Status of Low- FOFO Snake for Final Stage of 6D Ionization Cooling - - PowerPoint PPT Presentation

MAP vacuum RF cooling mini-workshop, FNAL, September 18-19 2013

• Y. Alexahin

(FNAL APC)

Status of Low- FOFO Snake for Final Stage of 6D Ionization Cooling

 This work is a continuation of effort reported at MCDW’09 (BNL) and NFMCC’10 (Miss. Univ.) and resumed now after a 3 year hiatus  Is it worthwhile?

Motivation

2

10 20 30 40 50 60 70 10 5 5 10 10 20 30 40 50 60 70 5 10 15 20 25 10 20 30 40 50 60 70 6 4 2 2

FOFO snake with phase advance >180/cell has a number of attractive features:  Apparent technological simplicity (RF between solenoids, not inside)  Potentially higher compactness: phase advance / absorber (+) is somewhat smaller than in RFOFO (3/2-)

• However, phase advance / period (2+)

is higher creating problems with beam dynamics. Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

z [cm] B [T] Bz By 10 “cell” x D [cm] z [cm]  [cm] Dx y Dy

• +

+

z [cm]

Problems with Low-Beta FOFO Snake

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Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013 This creates difficulties with the transverse acceptance as well

The major mechanism of losses is diffusion

• ver the maximum of long. “kinetic energy” –

change of the slip factor sign at higher values

• f momentum.

=L(p)/L(0) – relative length of the periodic

• rbit

p

0.10 0.05 0.05 0.10 0.15 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030

p0 = 120 MeV/c



 

p

d K

p 

       ] ) ( ) ( 1 [ ) (

p0 = 100 MeV/c

 Dispersion = 0 at focal points  stronger transverse field is required  Large difference in cooling rates of the two transverse normal modes  Momentum acceptance limited from above by sign change in the slippage factor  Momentum acceptance limited from below by fast increase in the ionization loss rate

z r

B z B r

3 3 3 3

~    

 Maximum  is reached between solenoids where the field nonlinearity is also at maximum:

Geometry & Parameters

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Total length of 2-cell period 2  38cm = 76cm Bz_axis=11.5T (Bz_coil=17.3T, j < 200A/mm2) for p0=100MeV/c, constant By=0.01T The transverse modes cooling rates can be equalized by 1-periodic quadrupole field with gradient 1.1T/m between the solenoids (proposed by R.Palmer difference in solenoids also works but makes transition worse). Normal mode tunes (including cooling rates) and normalized equilibrium emittances: tune* 1.229 + 0.00149 i 1.245 + 0.00144 i 0.109 +0.00042 i N (mm) 0.183 0.201 1.03

*) Transverse phase advance / period is (almost) 2.5

2cm LH2 absorber with 18 LiH wedges making use of large Dy Rout= 38cm 2  8cm open cell 600 MHz RF cavities, Emax=18MV/m 16cm 38cm Rin= 14.5cm 16cm

+

• Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

G4BL Tracking

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Normalized emittances (Gaussian fit) and intensity over 100 periods . Final =0.21mm, total losses (with decay) = 40%.

4 2 2 0.4 0.2 0.2 0.4 0.6

2 2 4 0.4 0.2 0.2 0.4 0.6

0.2 0.2 0.4 0.6 0.1 0.1 0.2

x (cm) y (cm) t (ns) px/p0 py/p0 p/p0

10 20 30 40 50 60 70 7500 8000 8500 9000 9500 10000

decays

• ff

N z (m)

10 20 30 40 50 60 70 0.02 0.04 0.06 0.08

z (m) 1 (cm) 2 (cm) z (cm)

Evolution of the initial Gaussian distribution truncated at 3sigma (blue dots) over 100 periods (76m) - red dots z0.1ns*v 2cm

Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

quadrupole not strong enough!

