implyweaker octupoles. The integrated octupolestrengthes are 32 T/m2 and 63 T/m2.


Dynamic aperture with octupoles

0

5

10

15

20

25

30

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25

Num

ber

of σ

y

Number of σx

∂Q

x∂ε

x=

425m

−1,

∂Q

y∂ε

y=

1155m

−1

no octupolesoctupoles in the arcsoctupoles in the straight section


Dynamic aperture with another ∂Qx/∂εx

0

5

10

15

20

25

30

-30 -20 -10 0 10 20 30

Num

ber

of σ

y

Number of σx

∂Q

x∂ε

x=−

425m

−1,

∂Q

y∂ε

y=

1155m

−1

no octupolesoctupoles in the arcsoctupoles in the straight section


Summary of the amplitude detuning

We have studied the impact of an octupoledetuning in the decay ring.Although the phase advances are not optimal inthe long straight section, it is more interesting to putthe octupoles in this section. The needed octupolesare much weaker for this solution with a similar (oreven larger) dynamic aperture.If only the derivative ∂Qy/∂εy is significant to reducethe collective effects, it is possible to optimize theoctupole strenghtes to enlarge significantly thedynamic aperture.Amplitude detuning is affordable if only thedynamic aperture is considered.

BUT The gain is very small on the intensity limit (seeHansen’s simulations).


New RF merging program

The slipping factor η was enlarged:η1 = 0.28% (against η0 = 1.28% before).

The RF program can be obtained from thereference by multiplying the RF voltages by thescaling factor η1/η0.The maximum RF cavity voltage becomes:

43.9 MV for 6He2+(against 20 MV before)26.3 MV for 18Ne10+(against 11.9 MV before)

The injected beam was assumed with a parabolicdistribution.The injection parameters (phase delay andlongitudinal α) was chosen to optimize the captureat the injection (95% for both ions).


Merging results

Accumulation

Losses by collimation

The injection occurs every6 (3.6) seconds for6He2+(18Ne10+).

After stacking, the storedintensity is 9.8 (15.7) timesthe injected intensity for6He2+(18Ne10+).

The lifetime of an ion isabout 13.1 (17.2) injectioncycles for 6He2+(18Ne10+).

Between two successiveinjections, about 53%(78%) of the injectedintensity is lost bymomentum collimation.


Consequences of more bunches

A larger θ13 enables to relax the constraints on theduty cycle.What about more more bunches in the decay ring?

e.g: 80 bunches instead of 20 bunches.The PS can only store up to 20 bunches. Morebunches implies to make several PS cycles beforeinjecting into the decay ring.We assume that storing 80 bunches in the decayring means a repetition time of 16.8 s for 6He2+and14.4 s for 18Ne10+.What consequences of a larger repetition time?

intensity to inject, collimation, . . .


Effects of a larger repetition time

Accumulation Intensity to inject

Intensity to collimate Collimated power


Summary of merging results

One of the consequences to enlarger the slippingfactor is to increase the RF budget (about twice).The RF program stays about the same by using ascaling rule.A scheme with more bunches decreasessignificantly the accumulation ratio. For example,80 bunches means

The accumulation ratio is less efficient (60% and 70%of the reference ratio for each ion).We need to inject less ions in each bunch, whichrelaxes the collective effects in the SPS.The power to collimate between two injections isreduced (62% and 72% of the reference).


Thank you for your attention!


Tune variations (1)

Octupoles in the arcs

Horizontal tune

22.19

22.195

22.2

22.205

22.21

22.215

22.22

22.225

22.23

22.235

22.24

4 6 8 10 12 14 16 18 20 22 24

Qx

Number of sigmas

Angle (deg)0.00

11.2522.5033.7545.0056.2567.5078.75

101.25112.50123.75135.00146.25157.50168.75180.00

Vertical tune

19.15

19.16

19.17

19.18

19.19

19.2

19.21

19.22

4 6 8 10 12 14 16 18 20 22 24

Qy

Number of sigmas

Angle (deg)0.00

11.2522.5033.7545.0056.2567.5078.75

101.25112.50123.75135.00146.25157.50168.75180.00


Tune variations (2)

Octupoles in the straight section

Horizontal tune

22.16

22.17

22.18

22.19

22.2

22.21

22.22

22.23

22.24

22.25

22.26

4 6 8 10 12 14 16 18 20 22 24 26

Qx

Number of sigmas

Angle (deg)0.00

11.2522.5033.7545.0056.2567.5078.75

101.25112.50123.75135.00146.25157.50168.75180.00

Vertical tune

19.12

19.13

19.14

19.15

19.16

19.17

19.18

19.19

19.2

19.21

19.22

4 6 8 10 12 14 16 18 20 22 24 26

Qy

Number of sigmas

Angle (deg)0.00

11.2522.5033.7545.0056.2567.5078.75

101.25112.50123.75135.00146.25157.50168.75180.00


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