Slow extraction from PS2

PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 11

Slow extraction from PS2Slow extraction from PS2

Preliminary design aspectsPreliminary design aspects


MT

EB

K

ExtKESMS1MS2

Du

K

InjK InjS

BD+1st sec

Prim2nd sec

MT

EB

KT

B1

B2

B3

B4B5


NormalizationNormalization Normalized dispersionNormalized dispersion

( ( NN = normalized = normalized ))

Normalized emittance Normalized emittance ((PS2PS2: : NN = 15µm = 15µm)) ((i.e.i.e. scaled withscaled with energyenergy))

Emittance in normalized phase Emittance in normalized phase space space

Beam size (area in phase space):Beam size (area in phase space):

Normalized beam size (stable area):Normalized beam size (stable area):

Nxx DD

c

vN

AA N

NN

N

In the program, the emittance in the normalized phase space has to be input instead of the stable phase space area (the factor is dealt with inside the code)

· A


above resonance : Q - Qres > 0 below resonance : Q - Qres < 0

KS

> 0K

S < 0

x

x

x

x

x´ x´

x´ x´


p

p

p/p

Q/Q

Q

Q1Qp

p

QQQQ oo

p

pDxx x0pCOCO

Choice of p and Q such that: (Qres-Qo)·(Qres-Q) > 0

i.e. resonance approach from below or above doesn't change !

Closed orbit and lens strength for off-momentum particles:Closed orbit and lens strength for off-momentum particles:

pp

0pS

S 1

KK

Parameters for separatrixParameters for separatrix


2Fx

4

33A

4F27

A2x

Stable area & fixed pointStable area & fixed point

S

res

S

res

K

Q348

K312A

Fx

33

A

4

1

K

Q

S

res


Machine parametersMachine parameters

S [m] µx to ES [º] Dx [m] x [m] y [m] Dx·(N/x)

1069.6 242.5 -0.8779 20.6 47.6 -1.4983

882.5 110.0 -0.8779 20.6 47.6 -1.4984

396.4 120.3 -0.8779 20.6 47.6 -1.4983

207.5 352.9 -0.5539 20.9 47.7 -0.9387

001.0Q

Q

Sextupole locationsSextupole locations

0003.0p

p

8115.1

p/p

Q/Q

Qo = 13.32


ES

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

48.7 mm


0 200 400 600 800 1000 1200 14000.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

Envelope for a max. normalized separatrix amplitude of 50 mm (scaled with ; N= 60 m) including Dx and orbit etc.

N

xx

Aperture requirements for extractionAperture requirements for extraction


700 800 900 1000 1100 1200 1300

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

Tracked separatrices

65 mm normalised to local beta

Separartrix envelope and 65 mm scaled aperture over one arc and LSS

Required aperture for extraction Required aperture for extraction compared with machine aperturecompared with machine aperture


Sextupole strengths + lengthsSextupole strengths + lengthsWith normalized Ks=.0037 mm-1, N = 60 m and S = 20.3 m one finds:

233

S

NSS m31.0

6.20

607.3k

K

Kick strength of a multipole of order n:

1nn

1nnn

xk'xxaB

dlap

3.0dla

p

ek n

cGeVn

1n

N

N

nn

K

LSE of SPS (l = .7m, Ø = 120mm, Imax = 395A) : m

TA395I3 9.165da

@ 50 GeV: k3 = .995 m-2 (~ 3 times the required strength !)


-100

-50

0

50

100

150

200

1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320

Beam envelope in extraction channelBeam envelope in extraction channel

ES

MS

1

MS

2

QMA


Enlarged QMAEnlarged QMAwith coil windowwith coil window

Coil window needs to be larger than in the QFA/QDA of the SPS since extracted beamPasses through 2 magnets


p

E

p

E

c

Lek

Electrostatic septumElectrostatic septumAngular deflection k of a particle with momentum p and relativistic speed c in an electrostatic field E of length L :

For high momentum particles (1) and for one ZS-unit, having an electric field length of L = 3m (length of the cathode), the conversion factor is :

cm/kV

c/GeVmrad

10

3

rad10

mrad

eV10

GeV

m10

cm

kV

V10

c1

m3e392

3

(Emax = 100 kV/cm)


Magnetic septaMagnetic septa

pkpkdBe

IdB

dB

II

max

max

max

max

Angular deflection k of a particle traversing a magnetic field B is proportional to the integrated field strength B·d and inversely proportional to the momentum p.

The necessary current in the magnet for a demanded deflection is given by

Assuming that the MS1 and MS2 have the same type of coils as the MST and MSE (but longer cores) the following values are found by scaling :

Type L [m] Imax [kA] Bmaxdl [Tm] Nº of units [A/mrad/(GeV/c)]

MST 2 1.1 7.5 1.0556 3 7.9

MSE 2 1.1 24 3.38 5 4.736

MS1 2 1.4 7.5 1.3435 1 18.6

MS2 2 1.4 24 4.30 2 9.3


Element Imax [A] Bmaxdl

[Tm] [A/mrad/(GeV/c)]

MPSH 395 0.952 1.384

MPLH 395 1.865 0.706

MPNH 500 2.203 0.75704

The 5 Bumpers are assumed to be of MPSH, MPLH and MPNH-type as in the SPS

Minimum real septum positionsMinimum real septum positionsSeptum upstream downstream

ES 45.9 mm 28.6 mm

MS1 39.6 mm 48.1 mm

MS2 49.0 mm 35.2 mm

Magnetic bumpersMagnetic bumpers


Momentum (GeV/c): 50.9

ZS-Strength (mrad): 0.82466130 MS1-Strength (mrad): 3.59243065 MS2-Strength (mrad): 21.64154794

Bumper-Strengths (mrad): MBP5A : -0.77039136 MBP4B : 1.17497994 MBP3B : 0.09878870 MBP2B : 2.12425185 MBP1B : -1.65216901

Required deflectionsRequired deflections


ES-Field (kV/cm): 70.00000 MS1-Current (Amp): 3403.10237 MS2-Current (Amp): 10250.49754

Bumper-Currents (Amp): MBP5A : -54.30266854 MBP4B : 42.24826035 MBP3B : 3.80890182 MBP2B : 76.38083163 MBP1B : -116.45663534

Required currentsRequired currents


ConclusionsConclusions

Slow extraction feasible with this layout and the proposed machine aperture

Lenses, bumpers & septa strong enough rreserve for CO-correction with bumpers!Suppression of 3rd bumper ?

Enlarged Quadrupoles with wider window than in the SPS

Thin septum MS1 may be suppressed (?)

Slow extraction from PS2

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