Cooling Efficiency

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Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

10 20 30 40 50 60 70 5 10

N d d Q

D D

log log

6 6

  decays included

z (m)

Average value Q6D  3

Q6D

• R. Palmer’s 6D quality factor

I tried to improve transmission by:  Larger wedge angle (25) – opposite result (!?)  Changing tunes: ~ constant for 1.2<Q<1.25, big drop for Q<1.2 (Q-2Qs SBR?) and Q1.375  Rotation of LiH wedges to utilize both Dy and Dx – no effect  Lower momentum (90MeV/c) – no effect (this is actually good!)  Deceleration from 100 to 90MeV/c over 50 periods – opposite result  Higher RF frequency (650MHz) and higher voltage (20MV/m) – opposite result (Q-2Qs SBR?)  Lower RF frequency (325MHz) and triangular pulse equivalent to 150MHz (this should also reduce space-charge effects)

325 MHz RF

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Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

20 40 60 80 100 6000 7000 8000 9000 10000 20 40 60 80 100 10 5 5 10

Normalized emittances (Gaussian fit), intensity and 6D quality factor over 150 periods (114m). Final =0.17mm, total losses (with decay) = 60%. decays on

N z (m)

20 40 60 80 100 0.02 0.04 0.06 0.08 0.10

1 (cm) 2 (cm) z (cm)

continuing “shaving” due to insufficient momentum acceptance quadrupole 50% stronger

Q6D

0.2 0.2 0.4 0.6 0.1 0.1 0.2

z (m) t (ns) p/p0

bunch length increase is smaller than expected decays off

Summary

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 Low-beta FOFO-snake with LiH wedges does work allowing for

normalized transverse emittance < 0.2mm

 Equalization of the transverse normal mode cooling rates can be achieved

with either the solenoid current difference or a weak periodic quadrupole field (<2T/m)  The major performance limitation is imposed by insufficient momentum acceptance  There are still some possibilities to explore in order to improve transmission – may take a week more to exhaust them

Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

MAP vacuum RF cooling mini-workshop, FNAL, September 18-19 2013

• Y. Alexahin

(FNAL APC)

325 MHz Helical FOFO Snake for Initial Stage of 6D Ionization Cooling

Basic Idea

2

absorbers RF cavities alternating solenoids z [cm] Bx50 B [T] Bz By 50 x, y [cm] x z [cm]

y

x y

• The idea: create rotating B field by

periodically tilting solenoids, e.g. with 6- solenoid period.

• Periodic orbits for μ+ and μ- look exactly

the same, just shifted by a half period (3 solenoids).

• With tune Q>1 (per period) rD>0

 muons with higher momentum make a longer path  longitudinal cooling achieved even with planar absorbers Periodic orbit for p=200MeV/c HFOFO Update - Y. Alexahin NUFACT09, IIT Chicago July 22, 2009

Optics Functions

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325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

50 100 150 200 250 300 350 4 2 2 4 50 100 150 200 250 300 350 25 30 35 40 45 50 55 50 100 150 200 250 300 350 40 20 20 40

z [cm] Bx100 B [T] Bz By 100 z [cm] x D [cm] z [cm]  [cm] Dx y Dy Total length of 6-cell period = 372cm vs 612cm @200MHz – I tried to reduce  as much as reasonably possible Bz_axis=3.8T (j < 200A/mm2) for p0=200MeV/c, solenoid pitch angle 5mrad The transverse modes cooling rates are equalized by costant quadrupole field with gradient 0.12T/m Normal mode tunes (including cooling rates) and normalized equilibrium emittances: tune 1.21 + 0.0069 i 1.24 + 0.0069 i 0.16 +0.0031 i N (mm) 2.47 2.39 3.48

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325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

G4BL Tracking

20 10 10 20 1.0 0.5 0.5 20 10 10 20 0.5 0.5 1.0 0.5 0.5 1.0 0.2 0.2 0.4 0.6 0.8

x (cm) y (cm) t (ns) px/p0 py/p0 p/p0

20 40 60 80 0.5 1.0 1.5 2.0 2.5

1 (cm) 2 (cm) z (cm) z (m)

Normalized emittances (Gaussian fit) over 25 periods (93m) . Final =3.5mm, || ~ twice larger Initial Gaussian distribution includes all correlations up to 2nd order (including energy-transverse amplitude^2) Horizontally beam extends over 20cm, transverse momentum exceeds p0=200MeV/c! - inevitably high losses in the beginning (next slide)

13

325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

Cooling Efficiency

20 40 60 80 3500 4000 4500 5000 20 40 60 80 5 10 15 20 25 30

decays on

N z (m) Q6D

decays off

z (m)

Final value of Q6D exceeds 20 – cooling can be continued. Now I should try Dave’s rotator output.