Slow extraction from PS2
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Transcript of 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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 22
MT
EB
K
ExtKESMS1MS2
Du
K
InjK InjS
BD+1st sec
Prim2nd sec
MT
EB
KT
B1
B2
B3
B4B5
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 33
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 44
above resonance : Q - Qres > 0 below resonance : Q - Qres < 0
KS
> 0K
S < 0
x
x
x
x
x´ x´
x´ x´
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 55
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 66
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 77
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 88
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 99
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1010
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1111
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 !)
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1212
-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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1313
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1414
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)
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1515
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1616
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1717
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1818
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
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 1919
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 (?)
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 2020
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 2121
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 2222
PS2 Project Meeting PS2 Project Meeting 11-2-200911-2-2009 M. Gyr, TE/ABT/BTPM. Gyr, TE/ABT/BTP Slide Slide 2323